%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRA134-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 06:33:47 PM UTC 2026
% Result : Unsatisfiable 1.14s 1.33s
% Output : Proof 2.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRA134-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.16/0.33 % Computer : n010.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 22:56:38 EDT 2026
% 0.16/0.33 % CPUTime :
% 1.14/1.33 % SZS status Unsatisfiable
% 1.14/1.33 % SZS output start Proof
% 1.14/1.33 tff(b_type, type, (
% 1.14/1.33 b: ( $i * $i ) > $o)).
% 1.14/1.33 tff(s_type, type, (
% 1.14/1.33 s: $i > $i)).
% 1.14/1.33 tff(z_type, type, (
% 1.14/1.33 z: $i)).
% 1.14/1.33 tff(elem_1_type, type, (
% 1.14/1.33 elem_1: $i)).
% 1.14/1.33 tff(r_type, type, (
% 1.14/1.33 r: ( $i * $i ) > $o)).
% 1.14/1.33 tff(inj_0_type, type, (
% 1.14/1.33 inj_0: $i > $i)).
% 1.14/1.33 tff(1,assumption,(~(s(s(elem!1)) = s(s(z)))), introduced(assumption)).
% 1.14/1.33 tff(2,assumption,(~b(s(s(z)), z)), introduced(assumption)).
% 1.14/1.33 tff(3,plain,
% 1.14/1.33 (^[X: $i] : refl((~(s(X) = z)) <=> (~(s(X) = z)))),
% 1.14/1.33 inference(bind,[status(th)],[])).
% 1.14/1.33 tff(4,plain,
% 1.14/1.33 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 1.14/1.33 inference(quant_intro,[status(thm)],[3])).
% 1.14/1.33 tff(5,plain,
% 1.14/1.33 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(6,axiom,(![X: $i] : (~(s(X) = z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','snz')).
% 1.14/1.33 tff(7,plain,
% 1.14/1.33 (![X: $i] : (~(s(X) = z))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[6, 5])).
% 1.14/1.33 tff(8,plain,(
% 1.14/1.33 ![X: $i] : (~(s(X) = z))),
% 1.14/1.33 inference(skolemize,[status(sab)],[7])).
% 1.14/1.33 tff(9,plain,
% 1.14/1.33 (![X: $i] : (~(s(X) = z))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[8, 4])).
% 1.14/1.33 tff(10,plain,
% 1.14/1.33 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(z)) = z))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(11,plain,
% 1.14/1.33 (~(s(s(z)) = z)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[10, 9])).
% 1.14/1.33 tff(12,plain,
% 1.14/1.33 (^[Y: $i, X: $i] : refl(((X = Y) | b(X, Y) | r(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 1.14/1.33 inference(bind,[status(th)],[])).
% 1.14/1.33 tff(13,plain,
% 1.14/1.33 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.14/1.33 inference(quant_intro,[status(thm)],[12])).
% 1.14/1.33 tff(14,plain,
% 1.14/1.33 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(15,plain,
% 1.14/1.33 (^[Y: $i, X: $i] : rewrite((((X = Y) | r(X, Y)) | b(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 1.14/1.33 inference(bind,[status(th)],[])).
% 1.14/1.33 tff(16,plain,
% 1.14/1.33 (![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.14/1.33 inference(quant_intro,[status(thm)],[15])).
% 1.14/1.33 tff(17,axiom,(![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rb')).
% 1.14/1.33 tff(18,plain,
% 1.14/1.33 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[17, 16])).
% 1.14/1.33 tff(19,plain,
% 1.14/1.33 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[18, 14])).
% 1.14/1.33 tff(20,plain,(
% 1.14/1.33 ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.14/1.33 inference(skolemize,[status(sab)],[19])).
% 1.14/1.33 tff(21,plain,
% 1.14/1.33 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[20, 13])).
% 1.14/1.33 tff(22,plain,
% 1.14/1.33 (((~![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))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(23,plain,
% 1.14/1.33 ((~![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))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(24,plain,
% 1.14/1.33 ((~![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)),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[23, 22])).
% 1.14/1.33 tff(25,plain,
% 1.14/1.33 (b(s(s(z)), z) | r(s(s(z)), z)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[24, 21, 11])).
% 1.14/1.33 tff(26,plain,
% 1.14/1.33 (r(s(s(z)), z)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[25, 2])).
% 1.14/1.33 tff(27,assumption,(r(z, s(z))), introduced(assumption)).
% 1.14/1.33 tff(28,assumption,(r(s(s(z)), z)), introduced(assumption)).
% 1.14/1.33 tff(29,assumption,(~r(s(s(s(s(s(s(z)))))), elem!1)), introduced(assumption)).
% 1.14/1.33 tff(30,assumption,(b(s(s(elem!1)), s(z))), introduced(assumption)).
% 1.14/1.33 tff(31,plain,
% 1.14/1.33 ((s(s(z)) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(z)))),
% 1.14/1.33 inference(commutativity,[status(thm)],[])).
% 1.14/1.33 tff(32,plain,
% 1.14/1.33 ((s(s(elem!1)) = s(s(z))) <=> (s(s(z)) = s(s(elem!1)))),
% 1.14/1.33 inference(symmetry,[status(thm)],[31])).
% 1.14/1.33 tff(33,plain,
% 1.14/1.33 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(s(z)) = s(s(elem!1))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[32])).
% 1.14/1.33 tff(34,plain,
% 1.14/1.33 (~(s(s(z)) = s(s(elem!1)))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[1, 33])).
% 1.14/1.33 tff(35,assumption,(r(s(s(z)), s(z))), introduced(assumption)).
% 1.14/1.33 tff(36,plain,
% 1.14/1.33 (^[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))))),
% 1.14/1.33 inference(bind,[status(th)],[])).
% 1.14/1.33 tff(37,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))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 1.14/1.33 inference(quant_intro,[status(thm)],[36])).
% 1.14/1.33 tff(38,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))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(39,plain,
% 1.14/1.33 (^[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)))))),
% 1.14/1.33 inference(bind,[status(th)],[])).
% 1.14/1.33 tff(40,plain,
% 1.14/1.33 (![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)))),
% 1.14/1.33 inference(quant_intro,[status(thm)],[39])).
% 1.14/1.33 tff(41,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')).
% 1.14/1.33 tff(42,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)))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[41, 40])).
% 1.14/1.33 tff(43,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)))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[42, 38])).
% 1.14/1.33 tff(44,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)))),
% 1.14/1.33 inference(skolemize,[status(sab)],[43])).
% 1.14/1.33 tff(45,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)))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[44, 37])).
% 1.14/1.33 tff(46,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(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(47,plain,
% 1.14/1.33 (((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z))) <=> ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(48,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(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[47])).
% 1.14/1.33 tff(49,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(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 1.14/1.33 inference(transitivity,[status(thm)],[48, 46])).
% 1.14/1.33 tff(50,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(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(51,plain,
% 1.14/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[50, 49])).
% 1.14/1.33 tff(52,plain,
% 1.14/1.33 ($false),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[51, 45, 27, 35, 28])).
% 1.14/1.33 tff(53,plain,((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.33 tff(54,plain,
% 1.14/1.33 (~r(s(s(z)), s(z))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[53, 27, 28])).
% 1.14/1.33 tff(55,plain,
% 1.14/1.33 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(56,plain,
% 1.14/1.33 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(57,plain,
% 1.14/1.33 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(58,axiom,(![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','sinj')).
% 1.14/1.33 tff(59,plain,
% 1.14/1.33 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[58, 57])).
% 1.14/1.33 tff(60,plain,(
% 1.14/1.33 ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.14/1.33 inference(skolemize,[status(sab)],[59])).
% 1.14/1.33 tff(61,plain,
% 1.14/1.33 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[60, 56])).
% 1.14/1.33 tff(62,plain,
% 1.14/1.33 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[61, 55])).
% 1.14/1.33 tff(63,plain,
% 1.14/1.33 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(z)) = z)),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(64,plain,
% 1.14/1.33 (inj_0(s(z)) = z),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[63, 62])).
% 1.14/1.33 tff(65,assumption,(s(z) = s(s(z))), introduced(assumption)).
% 1.14/1.33 tff(66,plain,
% 1.14/1.33 (inj_0(s(z)) = inj_0(s(s(z)))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[65])).
% 1.14/1.33 tff(67,plain,
% 1.14/1.33 (inj_0(s(s(z))) = inj_0(s(z))),
% 1.14/1.33 inference(symmetry,[status(thm)],[66])).
% 1.14/1.33 tff(68,plain,
% 1.14/1.33 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(z))) = s(z))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(69,plain,
% 1.14/1.33 (inj_0(s(s(z))) = s(z)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[68, 62])).
% 1.14/1.33 tff(70,plain,
% 1.14/1.33 (s(z) = inj_0(s(s(z)))),
% 1.14/1.33 inference(symmetry,[status(thm)],[69])).
% 1.14/1.33 tff(71,plain,
% 1.14/1.33 (s(s(z)) = s(z)),
% 1.14/1.33 inference(symmetry,[status(thm)],[65])).
% 1.14/1.33 tff(72,plain,
% 1.14/1.33 (s(s(z)) = z),
% 1.14/1.33 inference(transitivity,[status(thm)],[71, 70, 67, 64])).
% 1.14/1.33 tff(73,plain,
% 1.14/1.33 ($false),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[11, 72])).
% 1.14/1.33 tff(74,plain,(~(s(z) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.33 tff(75,plain,
% 1.14/1.33 ((s(s(z)) = s(z)) <=> (s(z) = s(s(z)))),
% 1.14/1.33 inference(commutativity,[status(thm)],[])).
% 1.14/1.33 tff(76,assumption,(s(s(z)) = s(z)), introduced(assumption)).
% 1.14/1.33 tff(77,plain,
% 1.14/1.33 (s(z) = s(s(z))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[76, 75])).
% 1.14/1.33 tff(78,assumption,(~(s(z) = s(s(z)))), introduced(assumption)).
% 1.14/1.33 tff(79,plain,
% 1.14/1.33 ($false),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[78, 77])).
% 1.14/1.33 tff(80,plain,((~(s(s(z)) = s(z))) | (s(z) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.33 tff(81,plain,
% 1.14/1.33 (~(s(s(z)) = s(z))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[80, 74])).
% 1.14/1.33 tff(82,plain,
% 1.14/1.33 (((~![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)))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(83,plain,
% 1.14/1.33 ((~![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)))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(84,plain,
% 1.14/1.33 ((~![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))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[83, 82])).
% 1.14/1.33 tff(85,plain,
% 1.14/1.33 ((s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[84, 21])).
% 1.14/1.33 tff(86,plain,
% 1.14/1.33 (b(s(s(z)), s(z)) | r(s(s(z)), s(z))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[85, 81])).
% 1.14/1.33 tff(87,plain,
% 1.14/1.33 (b(s(s(z)), s(z))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[86, 54])).
% 1.14/1.33 tff(88,assumption,(r(z, s(s(elem!1)))), introduced(assumption)).
% 1.14/1.33 tff(89,assumption,(r(s(z), s(s(elem!1)))), introduced(assumption)).
% 1.14/1.33 tff(90,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(z))) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(91,plain,
% 1.14/1.33 (((~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(92,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), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1))))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[91])).
% 1.14/1.33 tff(93,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), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))))),
% 1.14/1.33 inference(transitivity,[status(thm)],[92, 90])).
% 1.14/1.33 tff(94,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), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(95,plain,
% 1.14/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1))))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[94, 93])).
% 1.14/1.33 tff(96,plain,
% 1.14/1.33 ($false),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[95, 45, 27, 88, 89])).
% 1.14/1.33 tff(97,plain,((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.33 tff(98,plain,
% 1.14/1.33 (~r(s(z), s(s(elem!1)))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[97, 88, 27])).
% 1.14/1.33 tff(99,plain,
% 1.14/1.33 ((s(z) = s(s(elem!1))) <=> (s(s(elem!1)) = s(z))),
% 1.14/1.33 inference(commutativity,[status(thm)],[])).
% 1.14/1.33 tff(100,plain,
% 1.14/1.33 ((s(s(elem!1)) = s(z)) <=> (s(z) = s(s(elem!1)))),
% 1.14/1.33 inference(symmetry,[status(thm)],[99])).
% 1.14/1.33 tff(101,plain,
% 1.14/1.33 ((~(s(s(elem!1)) = s(z))) <=> (~(s(z) = s(s(elem!1))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[100])).
% 1.14/1.33 tff(102,assumption,(s(s(elem!1)) = s(z)), introduced(assumption)).
% 1.14/1.33 tff(103,plain,
% 1.14/1.33 (inj_0(s(s(elem!1))) = inj_0(s(z))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[102])).
% 1.14/1.33 tff(104,plain,
% 1.14/1.33 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(elem!1))) = s(elem!1))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(105,plain,
% 1.14/1.33 (inj_0(s(s(elem!1))) = s(elem!1)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[104, 62])).
% 1.14/1.33 tff(106,plain,
% 1.14/1.33 (s(elem!1) = inj_0(s(s(elem!1)))),
% 1.14/1.33 inference(symmetry,[status(thm)],[105])).
% 1.14/1.33 tff(107,plain,
% 1.14/1.33 (s(elem!1) = z),
% 1.14/1.33 inference(transitivity,[status(thm)],[106, 103, 64])).
% 1.14/1.33 tff(108,plain,
% 1.14/1.33 ((~![X: $i] : (~(s(X) = z))) | (~(s(elem!1) = z))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(109,plain,
% 1.14/1.33 (~(s(elem!1) = z)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[108, 9])).
% 1.14/1.33 tff(110,plain,
% 1.14/1.33 ($false),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[109, 107])).
% 1.14/1.33 tff(111,plain,(~(s(s(elem!1)) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.33 tff(112,plain,
% 1.14/1.33 (~(s(z) = s(s(elem!1)))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[111, 101])).
% 1.14/1.33 tff(113,plain,
% 1.14/1.33 (((~![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))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(114,plain,
% 1.14/1.33 ((~![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))))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(115,plain,
% 1.14/1.33 ((~![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)))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[114, 113])).
% 1.14/1.33 tff(116,plain,
% 1.14/1.33 ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[115, 21])).
% 1.14/1.33 tff(117,plain,
% 1.14/1.33 (b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[116, 112])).
% 1.14/1.33 tff(118,plain,
% 1.14/1.33 (b(s(z), s(s(elem!1)))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[117, 98])).
% 1.14/1.33 tff(119,plain,
% 1.14/1.33 (^[X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : refl(((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))))),
% 1.14/1.33 inference(bind,[status(th)],[])).
% 1.14/1.33 tff(120,plain,
% 1.14/1.33 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.14/1.33 inference(quant_intro,[status(thm)],[119])).
% 1.14/1.33 tff(121,plain,
% 1.14/1.33 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(122,plain,
% 1.14/1.33 (^[X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(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(X0, X4))) <=> (((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X0, X4))))), rewrite((((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X0, X4))) <=> ((~b(X0, 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(X0, X4))) <=> ((~b(X0, 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(X0, X4))) | (~b(X3, X4))) <=> (((~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X3, X4))))), rewrite((((~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X3, X4))) <=> ((~b(X3, X4)) | (~b(X0, 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(X0, X4))) | (~b(X3, X4))) <=> ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))))),
% 1.14/1.33 inference(bind,[status(th)],[])).
% 1.14/1.33 tff(123,plain,
% 1.14/1.33 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X0, X4))) | (~b(X3, X4))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.14/1.33 inference(quant_intro,[status(thm)],[122])).
% 1.14/1.33 tff(124,axiom,(![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X0, X4))) | (~b(X3, X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axb')).
% 1.14/1.33 tff(125,plain,
% 1.14/1.33 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[124, 123])).
% 1.14/1.33 tff(126,plain,
% 1.14/1.33 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[125, 121])).
% 1.14/1.33 tff(127,plain,(
% 1.14/1.33 ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.14/1.33 inference(skolemize,[status(sab)],[126])).
% 1.14/1.33 tff(128,plain,
% 1.14/1.33 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[127, 120])).
% 1.14/1.33 tff(129,plain,
% 1.14/1.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(130,plain,
% 1.14/1.33 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(131,plain,
% 1.14/1.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(s(z)), s(s(elem!1))))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[130])).
% 1.14/1.33 tff(132,plain,
% 1.14/1.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.14/1.33 inference(transitivity,[status(thm)],[131, 129])).
% 1.14/1.33 tff(133,plain,
% 1.14/1.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(134,plain,
% 1.14/1.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(s(z)), s(s(elem!1))))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[133, 132])).
% 1.14/1.33 tff(135,plain,
% 1.14/1.33 (~b(s(s(z)), s(s(elem!1)))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[134, 128, 30, 118, 87])).
% 1.14/1.33 tff(136,plain,
% 1.14/1.33 (((~![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))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(137,plain,
% 1.14/1.33 ((~![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))))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(138,plain,
% 1.14/1.33 ((~![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)))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[137, 136])).
% 1.14/1.33 tff(139,plain,
% 1.14/1.33 ((s(s(z)) = s(s(elem!1))) | r(s(s(z)), s(s(elem!1)))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[138, 21, 135])).
% 1.14/1.33 tff(140,plain,
% 1.14/1.33 (r(s(s(z)), s(s(elem!1)))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[139, 34])).
% 1.14/1.33 tff(141,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(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(142,plain,
% 1.14/1.33 (((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(z)), z))) <=> ((~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(143,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(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1))))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[142])).
% 1.14/1.33 tff(144,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(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.14/1.33 inference(transitivity,[status(thm)],[143, 141])).
% 1.14/1.33 tff(145,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(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(146,plain,
% 1.14/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1))))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[145, 144])).
% 1.14/1.33 tff(147,plain,
% 1.14/1.33 ($false),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[146, 45, 27, 88, 28, 140])).
% 1.14/1.33 tff(148,plain,((~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (s(s(elem!1)) = s(s(z))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.33 tff(149,plain,
% 1.14/1.33 (~r(z, s(s(elem!1)))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[148, 1, 28, 27, 30])).
% 1.14/1.34 tff(150,plain,
% 1.14/1.34 ((z = s(s(elem!1))) <=> (s(s(elem!1)) = z)),
% 1.14/1.34 inference(commutativity,[status(thm)],[])).
% 1.14/1.34 tff(151,plain,
% 1.14/1.34 ((s(s(elem!1)) = z) <=> (z = s(s(elem!1)))),
% 1.14/1.34 inference(symmetry,[status(thm)],[150])).
% 1.14/1.34 tff(152,plain,
% 1.14/1.34 ((~(s(s(elem!1)) = z)) <=> (~(z = s(s(elem!1))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[151])).
% 1.14/1.34 tff(153,plain,
% 1.14/1.34 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(elem!1)) = z))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(154,plain,
% 1.14/1.34 (~(s(s(elem!1)) = z)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[153, 9])).
% 1.14/1.34 tff(155,plain,
% 1.14/1.34 (~(z = s(s(elem!1)))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[154, 152])).
% 1.14/1.34 tff(156,plain,
% 1.14/1.34 (((~![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))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(157,plain,
% 1.14/1.34 ((~![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))))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(158,plain,
% 1.14/1.34 ((~![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)))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[157, 156])).
% 1.14/1.34 tff(159,plain,
% 1.14/1.34 ((z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1)))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[158, 21])).
% 1.14/1.34 tff(160,plain,
% 1.14/1.34 (b(z, s(s(elem!1))) | r(z, s(s(elem!1)))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[159, 155])).
% 1.14/1.34 tff(161,plain,
% 1.14/1.34 (b(z, s(s(elem!1)))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[160, 149])).
% 1.14/1.34 tff(162,plain,
% 1.14/1.34 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(163,plain,
% 1.14/1.34 (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[162, 62])).
% 1.14/1.34 tff(164,assumption,(~b(s(z), z)), introduced(assumption)).
% 1.14/1.34 tff(165,plain,
% 1.14/1.34 ((~![X: $i] : (~(s(X) = z))) | (~(s(z) = z))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(166,plain,
% 1.14/1.34 (~(s(z) = z)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[165, 9])).
% 1.14/1.34 tff(167,plain,
% 1.14/1.34 (((~![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))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(168,plain,
% 1.14/1.34 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = z) | b(s(z), z) | r(s(z), z))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(169,plain,
% 1.14/1.34 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = z) | b(s(z), z) | r(s(z), z)),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[168, 167])).
% 1.14/1.34 tff(170,plain,
% 1.14/1.34 (b(s(z), z) | r(s(z), z)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[169, 21, 166])).
% 1.14/1.34 tff(171,plain,
% 1.14/1.34 (r(s(z), z)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[170, 164])).
% 1.14/1.34 tff(172,assumption,(~r(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 1.14/1.34 tff(173,assumption,(z = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.14/1.34 tff(174,plain,
% 1.14/1.34 (s(s(s(s(elem!1)))) = z),
% 1.14/1.34 inference(symmetry,[status(thm)],[173])).
% 1.14/1.34 tff(175,plain,
% 1.14/1.34 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(elem!1)))) = z))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(176,plain,
% 1.14/1.34 (~(s(s(s(s(elem!1)))) = z)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[175, 9])).
% 1.14/1.34 tff(177,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[176, 174])).
% 1.14/1.34 tff(178,plain,(~(z = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(179,plain,
% 1.14/1.34 ((s(s(s(elem!1))) = s(z)) <=> (s(z) = s(s(s(elem!1))))),
% 1.14/1.34 inference(commutativity,[status(thm)],[])).
% 1.14/1.34 tff(180,plain,
% 1.14/1.34 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(z))),
% 1.14/1.34 inference(symmetry,[status(thm)],[179])).
% 1.14/1.34 tff(181,plain,
% 1.14/1.34 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(z)))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[180])).
% 1.14/1.34 tff(182,assumption,(s(z) = s(s(s(elem!1)))), introduced(assumption)).
% 1.14/1.34 tff(183,plain,
% 1.14/1.34 (inj_0(s(z)) = inj_0(s(s(s(elem!1))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[182])).
% 1.14/1.34 tff(184,plain,
% 1.14/1.34 (inj_0(s(s(s(elem!1)))) = inj_0(s(z))),
% 1.14/1.34 inference(symmetry,[status(thm)],[183])).
% 1.14/1.34 tff(185,plain,
% 1.14/1.34 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(186,plain,
% 1.14/1.34 (inj_0(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[185, 62])).
% 1.14/1.34 tff(187,plain,
% 1.14/1.34 (s(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 1.14/1.34 inference(symmetry,[status(thm)],[186])).
% 1.14/1.34 tff(188,plain,
% 1.14/1.34 (s(s(elem!1)) = z),
% 1.14/1.34 inference(transitivity,[status(thm)],[187, 184, 64])).
% 1.14/1.34 tff(189,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[154, 188])).
% 1.14/1.34 tff(190,plain,(~(s(z) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(191,plain,
% 1.14/1.34 (~(s(s(s(elem!1))) = s(z))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[190, 181])).
% 1.14/1.34 tff(192,plain,
% 1.14/1.34 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z)))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(193,plain,
% 1.14/1.34 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z)))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(194,plain,
% 1.14/1.34 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[193, 192])).
% 1.14/1.34 tff(195,plain,
% 1.14/1.34 ((s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[194, 21])).
% 1.14/1.34 tff(196,plain,
% 1.14/1.34 (b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[195, 191])).
% 1.14/1.34 tff(197,plain,
% 1.14/1.34 (b(s(s(s(elem!1))), s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[196, 172])).
% 1.14/1.34 tff(198,assumption,(~b(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 1.14/1.34 tff(199,assumption,(s(s(elem!1)) = elem!1), introduced(assumption)).
% 1.14/1.34 tff(200,plain,
% 1.14/1.34 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(elem!1)) = elem!1)),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(201,plain,
% 1.14/1.34 (inj_0(s(elem!1)) = elem!1),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[200, 62])).
% 1.14/1.34 tff(202,plain,
% 1.14/1.34 (elem!1 = s(s(elem!1))),
% 1.14/1.34 inference(symmetry,[status(thm)],[199])).
% 1.14/1.34 tff(203,assumption,(s(s(s(s(s(s(z)))))) = elem!1), introduced(assumption)).
% 1.14/1.34 tff(204,plain,
% 1.14/1.34 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 1.14/1.34 inference(transitivity,[status(thm)],[203, 202])).
% 1.14/1.34 tff(205,plain,
% 1.14/1.34 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(elem!1)))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[204])).
% 1.14/1.34 tff(206,plain,
% 1.14/1.34 ((~![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))))))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(207,plain,
% 1.14/1.34 (inj_0(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[206, 62])).
% 1.14/1.34 tff(208,plain,
% 1.14/1.34 (s(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.14/1.34 inference(symmetry,[status(thm)],[207])).
% 1.14/1.34 tff(209,plain,
% 1.14/1.34 (s(s(s(s(s(z))))) = s(elem!1)),
% 1.14/1.34 inference(transitivity,[status(thm)],[208, 205, 105])).
% 1.14/1.34 tff(210,plain,
% 1.14/1.34 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(elem!1))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[209])).
% 1.14/1.34 tff(211,plain,
% 1.14/1.34 (s(s(s(s(z)))) = inj_0(s(s(s(s(s(z))))))),
% 1.14/1.34 inference(symmetry,[status(thm)],[163])).
% 1.14/1.34 tff(212,plain,
% 1.14/1.34 (s(s(s(s(z)))) = elem!1),
% 1.14/1.34 inference(transitivity,[status(thm)],[211, 210, 201])).
% 1.14/1.34 tff(213,assumption,(s(s(s(s(z)))) = elem!1), introduced(assumption)).
% 1.14/1.34 tff(214,plain,
% 1.14/1.34 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.14/1.34 inference(transitivity,[status(thm)],[213, 202])).
% 1.14/1.34 tff(215,plain,
% 1.14/1.34 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[214])).
% 1.14/1.34 tff(216,plain,
% 1.14/1.34 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(z))))) = s(s(s(z))))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(217,plain,
% 1.14/1.34 (inj_0(s(s(s(s(z))))) = s(s(s(z)))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[216, 62])).
% 1.14/1.34 tff(218,plain,
% 1.14/1.34 (s(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 1.14/1.34 inference(symmetry,[status(thm)],[217])).
% 1.14/1.34 tff(219,plain,
% 1.14/1.34 (s(s(s(z))) = s(elem!1)),
% 1.14/1.34 inference(transitivity,[status(thm)],[218, 215, 105])).
% 1.14/1.34 tff(220,plain,
% 1.14/1.34 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[219])).
% 1.14/1.34 tff(221,plain,
% 1.14/1.34 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(z)))) = s(s(z)))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(222,plain,
% 1.14/1.34 (inj_0(s(s(s(z)))) = s(s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[221, 62])).
% 1.14/1.34 tff(223,plain,
% 1.14/1.34 (s(s(z)) = inj_0(s(s(s(z))))),
% 1.14/1.34 inference(symmetry,[status(thm)],[222])).
% 1.14/1.34 tff(224,plain,
% 1.14/1.34 (s(s(z)) = elem!1),
% 1.14/1.34 inference(transitivity,[status(thm)],[223, 220, 201])).
% 1.14/1.34 tff(225,plain,
% 1.14/1.34 ((elem!1 = s(s(z))) <=> (s(s(z)) = elem!1)),
% 1.14/1.34 inference(commutativity,[status(thm)],[])).
% 1.14/1.34 tff(226,plain,
% 1.14/1.34 (s(s(s(elem!1))) = s(elem!1)),
% 1.14/1.34 inference(monotonicity,[status(thm)],[199])).
% 1.14/1.34 tff(227,plain,
% 1.14/1.34 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[226])).
% 1.14/1.34 tff(228,plain,
% 1.14/1.34 (s(s(s(s(elem!1)))) = elem!1),
% 1.14/1.34 inference(transitivity,[status(thm)],[227, 199])).
% 1.14/1.34 tff(229,plain,
% 1.14/1.34 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[228])).
% 1.14/1.34 tff(230,plain,
% 1.14/1.34 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 1.14/1.34 inference(transitivity,[status(thm)],[229, 225])).
% 1.14/1.34 tff(231,plain,
% 1.14/1.34 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[230])).
% 1.14/1.34 tff(232,plain,
% 1.14/1.34 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(233,plain,
% 1.14/1.34 (inj_0(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[232, 62])).
% 1.14/1.34 tff(234,assumption,(s(s(s(s(elem!1)))) = s(s(z))), introduced(assumption)).
% 1.14/1.34 tff(235,plain,
% 1.14/1.34 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(z)))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[234])).
% 1.14/1.34 tff(236,plain,
% 1.14/1.34 (inj_0(s(s(z))) = inj_0(s(s(s(s(elem!1)))))),
% 1.14/1.34 inference(symmetry,[status(thm)],[235])).
% 1.14/1.34 tff(237,plain,
% 1.14/1.34 (s(z) = s(s(s(elem!1)))),
% 1.14/1.34 inference(transitivity,[status(thm)],[70, 236, 233])).
% 1.14/1.34 tff(238,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[190, 237])).
% 1.14/1.34 tff(239,plain,(~(s(s(s(s(elem!1)))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(240,plain,
% 1.14/1.34 (~(s(s(z)) = elem!1)),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[239, 231])).
% 1.14/1.34 tff(241,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[240, 224])).
% 1.14/1.34 tff(242,plain,((~(s(s(s(s(z)))) = elem!1)) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(243,plain,
% 1.14/1.34 (~(s(s(s(s(z)))) = elem!1)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[242, 199])).
% 1.14/1.34 tff(244,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[243, 212])).
% 1.14/1.34 tff(245,plain,((~(s(s(s(s(s(s(z)))))) = elem!1)) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(246,plain,
% 1.14/1.34 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[245, 199])).
% 1.14/1.34 tff(247,plain,
% 1.14/1.34 ((elem!1 = z) <=> (z = elem!1)),
% 1.14/1.34 inference(commutativity,[status(thm)],[])).
% 1.14/1.34 tff(248,plain,
% 1.14/1.34 ((s(s(elem!1)) = z) <=> (elem!1 = z)),
% 1.14/1.34 inference(monotonicity,[status(thm)],[199])).
% 1.14/1.34 tff(249,plain,
% 1.14/1.34 ((s(s(elem!1)) = z) <=> (z = elem!1)),
% 1.14/1.34 inference(transitivity,[status(thm)],[248, 247])).
% 1.14/1.34 tff(250,plain,
% 1.14/1.34 ((~(s(s(elem!1)) = z)) <=> (~(z = elem!1))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[249])).
% 1.14/1.34 tff(251,plain,
% 1.14/1.34 (~(z = elem!1)),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[154, 250])).
% 1.14/1.34 tff(252,plain,
% 1.14/1.34 ((s(z) = elem!1) <=> (elem!1 = s(z))),
% 1.14/1.34 inference(commutativity,[status(thm)],[])).
% 1.14/1.34 tff(253,plain,
% 1.14/1.34 ((elem!1 = s(z)) <=> (s(z) = elem!1)),
% 1.14/1.34 inference(symmetry,[status(thm)],[252])).
% 1.14/1.34 tff(254,plain,
% 1.14/1.34 ((s(s(elem!1)) = s(z)) <=> (elem!1 = s(z))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[199])).
% 1.14/1.34 tff(255,plain,
% 1.14/1.34 ((s(s(elem!1)) = s(z)) <=> (s(z) = elem!1)),
% 1.14/1.34 inference(transitivity,[status(thm)],[254, 253])).
% 1.14/1.34 tff(256,plain,
% 1.14/1.34 ((~(s(s(elem!1)) = s(z))) <=> (~(s(z) = elem!1))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[255])).
% 1.14/1.34 tff(257,plain,
% 1.14/1.34 (~(s(z) = elem!1)),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[111, 256])).
% 1.14/1.34 tff(258,plain,
% 1.14/1.34 (r(s(s(s(elem!1))), s(z)) <=> r(s(elem!1), s(z))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[226])).
% 1.14/1.34 tff(259,plain,
% 1.14/1.34 ((~r(s(s(s(elem!1))), s(z))) <=> (~r(s(elem!1), s(z)))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[258])).
% 1.14/1.34 tff(260,plain,
% 1.14/1.34 (~r(s(elem!1), s(z))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[172, 259])).
% 1.14/1.34 tff(261,plain,
% 1.14/1.34 (b(s(s(s(elem!1))), s(z)) <=> b(s(elem!1), s(z))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[226])).
% 1.14/1.34 tff(262,plain,
% 1.14/1.34 (b(s(elem!1), s(z))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[197, 261])).
% 1.14/1.34 tff(263,assumption,(b(s(elem!1), s(z))), introduced(assumption)).
% 1.14/1.34 tff(264,plain,
% 1.14/1.34 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(elem!1))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[226])).
% 1.14/1.34 tff(265,plain,
% 1.14/1.34 ((~b(elem!1, s(s(s(elem!1))))) <=> (~b(elem!1, s(elem!1)))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[264])).
% 1.14/1.34 tff(266,plain,
% 1.14/1.34 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[199])).
% 1.14/1.34 tff(267,plain,
% 1.14/1.34 ((~b(s(s(elem!1)), s(s(s(elem!1))))) <=> (~b(elem!1, s(s(s(elem!1)))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[266])).
% 1.14/1.34 tff(268,plain,
% 1.14/1.34 (~b(elem!1, s(s(s(elem!1))))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[198, 267])).
% 1.14/1.34 tff(269,plain,
% 1.14/1.34 (~b(elem!1, s(elem!1))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[268, 265])).
% 1.14/1.34 tff(270,plain,
% 1.14/1.34 (b(s(s(elem!1)), s(z)) <=> b(elem!1, s(z))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[199])).
% 1.14/1.34 tff(271,assumption,(~r(s(elem!1), s(z))), introduced(assumption)).
% 1.14/1.34 tff(272,assumption,(r(s(z), z)), introduced(assumption)).
% 1.14/1.34 tff(273,assumption,(b(s(s(z)), s(z))), introduced(assumption)).
% 1.14/1.34 tff(274,plain,
% 1.14/1.34 ((s(s(z)) = s(elem!1)) <=> (s(elem!1) = s(s(z)))),
% 1.14/1.34 inference(commutativity,[status(thm)],[])).
% 1.14/1.34 tff(275,plain,
% 1.14/1.34 ((s(elem!1) = s(s(z))) <=> (s(s(z)) = s(elem!1))),
% 1.14/1.34 inference(symmetry,[status(thm)],[274])).
% 1.14/1.34 tff(276,plain,
% 1.14/1.34 ((~(s(elem!1) = s(s(z)))) <=> (~(s(s(z)) = s(elem!1)))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[275])).
% 1.14/1.34 tff(277,plain,
% 1.14/1.34 ((s(s(s(elem!1))) = s(s(z))) <=> (s(elem!1) = s(s(z)))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[226])).
% 1.14/1.34 tff(278,plain,
% 1.14/1.34 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(elem!1) = s(s(z))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[277])).
% 1.14/1.34 tff(279,assumption,(s(s(s(elem!1))) = s(s(z))), introduced(assumption)).
% 1.14/1.34 tff(280,plain,
% 1.14/1.34 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(z)))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[279])).
% 1.14/1.34 tff(281,plain,
% 1.14/1.34 (s(s(elem!1)) = s(z)),
% 1.14/1.34 inference(transitivity,[status(thm)],[187, 280, 69])).
% 1.14/1.34 tff(282,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[111, 281])).
% 1.14/1.34 tff(283,plain,(~(s(s(s(elem!1))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(284,plain,
% 1.14/1.34 (~(s(elem!1) = s(s(z)))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[283, 278])).
% 1.14/1.34 tff(285,plain,
% 1.14/1.34 (~(s(s(z)) = s(elem!1))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[284, 276])).
% 1.14/1.34 tff(286,plain,
% 1.14/1.34 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(elem!1))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[226])).
% 1.14/1.34 tff(287,assumption,(~b(s(s(elem!1)), s(z))), introduced(assumption)).
% 1.14/1.34 tff(288,plain,
% 1.14/1.34 (((~![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)))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(289,plain,
% 1.14/1.34 ((~![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)))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(290,plain,
% 1.14/1.34 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[289, 288])).
% 1.14/1.34 tff(291,plain,
% 1.14/1.34 ((s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[290, 21])).
% 1.14/1.34 tff(292,plain,
% 1.14/1.34 (b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[291, 111])).
% 1.14/1.34 tff(293,plain,
% 1.14/1.34 (r(s(s(elem!1)), s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[292, 287])).
% 1.14/1.34 tff(294,plain,
% 1.14/1.34 ((~(s(s(elem!1)) = s(z))) <=> (~(elem!1 = s(z)))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[254])).
% 1.14/1.34 tff(295,plain,
% 1.14/1.34 (~(elem!1 = s(z))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[111, 294])).
% 1.14/1.34 tff(296,plain,
% 1.14/1.34 (b(elem!1, s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.14/1.34 inference(symmetry,[status(thm)],[270])).
% 1.14/1.34 tff(297,assumption,(b(elem!1, s(z))), introduced(assumption)).
% 1.14/1.34 tff(298,plain,
% 1.14/1.34 (b(s(s(elem!1)), s(z))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[297, 296])).
% 1.14/1.34 tff(299,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[287, 298])).
% 1.14/1.34 tff(300,plain,((~(s(s(elem!1)) = elem!1)) | b(s(s(elem!1)), s(z)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(301,plain,
% 1.14/1.34 (~b(elem!1, s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[300, 287, 199])).
% 1.14/1.34 tff(302,plain,
% 1.14/1.34 (((~![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)))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(303,plain,
% 1.14/1.34 ((~![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)))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(304,plain,
% 1.14/1.34 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[303, 302])).
% 1.14/1.34 tff(305,plain,
% 1.14/1.34 ((elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[304, 21])).
% 1.14/1.34 tff(306,plain,
% 1.14/1.34 (r(elem!1, s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[305, 301, 295])).
% 1.14/1.34 tff(307,assumption,(s(s(elem!1)) = s(s(s(elem!1)))), introduced(assumption)).
% 1.14/1.34 tff(308,plain,
% 1.14/1.34 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.14/1.34 inference(symmetry,[status(thm)],[307])).
% 1.14/1.34 tff(309,plain,
% 1.14/1.34 (s(elem!1) = s(s(s(elem!1)))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[202])).
% 1.14/1.34 tff(310,plain,
% 1.14/1.34 (s(elem!1) = elem!1),
% 1.14/1.34 inference(transitivity,[status(thm)],[309, 308, 199])).
% 1.14/1.34 tff(311,plain,
% 1.14/1.34 (r(s(elem!1), s(z)) <=> r(elem!1, s(z))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[310])).
% 1.14/1.34 tff(312,plain,
% 1.14/1.34 (r(elem!1, s(z)) <=> r(s(elem!1), s(z))),
% 1.14/1.34 inference(symmetry,[status(thm)],[311])).
% 1.14/1.34 tff(313,assumption,(r(elem!1, s(z))), introduced(assumption)).
% 1.14/1.34 tff(314,plain,
% 1.14/1.34 (r(s(elem!1), s(z))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[313, 312])).
% 1.14/1.34 tff(315,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[271, 314])).
% 1.14/1.34 tff(316,plain,((~(s(s(elem!1)) = s(s(s(elem!1))))) | r(s(elem!1), s(z)) | (~r(elem!1, s(z))) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(317,plain,
% 1.14/1.34 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[316, 306, 271, 199])).
% 1.14/1.34 tff(318,plain,
% 1.14/1.34 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(319,plain,
% 1.14/1.34 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(320,plain,
% 1.14/1.34 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[319, 318])).
% 1.14/1.34 tff(321,plain,
% 1.14/1.34 ((s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[320, 21])).
% 1.14/1.34 tff(322,plain,
% 1.14/1.34 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[321, 317, 198])).
% 1.14/1.34 tff(323,assumption,(r(s(z), s(s(s(elem!1))))), introduced(assumption)).
% 1.14/1.34 tff(324,assumption,(r(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 1.14/1.34 tff(325,assumption,(r(s(s(elem!1)), s(z))), introduced(assumption)).
% 1.14/1.34 tff(326,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(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(327,plain,
% 1.14/1.34 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(328,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(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[327])).
% 1.14/1.34 tff(329,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(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.14/1.34 inference(transitivity,[status(thm)],[328, 326])).
% 1.14/1.34 tff(330,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(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(331,plain,
% 1.14/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[330, 329])).
% 1.14/1.34 tff(332,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[331, 45, 325, 324, 323])).
% 1.14/1.34 tff(333,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(334,plain,
% 1.14/1.34 (~r(s(z), s(s(s(elem!1))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[333, 322, 293])).
% 1.14/1.34 tff(335,plain,
% 1.14/1.34 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1)))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(336,plain,
% 1.14/1.34 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1)))))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(337,plain,
% 1.14/1.34 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1))))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[336, 335])).
% 1.14/1.34 tff(338,plain,
% 1.14/1.34 ((s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[337, 21])).
% 1.14/1.34 tff(339,plain,
% 1.14/1.34 (b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[338, 190])).
% 1.14/1.34 tff(340,plain,
% 1.14/1.34 (b(s(z), s(s(s(elem!1))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[339, 334])).
% 1.14/1.34 tff(341,plain,
% 1.14/1.34 (b(s(z), s(elem!1))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[340, 286])).
% 1.14/1.34 tff(342,plain,
% 1.14/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(elem!1))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(343,plain,
% 1.14/1.34 (((~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(elem!1))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(344,plain,
% 1.14/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(elem!1)))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[343])).
% 1.14/1.34 tff(345,plain,
% 1.14/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(elem!1))))),
% 1.14/1.34 inference(transitivity,[status(thm)],[344, 342])).
% 1.14/1.34 tff(346,plain,
% 1.14/1.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(347,plain,
% 1.14/1.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(elem!1)))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[346, 345])).
% 1.14/1.34 tff(348,plain,
% 1.14/1.34 (~b(s(s(z)), s(elem!1))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[347, 128, 273, 341, 263])).
% 1.14/1.34 tff(349,plain,
% 1.14/1.34 (((~![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)))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(350,plain,
% 1.14/1.34 ((~![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)))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(351,plain,
% 1.14/1.34 ((~![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))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[350, 349])).
% 1.14/1.34 tff(352,plain,
% 1.14/1.34 ((s(s(z)) = s(elem!1)) | r(s(s(z)), s(elem!1))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[351, 21, 348])).
% 1.14/1.35 tff(353,plain,
% 1.14/1.35 (r(s(s(z)), s(elem!1))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[352, 285])).
% 1.14/1.35 tff(354,plain,
% 1.14/1.35 (s(elem!1) = s(s(s(elem!1)))),
% 1.14/1.35 inference(symmetry,[status(thm)],[226])).
% 1.14/1.35 tff(355,plain,
% 1.14/1.35 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(elem!1))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[354])).
% 1.14/1.35 tff(356,plain,
% 1.14/1.35 (r(elem!1, s(s(s(elem!1)))) <=> r(elem!1, s(elem!1))),
% 1.14/1.35 inference(symmetry,[status(thm)],[355])).
% 1.14/1.35 tff(357,plain,
% 1.14/1.35 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[199])).
% 1.14/1.35 tff(358,plain,
% 1.14/1.35 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(elem!1, s(elem!1))),
% 1.14/1.35 inference(transitivity,[status(thm)],[357, 356])).
% 1.14/1.35 tff(359,plain,
% 1.14/1.35 (r(elem!1, s(elem!1))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[322, 358])).
% 1.14/1.35 tff(360,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(z))) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(361,plain,
% 1.14/1.35 (((~r(elem!1, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1))) <=> ((~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(362,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(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1)))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[361])).
% 1.14/1.35 tff(363,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(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1))))),
% 1.14/1.35 inference(transitivity,[status(thm)],[362, 360])).
% 1.14/1.35 tff(364,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(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(365,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(z))) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(elem!1)))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[364, 363])).
% 1.14/1.35 tff(366,plain,
% 1.14/1.35 (~r(s(s(z)), elem!1)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[365, 45, 306, 359, 353])).
% 1.14/1.35 tff(367,plain,
% 1.14/1.35 (((~![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))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(368,plain,
% 1.14/1.35 ((~![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))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(369,plain,
% 1.14/1.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1)),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[368, 367])).
% 1.14/1.35 tff(370,plain,
% 1.14/1.35 ((s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[369, 21])).
% 1.14/1.35 tff(371,plain,
% 1.14/1.35 (b(s(s(z)), elem!1)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[370, 366, 240])).
% 1.14/1.35 tff(372,plain,
% 1.14/1.35 ((elem!1 = s(s(elem!1))) <=> (s(s(elem!1)) = elem!1)),
% 1.14/1.35 inference(commutativity,[status(thm)],[])).
% 1.14/1.35 tff(373,plain,
% 1.14/1.35 ((s(s(elem!1)) = elem!1) <=> (elem!1 = s(s(elem!1)))),
% 1.14/1.35 inference(symmetry,[status(thm)],[372])).
% 1.14/1.35 tff(374,plain,
% 1.14/1.35 (elem!1 = s(s(elem!1))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[199, 373])).
% 1.14/1.35 tff(375,assumption,(~(elem!1 = s(s(elem!1)))), introduced(assumption)).
% 1.14/1.35 tff(376,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[375, 374])).
% 1.14/1.35 tff(377,plain,((~(s(s(elem!1)) = elem!1)) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(378,plain,
% 1.14/1.35 (elem!1 = s(s(elem!1))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[377, 199])).
% 1.14/1.35 tff(379,assumption,(z = s(s(s(elem!1)))), introduced(assumption)).
% 1.14/1.35 tff(380,plain,
% 1.14/1.35 (s(s(s(elem!1))) = z),
% 1.14/1.35 inference(symmetry,[status(thm)],[379])).
% 1.14/1.35 tff(381,plain,
% 1.14/1.35 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(elem!1))) = z))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(382,plain,
% 1.14/1.35 (~(s(s(s(elem!1))) = z)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[381, 9])).
% 1.14/1.35 tff(383,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[382, 380])).
% 1.14/1.35 tff(384,plain,(~(z = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(385,assumption,(r(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 1.14/1.35 tff(386,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)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(387,plain,
% 1.14/1.35 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(388,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(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[387])).
% 1.14/1.35 tff(389,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(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.14/1.35 inference(transitivity,[status(thm)],[388, 386])).
% 1.14/1.35 tff(390,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(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(391,plain,
% 1.14/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[390, 389])).
% 1.14/1.35 tff(392,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[391, 45, 325, 324, 385])).
% 1.14/1.35 tff(393,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(394,plain,
% 1.14/1.35 (~r(s(s(s(elem!1))), s(z))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[393, 324, 325])).
% 1.14/1.35 tff(395,plain,
% 1.14/1.35 (b(s(s(s(elem!1))), s(z))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[195, 394, 191])).
% 1.14/1.35 tff(396,plain,
% 1.14/1.35 (~r(s(z), s(s(s(elem!1))))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[333, 324, 325])).
% 1.14/1.35 tff(397,plain,
% 1.14/1.35 (b(s(z), s(s(s(elem!1))))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[338, 396, 190])).
% 1.14/1.35 tff(398,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(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(399,plain,
% 1.14/1.35 (((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(400,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)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z)))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[399])).
% 1.14/1.35 tff(401,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)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))))),
% 1.14/1.35 inference(transitivity,[status(thm)],[400, 398])).
% 1.14/1.35 tff(402,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)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(403,plain,
% 1.14/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z)))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[402, 401])).
% 1.14/1.35 tff(404,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[403, 45, 325, 27, 88])).
% 1.14/1.35 tff(405,plain,((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(406,plain,
% 1.14/1.35 (~r(z, s(z))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[405, 88, 325])).
% 1.14/1.35 tff(407,plain,
% 1.14/1.35 ((z = s(z)) <=> (s(z) = z)),
% 1.14/1.35 inference(commutativity,[status(thm)],[])).
% 1.14/1.35 tff(408,plain,
% 1.14/1.35 ((s(z) = z) <=> (z = s(z))),
% 1.14/1.35 inference(symmetry,[status(thm)],[407])).
% 1.14/1.35 tff(409,plain,
% 1.14/1.35 ((~(s(z) = z)) <=> (~(z = s(z)))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[408])).
% 1.14/1.35 tff(410,plain,
% 1.14/1.35 (~(z = s(z))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[166, 409])).
% 1.14/1.35 tff(411,plain,
% 1.14/1.35 (((~![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)))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(412,plain,
% 1.14/1.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(z)) | b(z, s(z)) | r(z, s(z)))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(413,plain,
% 1.14/1.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[412, 411])).
% 1.14/1.35 tff(414,plain,
% 1.14/1.35 ((z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[413, 21])).
% 1.14/1.35 tff(415,plain,
% 1.14/1.35 (b(z, s(z)) | r(z, s(z))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[414, 410])).
% 1.14/1.35 tff(416,plain,
% 1.14/1.35 (b(z, s(z))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[415, 406])).
% 1.14/1.35 tff(417,plain,
% 1.14/1.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(418,plain,
% 1.14/1.35 (((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(419,plain,
% 1.14/1.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1)))))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[418])).
% 1.14/1.35 tff(420,plain,
% 1.14/1.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))))),
% 1.14/1.35 inference(transitivity,[status(thm)],[419, 417])).
% 1.14/1.35 tff(421,plain,
% 1.14/1.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(422,plain,
% 1.14/1.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1)))))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[421, 420])).
% 1.14/1.35 tff(423,plain,
% 1.14/1.35 (~b(z, s(s(s(elem!1))))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[422, 128, 416, 397, 395])).
% 1.14/1.35 tff(424,assumption,(r(z, s(s(s(elem!1))))), introduced(assumption)).
% 1.14/1.35 tff(425,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(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(426,plain,
% 1.14/1.35 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(427,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)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~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(s(s(elem!1)), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[426])).
% 1.14/1.35 tff(428,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)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~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(s(s(elem!1)), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.14/1.35 inference(transitivity,[status(thm)],[427, 425])).
% 1.14/1.35 tff(429,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)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(430,plain,
% 1.14/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[429, 428])).
% 1.14/1.35 tff(431,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[430, 45, 325, 88, 324, 424])).
% 1.14/1.35 tff(432,plain,((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(433,plain,
% 1.14/1.35 (~r(z, s(s(s(elem!1))))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[432, 324, 88, 325])).
% 1.14/1.35 tff(434,plain,
% 1.14/1.35 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1)))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(435,plain,
% 1.14/1.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1)))))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(436,plain,
% 1.14/1.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1))))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[435, 434])).
% 1.14/1.35 tff(437,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[436, 21, 433, 423, 384])).
% 1.14/1.35 tff(438,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(439,plain,
% 1.14/1.35 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[438, 293, 88])).
% 1.14/1.35 tff(440,plain,
% 1.14/1.35 (s(s(elem!1)) = s(s(s(elem!1)))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[321, 439, 198])).
% 1.14/1.35 tff(441,plain,
% 1.14/1.35 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.14/1.35 inference(symmetry,[status(thm)],[440])).
% 1.14/1.35 tff(442,plain,
% 1.14/1.35 (s(elem!1) = elem!1),
% 1.14/1.35 inference(transitivity,[status(thm)],[309, 441, 199])).
% 1.14/1.35 tff(443,plain,
% 1.14/1.35 (r(s(elem!1), s(z)) <=> r(elem!1, s(z))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[442])).
% 1.14/1.35 tff(444,plain,
% 1.14/1.35 (r(elem!1, s(z)) <=> r(s(elem!1), s(z))),
% 1.14/1.35 inference(symmetry,[status(thm)],[443])).
% 1.14/1.35 tff(445,plain,
% 1.14/1.35 (r(s(elem!1), s(z))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[306, 444])).
% 1.14/1.35 tff(446,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[271, 445])).
% 1.14/1.35 tff(447,plain,(b(s(s(elem!1)), s(z)) | r(s(elem!1), s(z)) | (~(s(s(elem!1)) = elem!1)) | b(s(s(elem!1)), s(s(s(elem!1)))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(448,plain,
% 1.14/1.35 (~r(z, s(s(elem!1)))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[447, 287, 199, 198, 271])).
% 1.14/1.35 tff(449,plain,
% 1.14/1.35 (b(z, s(s(elem!1)))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[160, 448])).
% 1.14/1.35 tff(450,assumption,(elem!1 = s(s(elem!1))), introduced(assumption)).
% 1.14/1.35 tff(451,plain,
% 1.14/1.35 (b(z, elem!1) <=> b(z, s(s(elem!1)))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[450])).
% 1.14/1.35 tff(452,plain,
% 1.14/1.35 (b(z, s(s(elem!1))) <=> b(z, elem!1)),
% 1.14/1.35 inference(symmetry,[status(thm)],[451])).
% 1.14/1.35 tff(453,assumption,(b(z, s(s(elem!1)))), introduced(assumption)).
% 1.14/1.35 tff(454,plain,
% 1.14/1.35 (b(z, elem!1)),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[453, 452])).
% 1.14/1.35 tff(455,assumption,(~b(z, elem!1)), introduced(assumption)).
% 1.14/1.35 tff(456,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[455, 454])).
% 1.14/1.35 tff(457,plain,((~(elem!1 = s(s(elem!1)))) | b(z, elem!1) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(458,plain,
% 1.14/1.35 (b(z, elem!1)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[457, 449, 378])).
% 1.14/1.35 tff(459,plain,
% 1.14/1.35 ((z = elem!1) <=> (elem!1 = z)),
% 1.14/1.35 inference(symmetry,[status(thm)],[247])).
% 1.14/1.35 tff(460,plain,
% 1.14/1.35 ((s(s(elem!1)) = z) <=> (elem!1 = z)),
% 1.14/1.35 inference(transitivity,[status(thm)],[249, 459])).
% 1.14/1.35 tff(461,plain,
% 1.14/1.35 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = z))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[460])).
% 1.14/1.35 tff(462,plain,
% 1.14/1.35 (~(elem!1 = z)),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[154, 461])).
% 1.14/1.35 tff(463,plain,
% 1.14/1.35 (r(s(elem!1), s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[354])).
% 1.14/1.35 tff(464,plain,
% 1.14/1.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(z)))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(465,plain,
% 1.14/1.35 (((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z))))) <=> ((~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(z)))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(466,plain,
% 1.14/1.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(z))))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[465])).
% 1.14/1.35 tff(467,plain,
% 1.14/1.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(z)))))),
% 1.14/1.35 inference(transitivity,[status(thm)],[466, 464])).
% 1.14/1.35 tff(468,plain,
% 1.14/1.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(469,plain,
% 1.14/1.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(z))))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[468, 467])).
% 1.14/1.35 tff(470,plain,
% 1.14/1.35 (~b(s(elem!1), s(s(z)))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[469, 128, 273, 341, 263])).
% 1.14/1.35 tff(471,plain,
% 1.14/1.35 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(z))) | b(s(elem!1), s(s(z))) | r(s(elem!1), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(z))) | b(s(elem!1), s(s(z))) | r(s(elem!1), s(s(z))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(472,plain,
% 1.14/1.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(z))) | b(s(elem!1), s(s(z))) | r(s(elem!1), s(s(z))))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(473,plain,
% 1.14/1.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(z))) | b(s(elem!1), s(s(z))) | r(s(elem!1), s(s(z)))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[472, 471])).
% 1.14/1.35 tff(474,plain,
% 1.14/1.35 (r(s(elem!1), s(s(z)))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[473, 21, 284, 470])).
% 1.14/1.35 tff(475,plain,
% 1.14/1.35 (r(s(s(s(elem!1))), s(s(z)))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[474, 463])).
% 1.14/1.35 tff(476,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(elem!1))) | (~r(elem!1, 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(elem!1, s(elem!1))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(elem!1))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(477,plain,
% 1.14/1.35 (((~r(s(s(z)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(elem!1, s(s(z))))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(elem!1))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(478,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(z)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(elem!1)))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[477])).
% 1.14/1.35 tff(479,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(z)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(elem!1))))),
% 1.14/1.35 inference(transitivity,[status(thm)],[478, 476])).
% 1.14/1.35 tff(480,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(z)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(elem!1, s(s(z)))))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(481,plain,
% 1.14/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(elem!1)))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[480, 479])).
% 1.14/1.35 tff(482,plain,
% 1.14/1.35 (~r(elem!1, s(s(z)))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[481, 45, 359, 353])).
% 1.14/1.35 tff(483,assumption,(~r(elem!1, s(s(z)))), introduced(assumption)).
% 1.14/1.35 tff(484,assumption,(~(s(s(z)) = elem!1)), introduced(assumption)).
% 1.14/1.35 tff(485,assumption,(elem!1 = s(s(z))), introduced(assumption)).
% 1.14/1.35 tff(486,plain,
% 1.14/1.35 (s(s(z)) = elem!1),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[485, 225])).
% 1.14/1.35 tff(487,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[484, 486])).
% 1.14/1.35 tff(488,plain,((~(elem!1 = s(s(z)))) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(489,plain,
% 1.14/1.35 (~(elem!1 = s(s(z)))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[488, 484])).
% 1.14/1.35 tff(490,plain,
% 1.14/1.35 (((~![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))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(491,plain,
% 1.14/1.35 ((~![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))))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(492,plain,
% 1.14/1.35 ((~![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)))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[491, 490])).
% 1.14/1.35 tff(493,plain,
% 1.14/1.35 ((elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z)))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[492, 21])).
% 1.14/1.36 tff(494,plain,
% 1.14/1.36 (b(elem!1, s(s(z)))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[493, 489, 483])).
% 1.14/1.36 tff(495,assumption,(b(z, s(s(z)))), introduced(assumption)).
% 1.14/1.36 tff(496,assumption,(~r(s(s(z)), elem!1)), introduced(assumption)).
% 1.14/1.36 tff(497,plain,
% 1.14/1.36 (b(s(s(z)), elem!1)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[370, 484, 496])).
% 1.14/1.36 tff(498,assumption,(b(z, elem!1)), introduced(assumption)).
% 1.14/1.36 tff(499,plain,
% 1.14/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(500,plain,
% 1.14/1.36 (((~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(z))))) <=> ((~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(501,plain,
% 1.14/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[500])).
% 1.14/1.36 tff(502,plain,
% 1.14/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 1.14/1.36 inference(transitivity,[status(thm)],[501, 499])).
% 1.14/1.36 tff(503,plain,
% 1.14/1.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(z)))))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(504,plain,
% 1.14/1.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[503, 502])).
% 1.14/1.36 tff(505,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[504, 128, 498, 497, 495, 494])).
% 1.14/1.36 tff(506,plain,((s(s(z)) = elem!1) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | r(elem!1, s(s(z))) | r(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(507,plain,
% 1.14/1.36 (~b(z, s(s(z)))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[506, 482, 240, 458, 366])).
% 1.14/1.36 tff(508,plain,
% 1.14/1.36 ((z = s(s(z))) <=> (s(s(z)) = z)),
% 1.14/1.36 inference(commutativity,[status(thm)],[])).
% 1.14/1.36 tff(509,plain,
% 1.14/1.36 ((s(s(z)) = z) <=> (z = s(s(z)))),
% 1.14/1.36 inference(symmetry,[status(thm)],[508])).
% 1.14/1.36 tff(510,plain,
% 1.14/1.36 ((~(s(s(z)) = z)) <=> (~(z = s(s(z))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[509])).
% 1.14/1.36 tff(511,plain,
% 1.14/1.36 (~(z = s(s(z)))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[11, 510])).
% 1.14/1.36 tff(512,plain,
% 1.14/1.36 (((~![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))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(513,plain,
% 1.14/1.36 ((~![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))))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(514,plain,
% 1.14/1.36 ((~![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)))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[513, 512])).
% 1.14/1.36 tff(515,plain,
% 1.14/1.36 ((z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z)))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[514, 21])).
% 1.14/1.36 tff(516,plain,
% 1.14/1.36 (b(z, s(s(z))) | r(z, s(s(z)))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[515, 511])).
% 1.14/1.36 tff(517,plain,
% 1.14/1.36 (r(z, s(s(z)))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[516, 507])).
% 1.14/1.36 tff(518,assumption,(r(s(s(s(elem!1))), s(s(z)))), introduced(assumption)).
% 1.14/1.36 tff(519,assumption,(r(z, s(s(z)))), introduced(assumption)).
% 1.14/1.36 tff(520,assumption,(r(s(s(s(elem!1))), z)), introduced(assumption)).
% 1.14/1.36 tff(521,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, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(522,plain,
% 1.14/1.36 (((~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(523,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, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[522])).
% 1.14/1.36 tff(524,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, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.14/1.36 inference(transitivity,[status(thm)],[523, 521])).
% 1.14/1.36 tff(525,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, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(526,plain,
% 1.14/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z))))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[525, 524])).
% 1.14/1.36 tff(527,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[526, 45, 520, 519, 518])).
% 1.14/1.36 tff(528,plain,((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(529,plain,
% 1.14/1.36 (~r(s(s(s(elem!1))), z)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[528, 517, 475])).
% 1.14/1.36 tff(530,plain,
% 1.14/1.36 (r(z, s(elem!1)) <=> r(z, s(s(s(elem!1))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[354])).
% 1.14/1.36 tff(531,plain,
% 1.14/1.36 ((~r(z, s(elem!1))) <=> (~r(z, s(s(s(elem!1)))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[530])).
% 1.14/1.36 tff(532,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, s(s(z)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(z)))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(533,plain,
% 1.14/1.36 (((~r(s(elem!1), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(z, s(elem!1)))) <=> ((~r(z, s(s(z)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(z)))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(534,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(z)))) | (~r(z, s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(z))))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[533])).
% 1.14/1.36 tff(535,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(z)))) | (~r(z, s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(z)))))),
% 1.14/1.36 inference(transitivity,[status(thm)],[534, 532])).
% 1.14/1.36 tff(536,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(z)))) | (~r(z, s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(z, s(elem!1))))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(537,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, s(s(z)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(z))))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[536, 535])).
% 1.14/1.36 tff(538,plain,
% 1.14/1.36 (~r(z, s(elem!1))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[537, 45, 517, 474])).
% 1.14/1.36 tff(539,plain,
% 1.14/1.36 (~r(z, s(s(s(elem!1))))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[538, 531])).
% 1.14/1.36 tff(540,plain,
% 1.14/1.36 ((z = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = z)),
% 1.14/1.36 inference(commutativity,[status(thm)],[])).
% 1.14/1.36 tff(541,plain,
% 1.14/1.36 ((s(s(s(elem!1))) = z) <=> (z = s(s(s(elem!1))))),
% 1.14/1.36 inference(symmetry,[status(thm)],[540])).
% 1.14/1.36 tff(542,plain,
% 1.14/1.36 ((~(s(s(s(elem!1))) = z)) <=> (~(z = s(s(s(elem!1)))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[541])).
% 1.14/1.36 tff(543,plain,
% 1.14/1.36 (~(z = s(s(s(elem!1))))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[382, 542])).
% 1.14/1.36 tff(544,assumption,(~r(s(s(s(elem!1))), z)), introduced(assumption)).
% 1.14/1.36 tff(545,plain,
% 1.14/1.36 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = z) | b(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = z) | b(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), z))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(546,plain,
% 1.14/1.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = z) | b(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), z))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(547,plain,
% 1.14/1.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = z) | b(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), z)),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[546, 545])).
% 1.14/1.36 tff(548,plain,
% 1.14/1.36 (b(s(s(s(elem!1))), z)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[547, 21, 382, 544])).
% 1.14/1.36 tff(549,assumption,(b(s(z), s(s(s(elem!1))))), introduced(assumption)).
% 1.14/1.36 tff(550,assumption,(b(z, s(z))), introduced(assumption)).
% 1.14/1.36 tff(551,plain,
% 1.14/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(552,plain,
% 1.14/1.36 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(553,plain,
% 1.14/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1)))))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[552])).
% 1.14/1.36 tff(554,plain,
% 1.14/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))),
% 1.14/1.36 inference(transitivity,[status(thm)],[553, 551])).
% 1.14/1.36 tff(555,plain,
% 1.14/1.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(556,plain,
% 1.14/1.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1)))))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[555, 554])).
% 1.14/1.36 tff(557,plain,
% 1.14/1.36 (~b(z, s(s(s(elem!1))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[556, 128, 550, 549, 548])).
% 1.14/1.36 tff(558,assumption,(~r(z, s(s(s(elem!1))))), introduced(assumption)).
% 1.14/1.36 tff(559,plain,
% 1.14/1.36 ((z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[436, 21, 558])).
% 1.14/1.36 tff(560,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[559, 557, 543])).
% 1.14/1.36 tff(561,plain,(r(z, s(s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | r(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(562,plain,
% 1.14/1.36 (~b(z, s(z))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[561, 539, 340, 529])).
% 1.14/1.36 tff(563,plain,
% 1.14/1.36 (r(z, s(z))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[415, 562])).
% 1.14/1.36 tff(564,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, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(565,plain,
% 1.14/1.36 (((~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z))) <=> ((~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(566,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, s(z))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[565])).
% 1.14/1.36 tff(567,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, s(z))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)))),
% 1.14/1.36 inference(transitivity,[status(thm)],[566, 564])).
% 1.14/1.36 tff(568,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, s(z))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z)))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(569,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, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[568, 567])).
% 1.14/1.36 tff(570,plain,
% 1.14/1.36 (~r(elem!1, z)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[569, 45, 306, 563])).
% 1.14/1.36 tff(571,plain,
% 1.14/1.36 (((~![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))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(572,plain,
% 1.14/1.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = z) | b(elem!1, z) | r(elem!1, z))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(573,plain,
% 1.14/1.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = z) | b(elem!1, z) | r(elem!1, z)),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[572, 571])).
% 1.14/1.36 tff(574,plain,
% 1.14/1.36 ((elem!1 = z) | b(elem!1, z) | r(elem!1, z)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[573, 21])).
% 1.14/1.36 tff(575,plain,
% 1.14/1.36 (b(elem!1, z)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[574, 570, 462])).
% 1.14/1.36 tff(576,assumption,(b(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 1.14/1.36 tff(577,assumption,(b(elem!1, z)), introduced(assumption)).
% 1.14/1.36 tff(578,plain,
% 1.14/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), elem!1)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), elem!1)) | (~b(s(s(s(s(z)))), z)))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(579,plain,
% 1.14/1.36 (((~b(z, elem!1)) | (~b(s(s(s(s(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(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(580,plain,
% 1.14/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, z)) | (~b(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(X0, 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)))), elem!1)) | (~b(s(s(s(s(z)))), z))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[579])).
% 1.14/1.36 tff(581,plain,
% 1.14/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, z)) | (~b(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(X0, 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)))), elem!1)) | (~b(s(s(s(s(z)))), z)))),
% 1.14/1.36 inference(transitivity,[status(thm)],[580, 578])).
% 1.14/1.36 tff(582,plain,
% 1.14/1.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(583,plain,
% 1.14/1.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), elem!1)) | (~b(s(s(s(s(z)))), z))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[582, 581])).
% 1.14/1.36 tff(584,plain,
% 1.14/1.36 (~b(s(s(s(s(z)))), z)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[583, 128, 498, 577, 576])).
% 1.14/1.36 tff(585,plain,
% 1.14/1.36 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(z)))) = z))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(586,plain,
% 1.14/1.36 (~(s(s(s(s(z)))) = z)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[585, 9])).
% 1.14/1.36 tff(587,plain,
% 1.14/1.36 (((~![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))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(588,plain,
% 1.14/1.36 ((~![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))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(589,plain,
% 1.14/1.36 ((~![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)),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[588, 587])).
% 1.14/1.36 tff(590,plain,
% 1.14/1.36 (r(s(s(s(s(z)))), z)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[589, 21, 586, 584])).
% 1.14/1.36 tff(591,assumption,(b(s(s(z)), elem!1)), introduced(assumption)).
% 1.14/1.36 tff(592,plain,
% 1.14/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), elem!1)) | (~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(X0, 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)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(593,plain,
% 1.14/1.36 (((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, 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(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(594,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(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(X0, 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)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[593])).
% 1.14/1.37 tff(595,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(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(X0, 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)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 1.14/1.37 inference(transitivity,[status(thm)],[594, 592])).
% 1.14/1.37 tff(596,plain,
% 1.14/1.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(597,plain,
% 1.14/1.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[596, 595])).
% 1.14/1.37 tff(598,plain,
% 1.14/1.37 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[597, 128, 498, 577, 591, 576])).
% 1.14/1.37 tff(599,assumption,(s(s(z)) = s(s(s(s(z))))), introduced(assumption)).
% 1.14/1.37 tff(600,plain,
% 1.14/1.37 (inj_0(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[599])).
% 1.14/1.37 tff(601,plain,
% 1.14/1.37 (s(z) = s(s(s(z)))),
% 1.14/1.37 inference(transitivity,[status(thm)],[70, 600, 217])).
% 1.14/1.37 tff(602,plain,
% 1.14/1.37 (inj_0(s(z)) = inj_0(s(s(s(z))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[601])).
% 1.14/1.37 tff(603,plain,
% 1.14/1.37 (inj_0(s(s(s(z)))) = inj_0(s(z))),
% 1.14/1.37 inference(symmetry,[status(thm)],[602])).
% 1.14/1.37 tff(604,plain,
% 1.14/1.37 (s(s(s(s(z)))) = s(s(z))),
% 1.14/1.37 inference(symmetry,[status(thm)],[599])).
% 1.14/1.37 tff(605,plain,
% 1.14/1.37 (s(s(s(s(z)))) = z),
% 1.14/1.37 inference(transitivity,[status(thm)],[604, 223, 603, 64])).
% 1.14/1.37 tff(606,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[586, 605])).
% 1.14/1.37 tff(607,plain,(~(s(s(z)) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(608,plain,
% 1.14/1.37 (((~![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))))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(609,plain,
% 1.14/1.37 ((~![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))))))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(610,plain,
% 1.14/1.37 ((~![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)))))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[609, 608])).
% 1.14/1.37 tff(611,plain,
% 1.14/1.37 (r(s(s(z)), s(s(s(s(z)))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[610, 21, 607, 598])).
% 1.14/1.37 tff(612,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z)), elem!1)))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(613,plain,
% 1.14/1.37 (((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(614,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z)) | (~b(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(X0, 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(z)), elem!1))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[613])).
% 1.14/1.37 tff(615,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z)) | (~b(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(X0, 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(z)), elem!1)))),
% 1.14/1.37 inference(transitivity,[status(thm)],[614, 612])).
% 1.14/1.37 tff(616,plain,
% 1.14/1.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(617,plain,
% 1.14/1.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z)), elem!1))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[616, 615])).
% 1.14/1.37 tff(618,plain,
% 1.14/1.37 (~b(s(s(z)), z)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[617, 128, 498, 577, 591])).
% 1.14/1.37 tff(619,plain,
% 1.14/1.37 (r(s(s(z)), z)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[25, 618])).
% 1.14/1.37 tff(620,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(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(621,plain,
% 1.14/1.37 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(622,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(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[621])).
% 1.14/1.37 tff(623,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(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.14/1.37 inference(transitivity,[status(thm)],[622, 620])).
% 1.14/1.37 tff(624,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(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)))))))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(625,plain,
% 1.14/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[624, 623])).
% 1.14/1.37 tff(626,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[625, 45, 619, 611, 590])).
% 1.14/1.37 tff(627,plain,((~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(628,plain,
% 1.14/1.37 (~b(s(s(s(s(z)))), elem!1)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[627, 575, 458, 371])).
% 1.14/1.37 tff(629,plain,
% 1.14/1.37 (((~![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))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(630,plain,
% 1.14/1.37 ((~![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))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(631,plain,
% 1.14/1.37 ((~![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)),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[630, 629])).
% 1.14/1.37 tff(632,plain,
% 1.14/1.37 ((s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[631, 21])).
% 1.14/1.37 tff(633,plain,
% 1.14/1.37 (r(s(s(s(s(z)))), elem!1)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[632, 628, 243])).
% 1.14/1.37 tff(634,assumption,(r(s(z), s(s(z)))), introduced(assumption)).
% 1.14/1.37 tff(635,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(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)))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(636,plain,
% 1.14/1.37 (((~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)))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(637,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(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))))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[636])).
% 1.14/1.37 tff(638,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(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)))))),
% 1.14/1.37 inference(transitivity,[status(thm)],[637, 635])).
% 1.14/1.37 tff(639,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(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), z)))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(640,plain,
% 1.14/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z))))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[639, 638])).
% 1.14/1.37 tff(641,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[640, 45, 272, 519, 634])).
% 1.14/1.37 tff(642,plain,((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(643,plain,
% 1.14/1.37 (~r(s(z), s(s(z)))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[642, 517, 272])).
% 1.14/1.37 tff(644,plain,
% 1.14/1.37 (((~![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))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(645,plain,
% 1.14/1.37 ((~![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))))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(646,plain,
% 1.14/1.37 ((~![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)))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[645, 644])).
% 1.14/1.37 tff(647,plain,
% 1.14/1.37 ((s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z)))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[646, 21])).
% 1.14/1.37 tff(648,plain,
% 1.14/1.37 (b(s(z), s(s(z))) | r(s(z), s(s(z)))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[647, 74])).
% 1.14/1.37 tff(649,plain,
% 1.14/1.37 (b(s(z), s(s(z)))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[648, 643])).
% 1.14/1.37 tff(650,plain,
% 1.14/1.37 ((s(s(z)) = elem!1) <=> (elem!1 = s(s(z)))),
% 1.14/1.37 inference(symmetry,[status(thm)],[225])).
% 1.14/1.37 tff(651,plain,
% 1.14/1.37 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 1.14/1.37 inference(transitivity,[status(thm)],[230, 650])).
% 1.14/1.37 tff(652,plain,
% 1.14/1.37 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(elem!1 = s(s(z))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[651])).
% 1.14/1.37 tff(653,plain,
% 1.14/1.37 (~(elem!1 = s(s(z)))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[239, 652])).
% 1.14/1.37 tff(654,plain,
% 1.14/1.37 (b(elem!1, s(s(z)))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[493, 482, 653])).
% 1.14/1.37 tff(655,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(656,plain,
% 1.14/1.37 (((~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(657,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[656])).
% 1.14/1.37 tff(658,plain,
% 1.14/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 1.14/1.37 inference(transitivity,[status(thm)],[657, 655])).
% 1.14/1.37 tff(659,plain,
% 1.14/1.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1)))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(660,plain,
% 1.14/1.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[659, 658])).
% 1.14/1.37 tff(661,plain,
% 1.14/1.37 (~b(s(z), elem!1)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[660, 128, 371, 654, 649])).
% 1.14/1.37 tff(662,plain,
% 1.14/1.37 (((~![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))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(663,plain,
% 1.14/1.37 ((~![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))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(664,plain,
% 1.14/1.37 ((~![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)),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[663, 662])).
% 1.14/1.37 tff(665,plain,
% 1.14/1.37 ((s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[664, 21])).
% 1.14/1.37 tff(666,plain,
% 1.14/1.37 (r(s(z), elem!1)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[665, 661, 257])).
% 1.14/1.37 tff(667,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(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(668,plain,
% 1.14/1.37 (((~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(669,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(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z))))))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[668])).
% 1.14/1.37 tff(670,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(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))))),
% 1.14/1.37 inference(transitivity,[status(thm)],[669, 667])).
% 1.14/1.37 tff(671,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(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(672,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(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z))))))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[671, 670])).
% 1.14/1.37 tff(673,plain,
% 1.14/1.37 (~r(s(z), s(s(s(s(z)))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[672, 45, 666, 633])).
% 1.14/1.37 tff(674,assumption,(s(z) = s(s(s(s(z))))), introduced(assumption)).
% 1.14/1.37 tff(675,plain,
% 1.14/1.37 (inj_0(s(z)) = inj_0(s(s(s(s(z)))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[674])).
% 1.14/1.37 tff(676,plain,
% 1.14/1.37 (inj_0(s(s(s(s(z))))) = inj_0(s(z))),
% 1.14/1.37 inference(symmetry,[status(thm)],[675])).
% 1.14/1.37 tff(677,plain,
% 1.14/1.37 (s(s(s(z))) = z),
% 1.14/1.37 inference(transitivity,[status(thm)],[218, 676, 64])).
% 1.14/1.37 tff(678,plain,
% 1.14/1.37 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(z))) = z))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(679,plain,
% 1.14/1.37 (~(s(s(s(z))) = z)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[678, 9])).
% 1.14/1.37 tff(680,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[679, 677])).
% 1.14/1.37 tff(681,plain,(~(s(z) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(682,plain,
% 1.14/1.37 (((~![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))))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(683,plain,
% 1.14/1.37 ((~![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))))))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(684,plain,
% 1.14/1.37 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[683, 682])).
% 1.14/1.37 tff(685,plain,
% 1.14/1.37 (b(s(z), s(s(s(s(z)))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[684, 21, 681, 673])).
% 1.14/1.37 tff(686,plain,
% 1.14/1.37 (r(s(elem!1), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 1.14/1.37 inference(monotonicity,[status(thm)],[354])).
% 1.14/1.37 tff(687,plain,
% 1.14/1.37 (r(s(s(s(elem!1))), elem!1) <=> r(s(elem!1), elem!1)),
% 1.14/1.37 inference(symmetry,[status(thm)],[686])).
% 1.14/1.37 tff(688,assumption,(s(s(s(elem!1))) = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.14/1.37 tff(689,plain,
% 1.14/1.37 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(elem!1)))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[688])).
% 1.14/1.37 tff(690,plain,
% 1.14/1.37 (s(s(elem!1)) = s(s(s(elem!1)))),
% 1.14/1.37 inference(transitivity,[status(thm)],[187, 689, 233])).
% 1.14/1.37 tff(691,assumption,(~(s(s(elem!1)) = s(s(s(elem!1))))), introduced(assumption)).
% 1.14/1.37 tff(692,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[691, 690])).
% 1.14/1.37 tff(693,plain,((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(694,plain,
% 1.14/1.37 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[693, 317])).
% 1.14/1.37 tff(695,plain,
% 1.14/1.37 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.14/1.37 inference(commutativity,[status(thm)],[])).
% 1.14/1.37 tff(696,assumption,(s(s(s(s(elem!1)))) = s(s(s(elem!1)))), introduced(assumption)).
% 1.14/1.37 tff(697,plain,
% 1.14/1.37 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[696, 695])).
% 1.14/1.37 tff(698,assumption,(~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.14/1.37 tff(699,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[698, 697])).
% 1.14/1.37 tff(700,plain,((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(701,plain,
% 1.14/1.37 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[700, 694])).
% 1.14/1.37 tff(702,plain,
% 1.14/1.37 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.14/1.37 inference(symmetry,[status(thm)],[695])).
% 1.14/1.37 tff(703,plain,
% 1.14/1.37 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[226])).
% 1.14/1.37 tff(704,plain,
% 1.14/1.37 ((s(elem!1) = s(s(s(s(elem!1))))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.14/1.37 inference(symmetry,[status(thm)],[703])).
% 1.14/1.37 tff(705,plain,
% 1.14/1.37 ((s(s(s(elem!1))) = elem!1) <=> (elem!1 = s(s(s(elem!1))))),
% 1.14/1.37 inference(commutativity,[status(thm)],[])).
% 1.14/1.37 tff(706,plain,
% 1.14/1.37 ((s(elem!1) = s(s(s(s(elem!1))))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.14/1.37 inference(monotonicity,[status(thm)],[354, 228])).
% 1.14/1.37 tff(707,plain,
% 1.14/1.37 ((s(elem!1) = s(s(s(s(elem!1))))) <=> (elem!1 = s(s(s(elem!1))))),
% 1.14/1.37 inference(transitivity,[status(thm)],[706, 705])).
% 1.14/1.37 tff(708,plain,
% 1.14/1.37 ((elem!1 = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 1.14/1.37 inference(symmetry,[status(thm)],[707])).
% 1.14/1.37 tff(709,plain,
% 1.14/1.37 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.14/1.37 inference(transitivity,[status(thm)],[705, 708, 704, 702])).
% 1.14/1.37 tff(710,assumption,(s(s(s(elem!1))) = elem!1), introduced(assumption)).
% 1.14/1.37 tff(711,plain,
% 1.14/1.37 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[710, 709])).
% 1.14/1.37 tff(712,assumption,(~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))), introduced(assumption)).
% 1.14/1.37 tff(713,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[712, 711])).
% 1.14/1.37 tff(714,plain,((~(s(s(s(elem!1))) = elem!1)) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(715,plain,
% 1.14/1.37 (~(s(s(s(elem!1))) = elem!1)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[714, 701, 199])).
% 1.14/1.37 tff(716,plain,
% 1.14/1.37 (b(s(s(s(elem!1))), elem!1) <=> b(s(elem!1), elem!1)),
% 1.14/1.37 inference(monotonicity,[status(thm)],[226])).
% 1.14/1.37 tff(717,plain,
% 1.14/1.37 (b(s(elem!1), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 1.14/1.37 inference(symmetry,[status(thm)],[716])).
% 1.14/1.37 tff(718,plain,
% 1.14/1.37 ((~b(s(elem!1), elem!1)) <=> (~b(s(s(s(elem!1))), elem!1))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[717])).
% 1.14/1.37 tff(719,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(z, s(s(z)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(z)))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(720,plain,
% 1.14/1.37 (((~r(z, s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(elem!1), z))) <=> ((~r(z, s(s(z)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(z)))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(721,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(z, s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(z, 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(z, s(s(z)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(z))))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[720])).
% 1.14/1.37 tff(722,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(z, s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(z, 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(z, s(s(z)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(z)))))),
% 1.14/1.38 inference(transitivity,[status(thm)],[721, 719])).
% 1.14/1.38 tff(723,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(z, s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(elem!1), z)))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(724,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(z, s(s(z)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(z))))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[723, 722])).
% 1.14/1.38 tff(725,plain,
% 1.14/1.38 (~r(s(elem!1), z)),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[724, 45, 517, 474])).
% 1.14/1.38 tff(726,plain,
% 1.14/1.38 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = z) | b(s(elem!1), z) | r(s(elem!1), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = z) | b(s(elem!1), z) | r(s(elem!1), z))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(727,plain,
% 1.14/1.38 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = z) | b(s(elem!1), z) | r(s(elem!1), z))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(728,plain,
% 1.14/1.38 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = z) | b(s(elem!1), z) | r(s(elem!1), z)),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[727, 726])).
% 1.14/1.38 tff(729,plain,
% 1.14/1.38 (b(s(elem!1), z)),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[728, 21, 109, 725])).
% 1.14/1.38 tff(730,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(731,plain,
% 1.14/1.38 (((~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(732,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z))))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[731])).
% 1.14/1.38 tff(733,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))))),
% 1.14/1.38 inference(transitivity,[status(thm)],[732, 730])).
% 1.14/1.38 tff(734,plain,
% 1.14/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(735,plain,
% 1.14/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z))))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[734, 733])).
% 1.14/1.38 tff(736,plain,
% 1.14/1.38 ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[735, 128, 458, 654, 273, 263])).
% 1.14/1.38 tff(737,plain,
% 1.14/1.38 (~b(s(elem!1), elem!1)),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[736, 729])).
% 1.14/1.38 tff(738,plain,
% 1.14/1.38 (~b(s(s(s(elem!1))), elem!1)),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[737, 718])).
% 1.14/1.38 tff(739,plain,
% 1.14/1.38 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(740,plain,
% 1.14/1.38 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(741,plain,
% 1.14/1.38 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1)),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[740, 739])).
% 1.14/1.38 tff(742,plain,
% 1.14/1.38 ((s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1)),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[741, 21])).
% 1.14/1.38 tff(743,plain,
% 1.14/1.38 (r(s(s(s(elem!1))), elem!1)),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[742, 738, 715])).
% 1.14/1.38 tff(744,plain,
% 1.14/1.38 (r(s(elem!1), elem!1)),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[743, 687])).
% 1.14/1.38 tff(745,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), 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(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(746,plain,
% 1.14/1.38 (((~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(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(747,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)))), 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(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[746])).
% 1.14/1.38 tff(748,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)))), 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(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.14/1.38 inference(transitivity,[status(thm)],[747, 745])).
% 1.14/1.38 tff(749,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)))), 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)))))))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(750,plain,
% 1.14/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), s(s(s(s(z))))))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[749, 748])).
% 1.14/1.38 tff(751,plain,
% 1.14/1.38 (~r(s(elem!1), s(s(s(s(z)))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[750, 45, 633, 744])).
% 1.14/1.38 tff(752,assumption,(s(elem!1) = s(s(s(s(z))))), introduced(assumption)).
% 1.14/1.38 tff(753,plain,
% 1.14/1.38 (s(s(s(s(z)))) = s(elem!1)),
% 1.14/1.38 inference(symmetry,[status(thm)],[752])).
% 1.14/1.38 tff(754,plain,
% 1.14/1.38 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[753])).
% 1.14/1.38 tff(755,plain,
% 1.14/1.38 (s(s(s(z))) = s(s(elem!1))),
% 1.14/1.38 inference(transitivity,[status(thm)],[218, 754, 201, 202])).
% 1.14/1.38 tff(756,plain,
% 1.14/1.38 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[755])).
% 1.14/1.38 tff(757,plain,
% 1.14/1.38 (inj_0(s(s(elem!1))) = inj_0(s(s(s(z))))),
% 1.14/1.38 inference(symmetry,[status(thm)],[756])).
% 1.14/1.38 tff(758,plain,
% 1.14/1.38 (s(elem!1) = s(s(z))),
% 1.14/1.38 inference(transitivity,[status(thm)],[106, 757, 222])).
% 1.14/1.38 tff(759,assumption,(~(s(elem!1) = s(s(z)))), introduced(assumption)).
% 1.14/1.38 tff(760,plain,
% 1.14/1.38 ($false),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[759, 758])).
% 1.14/1.38 tff(761,plain,((~(s(elem!1) = s(s(s(s(z)))))) | (s(elem!1) = s(s(z))) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.38 tff(762,plain,
% 1.14/1.38 (~(s(elem!1) = s(s(s(s(z)))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[761, 284, 199])).
% 1.14/1.38 tff(763,plain,
% 1.14/1.38 (((~![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))))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(764,plain,
% 1.14/1.38 ((~![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))))))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(765,plain,
% 1.14/1.38 ((~![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)))))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[764, 763])).
% 1.14/1.38 tff(766,plain,
% 1.14/1.38 (b(s(elem!1), s(s(s(s(z)))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[765, 21, 762, 751])).
% 1.14/1.38 tff(767,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(z), elem!1)) | (~r(s(z), z)) | (~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(z), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(768,plain,
% 1.14/1.38 (((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(769,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(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z)))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[768])).
% 1.14/1.38 tff(770,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(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.14/1.38 inference(transitivity,[status(thm)],[769, 767])).
% 1.14/1.38 tff(771,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(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(772,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(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z)))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[771, 770])).
% 1.14/1.38 tff(773,plain,
% 1.14/1.38 (~r(s(s(s(s(z)))), s(z))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[772, 45, 272, 666, 633])).
% 1.14/1.38 tff(774,assumption,(~b(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.14/1.38 tff(775,assumption,(~r(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.14/1.38 tff(776,plain,
% 1.14/1.38 ((s(s(s(s(z)))) = s(z)) <=> (s(z) = s(s(s(s(z)))))),
% 1.14/1.38 inference(commutativity,[status(thm)],[])).
% 1.14/1.38 tff(777,plain,
% 1.14/1.38 ((s(z) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(z))),
% 1.14/1.38 inference(symmetry,[status(thm)],[776])).
% 1.14/1.38 tff(778,plain,
% 1.14/1.38 ((~(s(z) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(z)))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[777])).
% 1.14/1.38 tff(779,plain,
% 1.14/1.38 (~(s(s(s(s(z)))) = s(z))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[681, 778])).
% 1.14/1.38 tff(780,plain,
% 1.14/1.38 (((~![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)))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(781,plain,
% 1.14/1.38 ((~![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)))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(782,plain,
% 1.14/1.38 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[781, 780])).
% 1.14/1.38 tff(783,plain,
% 1.14/1.38 ($false),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[782, 21, 779, 775, 774])).
% 1.14/1.38 tff(784,plain,(b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.38 tff(785,plain,
% 1.14/1.38 (b(s(s(s(s(z)))), s(z))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[784, 773])).
% 1.14/1.38 tff(786,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(787,plain,
% 1.14/1.38 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(elem!1)))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(788,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[787])).
% 1.14/1.38 tff(789,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.14/1.38 inference(transitivity,[status(thm)],[788, 786])).
% 1.14/1.38 tff(790,plain,
% 1.14/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(elem!1))))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(791,plain,
% 1.14/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[790, 789])).
% 1.14/1.38 tff(792,plain,
% 1.14/1.38 ($false),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[791, 128, 649, 341, 785, 766, 685])).
% 1.14/1.38 tff(793,plain,(b(s(s(elem!1)), s(z)) | (~r(s(z), z)) | (~(s(s(elem!1)) = elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(elem!1), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.38 tff(794,plain,
% 1.14/1.38 (b(s(s(elem!1)), s(z))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[793, 273, 199, 272, 263, 198, 271])).
% 1.14/1.38 tff(795,plain,
% 1.14/1.38 (b(elem!1, s(z))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[794, 270])).
% 1.14/1.38 tff(796,plain,
% 1.14/1.38 (r(z, s(s(elem!1))) <=> r(z, elem!1)),
% 1.14/1.38 inference(monotonicity,[status(thm)],[199])).
% 1.14/1.38 tff(797,plain,
% 1.14/1.38 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(elem!1))), elem!1)),
% 1.14/1.38 inference(monotonicity,[status(thm)],[199])).
% 1.14/1.38 tff(798,plain,
% 1.14/1.38 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(elem!1), elem!1)),
% 1.14/1.38 inference(transitivity,[status(thm)],[797, 687])).
% 1.14/1.38 tff(799,plain,
% 1.14/1.38 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 1.14/1.38 inference(commutativity,[status(thm)],[])).
% 1.14/1.38 tff(800,assumption,(s(s(s(elem!1))) = s(s(elem!1))), introduced(assumption)).
% 1.14/1.38 tff(801,plain,
% 1.14/1.38 (s(s(elem!1)) = s(s(s(elem!1)))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[800, 799])).
% 1.14/1.38 tff(802,plain,
% 1.14/1.38 ($false),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[691, 801])).
% 1.14/1.38 tff(803,plain,((~(s(s(s(elem!1))) = s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.38 tff(804,plain,
% 1.14/1.38 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[803, 691])).
% 1.14/1.38 tff(805,plain,
% 1.14/1.38 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(elem!1))))),
% 1.14/1.38 inference(symmetry,[status(thm)],[286])).
% 1.14/1.38 tff(806,plain,
% 1.14/1.38 ((~b(s(z), s(elem!1))) <=> (~b(s(z), s(s(s(elem!1)))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[805])).
% 1.14/1.38 tff(807,plain,
% 1.14/1.38 (b(elem!1, s(z))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[30, 270])).
% 1.14/1.38 tff(808,plain,
% 1.14/1.38 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[693, 691])).
% 1.14/1.38 tff(809,plain,
% 1.14/1.38 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[700, 808])).
% 1.14/1.38 tff(810,plain,
% 1.14/1.38 (~(s(s(s(elem!1))) = elem!1)),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[714, 809, 199])).
% 1.14/1.38 tff(811,plain,
% 1.14/1.38 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[321, 691, 198])).
% 1.14/1.38 tff(812,plain,
% 1.14/1.38 (r(elem!1, s(elem!1))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[811, 358])).
% 1.14/1.38 tff(813,assumption,(b(s(z), s(elem!1))), introduced(assumption)).
% 1.14/1.38 tff(814,plain,
% 1.14/1.38 (~b(s(elem!1), s(s(z)))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[469, 128, 273, 813, 263])).
% 1.14/1.38 tff(815,plain,
% 1.14/1.38 (r(s(elem!1), s(s(z)))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[473, 21, 284, 814])).
% 1.14/1.38 tff(816,assumption,(r(elem!1, s(elem!1))), introduced(assumption)).
% 1.14/1.38 tff(817,assumption,(~(s(s(s(elem!1))) = elem!1)), introduced(assumption)).
% 1.14/1.38 tff(818,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(819,plain,
% 1.14/1.38 (((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(820,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1)))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[819])).
% 1.14/1.38 tff(821,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))))),
% 1.14/1.38 inference(transitivity,[status(thm)],[820, 818])).
% 1.14/1.38 tff(822,plain,
% 1.14/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), elem!1)))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(823,plain,
% 1.14/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1)))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[822, 821])).
% 1.14/1.38 tff(824,plain,
% 1.14/1.38 (~b(s(elem!1), elem!1)),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[823, 128, 297, 813, 263])).
% 1.14/1.38 tff(825,plain,
% 1.14/1.38 (~b(s(s(s(elem!1))), elem!1)),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[824, 718])).
% 1.14/1.38 tff(826,plain,
% 1.14/1.38 (r(s(s(s(elem!1))), elem!1)),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[742, 825, 817])).
% 1.14/1.38 tff(827,plain,
% 1.14/1.38 (r(s(elem!1), elem!1)),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[826, 687])).
% 1.14/1.38 tff(828,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(elem!1))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(829,plain,
% 1.14/1.38 (((~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z))))) <=> ((~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(elem!1))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(830,plain,
% 1.14/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(elem!1)))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[829])).
% 1.14/1.39 tff(831,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(elem!1))))),
% 1.14/1.39 inference(transitivity,[status(thm)],[830, 828])).
% 1.14/1.39 tff(832,plain,
% 1.14/1.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(833,plain,
% 1.14/1.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(elem!1)))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[832, 831])).
% 1.14/1.39 tff(834,plain,
% 1.14/1.39 (~b(elem!1, s(s(z)))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[833, 128, 297, 273, 813, 263])).
% 1.14/1.39 tff(835,plain,
% 1.14/1.39 (r(elem!1, s(s(z)))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[493, 834, 653])).
% 1.14/1.39 tff(836,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, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), s(s(z)))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(837,plain,
% 1.14/1.39 (((~r(s(elem!1), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), s(s(z)))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(838,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(elem!1), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), s(s(z))))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[837])).
% 1.14/1.39 tff(839,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(elem!1), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), s(s(z)))))),
% 1.14/1.39 inference(transitivity,[status(thm)],[838, 836])).
% 1.14/1.39 tff(840,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(elem!1), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(841,plain,
% 1.14/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), s(s(z))))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[840, 839])).
% 1.14/1.39 tff(842,plain,
% 1.14/1.39 ($false),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[841, 45, 835, 827, 816, 815])).
% 1.14/1.39 tff(843,plain,((~b(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~(s(s(elem!1)) = elem!1)) | (s(s(s(elem!1))) = elem!1) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.39 tff(844,plain,
% 1.14/1.39 (~b(s(z), s(elem!1))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[843, 812, 199, 810, 273, 263, 807])).
% 1.14/1.39 tff(845,plain,
% 1.14/1.39 (~b(s(z), s(s(s(elem!1))))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[844, 806])).
% 1.14/1.39 tff(846,plain,
% 1.14/1.39 (r(s(z), s(s(s(elem!1))))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[339, 845])).
% 1.14/1.39 tff(847,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), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(848,plain,
% 1.14/1.39 (((~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(849,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(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[848])).
% 1.14/1.39 tff(850,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(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.14/1.39 inference(transitivity,[status(thm)],[849, 847])).
% 1.14/1.39 tff(851,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(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(852,plain,
% 1.14/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[851, 850])).
% 1.14/1.39 tff(853,plain,
% 1.14/1.39 ($false),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[852, 45, 272, 323, 424])).
% 1.14/1.39 tff(854,plain,((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.39 tff(855,plain,
% 1.14/1.39 (~r(z, s(s(s(elem!1))))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[854, 846, 272])).
% 1.14/1.39 tff(856,assumption,(~b(z, s(s(s(elem!1))))), introduced(assumption)).
% 1.14/1.39 tff(857,plain,
% 1.14/1.39 ($false),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[436, 21, 558, 856, 384])).
% 1.14/1.39 tff(858,plain,(r(z, s(s(s(elem!1)))) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.39 tff(859,plain,
% 1.14/1.39 (b(z, s(s(s(elem!1))))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[858, 855])).
% 1.14/1.39 tff(860,plain,
% 1.14/1.39 (b(s(z), s(s(elem!1))) <=> b(s(z), elem!1)),
% 1.14/1.39 inference(monotonicity,[status(thm)],[199])).
% 1.14/1.39 tff(861,plain,
% 1.14/1.39 (b(s(z), elem!1) <=> b(s(z), s(s(elem!1)))),
% 1.14/1.39 inference(symmetry,[status(thm)],[860])).
% 1.14/1.39 tff(862,plain,
% 1.14/1.39 (r(s(z), s(elem!1)) <=> r(s(z), s(s(s(elem!1))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[354])).
% 1.14/1.39 tff(863,plain,
% 1.14/1.39 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(elem!1))),
% 1.14/1.39 inference(symmetry,[status(thm)],[862])).
% 1.14/1.39 tff(864,plain,
% 1.14/1.39 (r(s(z), s(elem!1))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[846, 863])).
% 1.14/1.39 tff(865,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), elem!1)) | (~r(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(z), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(866,plain,
% 1.14/1.39 (((~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1))) <=> ((~r(s(z), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(867,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, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1)))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[866])).
% 1.14/1.39 tff(868,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, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))))),
% 1.14/1.39 inference(transitivity,[status(thm)],[867, 865])).
% 1.14/1.39 tff(869,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, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(870,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), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1)))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[869, 868])).
% 1.14/1.39 tff(871,plain,
% 1.14/1.39 (~r(s(z), elem!1)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[870, 45, 812, 864])).
% 1.14/1.39 tff(872,plain,
% 1.14/1.39 (b(s(z), elem!1)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[665, 871, 257])).
% 1.14/1.39 tff(873,plain,
% 1.14/1.39 (b(s(z), s(s(elem!1)))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[872, 861])).
% 1.14/1.39 tff(874,assumption,(b(z, s(s(s(elem!1))))), introduced(assumption)).
% 1.14/1.39 tff(875,assumption,(b(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 1.14/1.39 tff(876,assumption,(b(s(z), s(s(elem!1)))), introduced(assumption)).
% 1.14/1.39 tff(877,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(878,plain,
% 1.14/1.39 (((~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(879,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[878])).
% 1.14/1.39 tff(880,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 1.14/1.39 inference(transitivity,[status(thm)],[879, 877])).
% 1.14/1.39 tff(881,plain,
% 1.14/1.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(882,plain,
% 1.14/1.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[881, 880])).
% 1.14/1.39 tff(883,plain,
% 1.14/1.39 ($false),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[882, 128, 30, 453, 876, 875, 874])).
% 1.14/1.39 tff(884,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.39 tff(885,plain,
% 1.14/1.39 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[884, 873, 859, 453, 30])).
% 1.14/1.39 tff(886,plain,
% 1.14/1.39 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(887,plain,
% 1.14/1.39 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(888,plain,
% 1.14/1.39 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[887, 886])).
% 1.14/1.39 tff(889,plain,
% 1.14/1.39 ((s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[888, 21])).
% 1.14/1.39 tff(890,plain,
% 1.14/1.39 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[889, 885, 804])).
% 1.14/1.39 tff(891,plain,
% 1.14/1.39 (r(s(elem!1), elem!1)),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[890, 798])).
% 1.14/1.39 tff(892,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)), elem!1)))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(893,plain,
% 1.14/1.39 (((~b(elem!1, s(z))) | (~b(s(s(z)), 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)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(894,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(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(X0, 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(s(z)), elem!1))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[893])).
% 1.14/1.39 tff(895,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(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(X0, 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(s(z)), elem!1)))),
% 1.14/1.39 inference(transitivity,[status(thm)],[894, 892])).
% 1.14/1.39 tff(896,plain,
% 1.14/1.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(897,plain,
% 1.14/1.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)), elem!1))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[896, 895])).
% 1.14/1.39 tff(898,plain,
% 1.14/1.39 (~b(s(s(z)), elem!1)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[897, 128, 807, 872, 273])).
% 1.14/1.39 tff(899,plain,
% 1.14/1.39 (r(s(s(z)), elem!1)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[370, 898, 240])).
% 1.14/1.39 tff(900,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(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), s(s(z)))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(901,plain,
% 1.14/1.39 (((~r(s(s(z)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), s(s(z))))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), s(s(z)))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(902,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(z)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), s(s(z))))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[901])).
% 1.14/1.39 tff(903,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(z)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), s(s(z)))))),
% 1.14/1.39 inference(transitivity,[status(thm)],[902, 900])).
% 1.14/1.39 tff(904,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(z)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), s(s(z)))))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(905,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(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), s(s(z))))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[904, 903])).
% 1.14/1.39 tff(906,plain,
% 1.14/1.39 (~r(s(elem!1), s(s(z)))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[905, 45, 899, 891])).
% 1.14/1.39 tff(907,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(908,plain,
% 1.14/1.39 (((~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(909,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z))))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[908])).
% 1.14/1.39 tff(910,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))))),
% 1.14/1.39 inference(transitivity,[status(thm)],[909, 907])).
% 1.14/1.39 tff(911,plain,
% 1.14/1.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(912,plain,
% 1.14/1.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z))))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[911, 910])).
% 1.14/1.39 tff(913,plain,
% 1.14/1.39 (~b(s(elem!1), s(s(z)))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[912, 128, 807, 872, 273, 263])).
% 1.14/1.39 tff(914,plain,
% 1.14/1.39 ($false),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[473, 21, 284, 913, 906])).
% 1.14/1.39 tff(915,plain,((s(s(elem!1)) = s(s(s(elem!1)))) | (~(s(s(elem!1)) = elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~r(s(z), z)) | b(s(s(elem!1)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.39 tff(916,plain,
% 1.14/1.39 (s(s(elem!1)) = s(s(s(elem!1)))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[915, 453, 199, 30, 273, 263, 272, 198])).
% 1.14/1.39 tff(917,plain,
% 1.14/1.39 (b(z, elem!1)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[457, 453, 378])).
% 1.14/1.39 tff(918,plain,
% 1.14/1.39 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 1.14/1.39 inference(commutativity,[status(thm)],[])).
% 1.14/1.39 tff(919,plain,
% 1.14/1.39 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 1.14/1.39 inference(symmetry,[status(thm)],[918])).
% 1.14/1.39 tff(920,plain,
% 1.14/1.39 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(z))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[919])).
% 1.14/1.39 tff(921,plain,
% 1.14/1.39 (~(s(s(s(s(z)))) = s(s(z)))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[607, 920])).
% 1.14/1.39 tff(922,assumption,(b(s(z), elem!1)), introduced(assumption)).
% 1.14/1.39 tff(923,plain,
% 1.14/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(X0, 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)))))))),
% 1.14/1.40 inference(rewrite,[status(thm)],[])).
% 1.14/1.40 tff(924,plain,
% 1.14/1.40 (((~b(s(z), elem!1)) | (~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)))))))),
% 1.14/1.40 inference(rewrite,[status(thm)],[])).
% 1.14/1.40 tff(925,plain,
% 1.14/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~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(X0, 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))))))))),
% 1.14/1.40 inference(monotonicity,[status(thm)],[924])).
% 1.14/1.40 tff(926,plain,
% 1.14/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~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(X0, 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)))))))),
% 1.14/1.40 inference(transitivity,[status(thm)],[925, 923])).
% 1.14/1.40 tff(927,plain,
% 1.14/1.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~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)))))))),
% 1.14/1.40 inference(quant_inst,[status(thm)],[])).
% 1.14/1.40 tff(928,plain,
% 1.14/1.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))))))),
% 1.14/1.40 inference(modus_ponens,[status(thm)],[927, 926])).
% 1.14/1.40 tff(929,plain,
% 1.14/1.40 (~b(s(z), s(s(s(s(z)))))),
% 1.14/1.40 inference(unit_resolution,[status(thm)],[928, 128, 297, 922, 576])).
% 1.14/1.40 tff(930,plain,
% 1.14/1.40 (r(s(z), s(s(s(s(z)))))),
% 1.14/1.40 inference(unit_resolution,[status(thm)],[684, 21, 681, 929])).
% 1.14/1.40 tff(931,plain,
% 1.14/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, 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(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))),
% 1.14/1.40 inference(rewrite,[status(thm)],[])).
% 1.14/1.40 tff(932,plain,
% 1.14/1.40 (((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))),
% 1.14/1.40 inference(rewrite,[status(thm)],[])).
% 1.14/1.40 tff(933,plain,
% 1.14/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, 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(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[932])).
% 1.24/1.40 tff(934,plain,
% 1.24/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, 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(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))),
% 1.24/1.40 inference(transitivity,[status(thm)],[933, 931])).
% 1.24/1.40 tff(935,plain,
% 1.24/1.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(936,plain,
% 1.24/1.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[935, 934])).
% 1.24/1.40 tff(937,plain,
% 1.24/1.40 (~b(s(s(s(s(z)))), z)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[936, 128, 498, 297, 922, 576])).
% 1.24/1.40 tff(938,plain,
% 1.24/1.40 (r(s(s(s(s(z)))), z)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[589, 21, 586, 937])).
% 1.24/1.40 tff(939,assumption,(r(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.24/1.40 tff(940,assumption,(r(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 1.24/1.40 tff(941,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(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(942,plain,
% 1.24/1.40 (((~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(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(943,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(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(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[942])).
% 1.24/1.40 tff(944,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(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(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.24/1.40 inference(transitivity,[status(thm)],[943, 941])).
% 1.24/1.40 tff(945,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(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(946,plain,
% 1.24/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[945, 944])).
% 1.24/1.40 tff(947,plain,
% 1.24/1.40 ($false),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[946, 45, 272, 940, 939])).
% 1.24/1.40 tff(948,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.40 tff(949,plain,
% 1.24/1.40 ($false),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[948, 938, 930, 272])).
% 1.24/1.40 tff(950,plain,((~b(s(s(s(s(z)))), elem!1)) | (~r(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.40 tff(951,plain,
% 1.24/1.40 (~b(s(s(s(s(z)))), elem!1)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[950, 922, 498, 297, 272])).
% 1.24/1.40 tff(952,plain,
% 1.24/1.40 (r(s(s(s(s(z)))), elem!1)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[632, 951, 243])).
% 1.24/1.40 tff(953,plain,
% 1.24/1.40 (s(s(s(elem!1))) = s(elem!1)),
% 1.24/1.40 inference(symmetry,[status(thm)],[309])).
% 1.24/1.40 tff(954,plain,
% 1.24/1.40 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[953])).
% 1.24/1.40 tff(955,plain,
% 1.24/1.40 (s(s(s(s(elem!1)))) = elem!1),
% 1.24/1.40 inference(transitivity,[status(thm)],[954, 199])).
% 1.24/1.40 tff(956,plain,
% 1.24/1.40 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[955])).
% 1.24/1.40 tff(957,plain,
% 1.24/1.40 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 1.24/1.40 inference(transitivity,[status(thm)],[956, 225])).
% 1.24/1.40 tff(958,plain,
% 1.24/1.40 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[957])).
% 1.24/1.40 tff(959,plain,
% 1.24/1.40 (~(s(s(z)) = elem!1)),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[239, 958])).
% 1.24/1.40 tff(960,plain,
% 1.24/1.40 (~b(s(s(z)), elem!1)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[897, 128, 297, 922, 273])).
% 1.24/1.40 tff(961,plain,
% 1.24/1.40 (r(s(s(z)), elem!1)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[370, 960, 959])).
% 1.24/1.40 tff(962,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(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(963,plain,
% 1.24/1.40 (((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(964,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(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[963])).
% 1.24/1.40 tff(965,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(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.24/1.40 inference(transitivity,[status(thm)],[964, 962])).
% 1.24/1.40 tff(966,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(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)))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(967,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(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[966, 965])).
% 1.24/1.40 tff(968,plain,
% 1.24/1.40 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[967, 45, 961, 952])).
% 1.24/1.40 tff(969,plain,
% 1.24/1.40 (((~![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))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(970,plain,
% 1.24/1.40 ((~![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))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(971,plain,
% 1.24/1.40 ((~![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)))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[970, 969])).
% 1.24/1.40 tff(972,plain,
% 1.24/1.40 ((s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[971, 21, 968])).
% 1.24/1.40 tff(973,plain,
% 1.24/1.40 (b(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[972, 921])).
% 1.24/1.40 tff(974,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(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(975,plain,
% 1.24/1.40 (((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(976,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(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(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(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[975])).
% 1.24/1.40 tff(977,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(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(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(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.24/1.40 inference(transitivity,[status(thm)],[976, 974])).
% 1.24/1.40 tff(978,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(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(979,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(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[978, 977])).
% 1.24/1.40 tff(980,plain,
% 1.24/1.40 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[979, 45, 961, 952])).
% 1.24/1.40 tff(981,plain,
% 1.24/1.40 (b(s(s(z)), s(s(s(s(z)))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[610, 21, 607, 980])).
% 1.24/1.40 tff(982,plain,
% 1.24/1.40 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.24/1.40 inference(symmetry,[status(thm)],[705])).
% 1.24/1.40 tff(983,plain,
% 1.24/1.40 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[199])).
% 1.24/1.40 tff(984,plain,
% 1.24/1.40 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.24/1.40 inference(transitivity,[status(thm)],[983, 982])).
% 1.24/1.40 tff(985,plain,
% 1.24/1.40 (s(s(s(elem!1))) = elem!1),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[307, 984])).
% 1.24/1.40 tff(986,plain,
% 1.24/1.40 (s(s(s(elem!1))) = elem!1),
% 1.24/1.40 inference(transitivity,[status(thm)],[308, 199])).
% 1.24/1.40 tff(987,plain,
% 1.24/1.40 (r(s(s(s(elem!1))), s(s(z))) <=> r(elem!1, s(s(z)))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[986])).
% 1.24/1.40 tff(988,plain,
% 1.24/1.40 (r(elem!1, s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 1.24/1.40 inference(symmetry,[status(thm)],[987])).
% 1.24/1.40 tff(989,plain,
% 1.24/1.40 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 1.24/1.40 inference(transitivity,[status(thm)],[957, 650])).
% 1.24/1.40 tff(990,plain,
% 1.24/1.40 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(elem!1 = s(s(z))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[989])).
% 1.24/1.40 tff(991,plain,
% 1.24/1.40 (~(elem!1 = s(s(z)))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[239, 990])).
% 1.24/1.40 tff(992,plain,
% 1.24/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, s(s(z)))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(993,plain,
% 1.24/1.40 (((~b(elem!1, s(z))) | (~b(elem!1, 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(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(994,plain,
% 1.24/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, 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(X0, 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(elem!1, s(s(z))))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[993])).
% 1.24/1.40 tff(995,plain,
% 1.24/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, 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(X0, 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(elem!1, s(s(z)))))),
% 1.24/1.40 inference(transitivity,[status(thm)],[994, 992])).
% 1.24/1.40 tff(996,plain,
% 1.24/1.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(997,plain,
% 1.24/1.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[996, 995])).
% 1.24/1.40 tff(998,plain,
% 1.24/1.40 (~b(elem!1, s(s(z)))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[997, 128, 297, 922, 273])).
% 1.24/1.40 tff(999,plain,
% 1.24/1.40 (r(elem!1, s(s(z)))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[493, 998, 991])).
% 1.24/1.40 tff(1000,plain,
% 1.24/1.40 (r(s(s(s(elem!1))), s(s(z)))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[999, 988])).
% 1.24/1.40 tff(1001,plain,
% 1.24/1.40 (~r(s(s(s(elem!1))), z)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[528, 519, 1000])).
% 1.24/1.40 tff(1002,plain,
% 1.24/1.40 (r(s(s(s(elem!1))), z) <=> r(elem!1, z)),
% 1.24/1.40 inference(monotonicity,[status(thm)],[710])).
% 1.24/1.40 tff(1003,plain,
% 1.24/1.40 (r(elem!1, z) <=> r(s(s(s(elem!1))), z)),
% 1.24/1.40 inference(symmetry,[status(thm)],[1002])).
% 1.24/1.40 tff(1004,assumption,(r(elem!1, z)), introduced(assumption)).
% 1.24/1.40 tff(1005,plain,
% 1.24/1.40 (r(s(s(s(elem!1))), z)),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[1004, 1003])).
% 1.24/1.40 tff(1006,plain,
% 1.24/1.40 ($false),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[544, 1005])).
% 1.24/1.40 tff(1007,plain,((~(s(s(s(elem!1))) = elem!1)) | r(s(s(s(elem!1))), z) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.40 tff(1008,plain,
% 1.24/1.40 (~r(elem!1, z)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[1007, 1001, 985])).
% 1.24/1.40 tff(1009,plain,
% 1.24/1.40 (b(elem!1, z)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[574, 1008, 462])).
% 1.24/1.40 tff(1010,assumption,(b(s(s(s(s(s(s(z)))))), elem!1)), introduced(assumption)).
% 1.24/1.40 tff(1011,plain,
% 1.24/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(1012,plain,
% 1.24/1.40 (((~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(1013,plain,
% 1.24/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), z))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[1012])).
% 1.24/1.40 tff(1014,plain,
% 1.24/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 1.24/1.40 inference(transitivity,[status(thm)],[1013, 1011])).
% 1.24/1.40 tff(1015,plain,
% 1.24/1.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(1016,plain,
% 1.24/1.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), z))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[1015, 1014])).
% 1.24/1.40 tff(1017,plain,
% 1.24/1.40 (~b(s(s(s(s(s(s(z)))))), z)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[1016, 128, 498, 577, 1010])).
% 1.24/1.40 tff(1018,plain,
% 1.24/1.40 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(s(z)))))) = z))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(1019,plain,
% 1.24/1.40 (~(s(s(s(s(s(s(z)))))) = z)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[1018, 9])).
% 1.24/1.40 tff(1020,plain,
% 1.24/1.40 (((~![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))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(1021,plain,
% 1.24/1.40 ((~![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))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(1022,plain,
% 1.24/1.40 ((~![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)),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[1021, 1020])).
% 1.24/1.41 tff(1023,plain,
% 1.24/1.41 (r(s(s(s(s(s(s(z)))))), z)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[1022, 21, 1019, 1017])).
% 1.24/1.41 tff(1024,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(1025,plain,
% 1.24/1.41 (((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(z))))))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(1026,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(z))))))))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[1025])).
% 1.24/1.41 tff(1027,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 1.24/1.41 inference(transitivity,[status(thm)],[1026, 1024])).
% 1.24/1.41 tff(1028,plain,
% 1.24/1.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(1029,plain,
% 1.24/1.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(z))))))))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[1028, 1027])).
% 1.24/1.41 tff(1030,plain,
% 1.24/1.41 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[1029, 128, 498, 577, 922, 1010])).
% 1.24/1.41 tff(1031,assumption,(s(z) = s(s(s(s(s(s(z))))))), introduced(assumption)).
% 1.24/1.41 tff(1032,plain,
% 1.24/1.41 (inj_0(s(z)) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[1031])).
% 1.24/1.41 tff(1033,plain,
% 1.24/1.41 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(z))),
% 1.24/1.41 inference(symmetry,[status(thm)],[1032])).
% 1.24/1.41 tff(1034,plain,
% 1.24/1.41 (s(s(s(s(s(z))))) = z),
% 1.24/1.41 inference(transitivity,[status(thm)],[208, 1033, 64])).
% 1.24/1.41 tff(1035,plain,
% 1.24/1.41 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(z))))) = z))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(1036,plain,
% 1.24/1.41 (~(s(s(s(s(s(z))))) = z)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[1035, 9])).
% 1.24/1.41 tff(1037,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[1036, 1034])).
% 1.24/1.41 tff(1038,plain,(~(s(z) = s(s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(1039,plain,
% 1.24/1.41 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(s(z))))))) | b(s(z), s(s(s(s(s(s(z))))))) | r(s(z), s(s(s(s(s(s(z))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(s(z))))))) | b(s(z), s(s(s(s(s(s(z))))))) | r(s(z), s(s(s(s(s(s(z))))))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(1040,plain,
% 1.24/1.41 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(s(z))))))) | b(s(z), s(s(s(s(s(s(z))))))) | r(s(z), s(s(s(s(s(s(z))))))))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(1041,plain,
% 1.24/1.41 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(s(z))))))) | b(s(z), s(s(s(s(s(s(z))))))) | r(s(z), s(s(s(s(s(s(z)))))))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[1040, 1039])).
% 1.24/1.41 tff(1042,plain,
% 1.24/1.41 (r(s(z), s(s(s(s(s(s(z)))))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[1041, 21, 1038, 1030])).
% 1.24/1.41 tff(1043,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(s(s(z)))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(1044,plain,
% 1.24/1.41 (((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(1045,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(s(s(z)))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, 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(z), z)) | (~r(s(z), s(s(s(s(s(s(z))))))))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[1044])).
% 1.24/1.41 tff(1046,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(s(s(z)))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, 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(z), z)) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 1.24/1.41 inference(transitivity,[status(thm)],[1045, 1043])).
% 1.24/1.41 tff(1047,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(s(s(z)))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(1048,plain,
% 1.24/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(z))))))))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[1047, 1046])).
% 1.24/1.41 tff(1049,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[1048, 45, 272, 1042, 1023])).
% 1.24/1.41 tff(1050,plain,((~b(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(1051,plain,
% 1.24/1.41 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[1050, 1009, 498, 272, 922])).
% 1.24/1.41 tff(1052,plain,
% 1.24/1.41 (((~![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))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(1053,plain,
% 1.24/1.41 ((~![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))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(1054,plain,
% 1.24/1.41 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = elem!1) | b(s(s(s(s(s(s(z)))))), elem!1) | r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[1053, 1052])).
% 1.24/1.41 tff(1055,plain,
% 1.24/1.41 ((s(s(s(s(s(s(z)))))) = elem!1) | b(s(s(s(s(s(s(z)))))), elem!1) | r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[1054, 21])).
% 1.24/1.41 tff(1056,plain,
% 1.24/1.41 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[1055, 1051, 246])).
% 1.24/1.41 tff(1057,plain,
% 1.24/1.41 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[307])).
% 1.24/1.41 tff(1058,plain,
% 1.24/1.41 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.24/1.41 inference(transitivity,[status(thm)],[1057, 695])).
% 1.24/1.41 tff(1059,plain,
% 1.24/1.41 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.24/1.41 inference(symmetry,[status(thm)],[1058])).
% 1.24/1.41 tff(1060,plain,
% 1.24/1.41 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[308])).
% 1.24/1.41 tff(1061,plain,
% 1.24/1.41 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 1.24/1.41 inference(symmetry,[status(thm)],[1060])).
% 1.24/1.41 tff(1062,plain,
% 1.24/1.41 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[1061, 1059])).
% 1.24/1.41 tff(1063,assumption,(~(s(s(s(s(elem!1)))) = s(s(elem!1)))), introduced(assumption)).
% 1.24/1.41 tff(1064,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[1063, 1062])).
% 1.24/1.41 tff(1065,plain,((~(s(s(elem!1)) = s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(1066,plain,
% 1.24/1.41 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[1065, 307])).
% 1.24/1.41 tff(1067,plain,
% 1.24/1.41 ((s(s(elem!1)) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.24/1.41 inference(commutativity,[status(thm)],[])).
% 1.24/1.41 tff(1068,plain,
% 1.24/1.41 ((~(s(s(elem!1)) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[1067])).
% 1.24/1.41 tff(1069,assumption,(~(s(s(elem!1)) = s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.24/1.41 tff(1070,plain,
% 1.24/1.41 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[1069, 1068])).
% 1.24/1.41 tff(1071,assumption,(s(s(s(s(elem!1)))) = s(s(elem!1))), introduced(assumption)).
% 1.24/1.41 tff(1072,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[1071, 1070])).
% 1.24/1.41 tff(1073,plain,((s(s(elem!1)) = s(s(s(s(elem!1))))) | (~(s(s(s(s(elem!1)))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(1074,plain,
% 1.24/1.41 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[1073, 1066])).
% 1.24/1.41 tff(1075,assumption,(s(s(elem!1)) = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.24/1.41 tff(1076,plain,
% 1.24/1.41 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[1075])).
% 1.24/1.41 tff(1077,plain,
% 1.24/1.41 (s(elem!1) = s(s(s(elem!1)))),
% 1.24/1.41 inference(transitivity,[status(thm)],[106, 1076, 233])).
% 1.24/1.41 tff(1078,plain,
% 1.24/1.41 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[1077])).
% 1.24/1.41 tff(1079,plain,
% 1.24/1.41 (elem!1 = inj_0(s(elem!1))),
% 1.24/1.41 inference(symmetry,[status(thm)],[201])).
% 1.24/1.41 tff(1080,plain,
% 1.24/1.41 (elem!1 = s(s(s(s(elem!1))))),
% 1.24/1.41 inference(transitivity,[status(thm)],[1079, 1078, 186, 1075])).
% 1.24/1.41 tff(1081,plain,
% 1.24/1.41 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.24/1.41 inference(symmetry,[status(thm)],[1075])).
% 1.24/1.41 tff(1082,plain,
% 1.24/1.41 ((elem!1 = s(s(s(s(elem!1))))) <=> (elem!1 = s(s(elem!1)))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[1081])).
% 1.24/1.41 tff(1083,plain,
% 1.24/1.41 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(elem!1)) = elem!1)),
% 1.24/1.41 inference(transitivity,[status(thm)],[1082, 372])).
% 1.24/1.41 tff(1084,plain,
% 1.24/1.41 ((s(s(elem!1)) = elem!1) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.24/1.41 inference(symmetry,[status(thm)],[1083])).
% 1.24/1.41 tff(1085,plain,
% 1.24/1.41 ((~(s(s(elem!1)) = elem!1)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[1084])).
% 1.24/1.41 tff(1086,assumption,(~(s(s(elem!1)) = elem!1)), introduced(assumption)).
% 1.24/1.41 tff(1087,plain,
% 1.24/1.41 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[1086, 1085])).
% 1.24/1.41 tff(1088,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[1087, 1080])).
% 1.24/1.41 tff(1089,plain,((~(s(s(elem!1)) = s(s(s(s(elem!1)))))) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(1090,plain,
% 1.24/1.41 (s(s(elem!1)) = elem!1),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[1089, 1074])).
% 1.24/1.41 tff(1091,plain,
% 1.24/1.41 (s(s(s(elem!1))) = elem!1),
% 1.24/1.41 inference(transitivity,[status(thm)],[308, 1090])).
% 1.24/1.41 tff(1092,plain,
% 1.24/1.41 (r(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.24/1.41 inference(monotonicity,[status(thm)],[1091])).
% 1.24/1.41 tff(1093,plain,
% 1.24/1.41 (r(s(s(s(s(s(s(z)))))), elem!1) <=> r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 1.24/1.41 inference(symmetry,[status(thm)],[1092])).
% 1.24/1.41 tff(1094,assumption,(r(s(s(s(s(s(s(z)))))), elem!1)), introduced(assumption)).
% 1.24/1.41 tff(1095,plain,
% 1.24/1.41 (r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[1094, 1093])).
% 1.24/1.41 tff(1096,assumption,(~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))), introduced(assumption)).
% 1.24/1.41 tff(1097,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[1096, 1095])).
% 1.24/1.41 tff(1098,plain,((~r(s(s(s(s(s(s(z)))))), elem!1)) | r(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))) | (~(s(s(elem!1)) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(1099,plain,
% 1.24/1.41 (r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[1098, 1056, 307])).
% 1.24/1.41 tff(1100,plain,
% 1.24/1.41 (elem!1 = s(s(elem!1))),
% 1.24/1.41 inference(symmetry,[status(thm)],[1090])).
% 1.24/1.41 tff(1101,plain,
% 1.24/1.41 (elem!1 = s(s(s(elem!1)))),
% 1.24/1.41 inference(transitivity,[status(thm)],[1100, 307])).
% 1.24/1.41 tff(1102,plain,
% 1.24/1.41 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(s(s(elem!1))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[1101])).
% 1.24/1.41 tff(1103,assumption,(r(s(s(z)), elem!1)), introduced(assumption)).
% 1.24/1.41 tff(1104,plain,
% 1.24/1.41 (r(s(s(z)), s(s(s(elem!1))))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[1103, 1102])).
% 1.24/1.41 tff(1105,assumption,(~r(s(s(z)), s(s(s(elem!1))))), introduced(assumption)).
% 1.24/1.41 tff(1106,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[1105, 1104])).
% 1.24/1.41 tff(1107,plain,((~r(s(s(z)), elem!1)) | r(s(s(z)), s(s(s(elem!1)))) | (~(s(s(elem!1)) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(1108,plain,
% 1.24/1.41 (r(s(s(z)), s(s(s(elem!1))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[1107, 961, 307])).
% 1.24/1.41 tff(1109,plain,
% 1.24/1.41 ((s(s(s(s(s(s(z)))))) = s(z)) <=> (s(z) = s(s(s(s(s(s(z)))))))),
% 1.24/1.41 inference(commutativity,[status(thm)],[])).
% 1.24/1.41 tff(1110,plain,
% 1.24/1.41 ((s(z) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(z))),
% 1.24/1.41 inference(symmetry,[status(thm)],[1109])).
% 1.24/1.41 tff(1111,plain,
% 1.24/1.41 ((~(s(z) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(s(s(z)))))) = s(z)))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[1110])).
% 1.24/1.41 tff(1112,plain,
% 1.24/1.41 (~(s(s(s(s(s(s(z)))))) = s(z))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[1038, 1111])).
% 1.24/1.41 tff(1113,plain,
% 1.24/1.41 ((s(s(s(s(s(s(z)))))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(s(s(z)))))))),
% 1.24/1.41 inference(commutativity,[status(thm)],[])).
% 1.24/1.41 tff(1114,plain,
% 1.24/1.41 ((s(s(z)) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(s(z)))),
% 1.24/1.41 inference(symmetry,[status(thm)],[1113])).
% 1.24/1.41 tff(1115,plain,
% 1.24/1.41 ((~(s(s(z)) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(s(s(z)))))) = s(s(z))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[1114])).
% 1.24/1.41 tff(1116,assumption,(s(s(z)) = s(s(s(s(s(s(z))))))), introduced(assumption)).
% 1.24/1.41 tff(1117,plain,
% 1.24/1.41 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[1116])).
% 1.24/1.41 tff(1118,plain,
% 1.24/1.41 (s(z) = s(s(s(s(s(z)))))),
% 1.24/1.41 inference(transitivity,[status(thm)],[70, 1117, 207])).
% 1.24/1.41 tff(1119,plain,
% 1.24/1.41 (inj_0(s(z)) = inj_0(s(s(s(s(s(z))))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[1118])).
% 1.24/1.41 tff(1120,plain,
% 1.24/1.41 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(z))),
% 1.24/1.41 inference(symmetry,[status(thm)],[1119])).
% 1.24/1.41 tff(1121,plain,
% 1.24/1.41 (s(s(s(s(z)))) = z),
% 1.24/1.41 inference(transitivity,[status(thm)],[211, 1120, 64])).
% 1.24/1.41 tff(1122,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[586, 1121])).
% 1.24/1.41 tff(1123,plain,(~(s(s(z)) = s(s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(1124,plain,
% 1.24/1.41 (~(s(s(s(s(s(s(z)))))) = s(s(z)))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[1123, 1115])).
% 1.24/1.41 tff(1125,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(z)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), 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(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(1126,plain,
% 1.24/1.41 (((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(z))))) <=> ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(1127,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(z)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), elem!1))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[1126])).
% 1.24/1.41 tff(1128,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(z)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.24/1.41 inference(transitivity,[status(thm)],[1127, 1125])).
% 1.24/1.41 tff(1129,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(z)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(1130,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(z)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), elem!1))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[1129, 1128])).
% 1.24/1.41 tff(1131,plain,
% 1.24/1.41 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[1130, 45, 961, 1056])).
% 1.24/1.41 tff(1132,plain,
% 1.24/1.41 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(z))) | b(s(s(s(s(s(s(z)))))), s(s(z))) | r(s(s(s(s(s(s(z)))))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(z))) | b(s(s(s(s(s(s(z)))))), s(s(z))) | r(s(s(s(s(s(s(z)))))), s(s(z))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(1133,plain,
% 1.24/1.41 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(z))) | b(s(s(s(s(s(s(z)))))), s(s(z))) | r(s(s(s(s(s(s(z)))))), s(s(z))))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(1134,plain,
% 1.24/1.41 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(z))) | b(s(s(s(s(s(s(z)))))), s(s(z))) | r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[1133, 1132])).
% 1.24/1.41 tff(1135,plain,
% 1.24/1.41 ((s(s(s(s(s(s(z)))))) = s(s(z))) | b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[1134, 21, 1131])).
% 1.24/1.41 tff(1136,plain,
% 1.24/1.41 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[1135, 1124])).
% 1.24/1.41 tff(1137,plain,
% 1.24/1.41 (~r(s(z), s(s(z)))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[642, 519, 272])).
% 1.24/1.41 tff(1138,plain,
% 1.24/1.41 (b(s(z), s(s(z)))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[648, 1137])).
% 1.24/1.41 tff(1139,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(s(z)))))), s(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(X0, 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(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(1140,plain,
% 1.24/1.41 (((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(1141,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[1140])).
% 1.24/1.41 tff(1142,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.24/1.41 inference(transitivity,[status(thm)],[1141, 1139])).
% 1.24/1.41 tff(1143,plain,
% 1.24/1.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(1144,plain,
% 1.24/1.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[1143, 1142])).
% 1.24/1.41 tff(1145,plain,
% 1.24/1.41 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[1144, 128, 1138, 273, 1136])).
% 1.24/1.41 tff(1146,plain,
% 1.24/1.41 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(z)) | b(s(s(s(s(s(s(z)))))), s(z)) | r(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(z)) | b(s(s(s(s(s(s(z)))))), s(z)) | r(s(s(s(s(s(s(z)))))), s(z)))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(1147,plain,
% 1.24/1.41 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(z)) | b(s(s(s(s(s(s(z)))))), s(z)) | r(s(s(s(s(s(s(z)))))), s(z)))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(1148,plain,
% 1.24/1.41 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(z)) | b(s(s(s(s(s(s(z)))))), s(z)) | r(s(s(s(s(s(s(z)))))), s(z))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[1147, 1146])).
% 1.24/1.41 tff(1149,plain,
% 1.24/1.41 ((s(s(s(s(s(s(z)))))) = s(z)) | r(s(s(s(s(s(s(z)))))), s(z))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[1148, 21, 1145])).
% 1.24/1.41 tff(1150,plain,
% 1.24/1.41 (r(s(s(s(s(s(s(z)))))), s(z))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[1149, 1112])).
% 1.24/1.41 tff(1151,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z, s(z))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(1152,plain,
% 1.24/1.41 (((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z)))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(1153,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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, 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(X0, 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(z, s(z)))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[1152])).
% 1.24/1.41 tff(1154,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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, 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(X0, 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(z, s(z))))),
% 1.24/1.41 inference(transitivity,[status(thm)],[1153, 1151])).
% 1.24/1.41 tff(1155,plain,
% 1.24/1.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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, 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(1156,plain,
% 1.24/1.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z, s(z)))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[1155, 1154])).
% 1.24/1.41 tff(1157,plain,
% 1.24/1.41 (~b(z, s(z))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[1156, 128, 498, 297, 922])).
% 1.24/1.41 tff(1158,plain,
% 1.24/1.41 (r(z, s(z))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[415, 1157])).
% 1.24/1.41 tff(1159,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(z))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(1160,plain,
% 1.24/1.41 (((~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(1161,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(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(z, 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(z))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z)))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[1160])).
% 1.24/1.41 tff(1162,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(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(z, 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(z))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 1.24/1.41 inference(transitivity,[status(thm)],[1161, 1159])).
% 1.24/1.42 tff(1163,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(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(1164,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(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z)))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[1163, 1162])).
% 1.24/1.42 tff(1165,plain,
% 1.24/1.42 (~r(s(s(s(s(s(s(z)))))), z)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[1164, 45, 1158, 1150])).
% 1.24/1.42 tff(1166,plain,
% 1.24/1.42 (b(s(s(s(s(s(s(z)))))), z)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[1022, 21, 1019, 1165])).
% 1.24/1.42 tff(1167,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)), elem!1)) | (~r(s(s(z)), s(s(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(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(1168,plain,
% 1.24/1.42 (((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(1169,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(s(z)))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~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)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), elem!1))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[1168])).
% 1.24/1.42 tff(1170,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(s(z)))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~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)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.24/1.42 inference(transitivity,[status(thm)],[1169, 1167])).
% 1.24/1.42 tff(1171,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(s(z)))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(1172,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)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), elem!1))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[1171, 1170])).
% 1.24/1.42 tff(1173,plain,
% 1.24/1.42 (~r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[1172, 45, 961, 1056])).
% 1.24/1.42 tff(1174,plain,
% 1.24/1.42 (((~![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))))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(1175,plain,
% 1.24/1.42 ((~![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))))))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(1176,plain,
% 1.24/1.42 ((~![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)))))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[1175, 1174])).
% 1.24/1.42 tff(1177,plain,
% 1.24/1.42 (b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[1176, 21, 1123, 1173])).
% 1.24/1.42 tff(1178,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(1179,plain,
% 1.24/1.42 (((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(1180,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), 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(X0, 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(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[1179])).
% 1.24/1.42 tff(1181,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), 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(X0, 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(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 1.24/1.42 inference(transitivity,[status(thm)],[1180, 1178])).
% 1.24/1.42 tff(1182,plain,
% 1.24/1.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(1183,plain,
% 1.24/1.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[1182, 1181])).
% 1.24/1.42 tff(1184,plain,
% 1.24/1.42 (~b(s(s(z)), z)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[1183, 128, 498, 297, 273, 1177, 1166])).
% 1.24/1.42 tff(1185,plain,
% 1.24/1.42 (r(s(s(z)), z)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[25, 1184])).
% 1.24/1.42 tff(1186,assumption,(r(s(s(s(s(z)))), s(s(s(elem!1))))), introduced(assumption)).
% 1.24/1.42 tff(1187,assumption,(r(s(s(z)), s(s(s(elem!1))))), introduced(assumption)).
% 1.24/1.42 tff(1188,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(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(1189,plain,
% 1.24/1.42 (((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(1190,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(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[1189])).
% 1.24/1.42 tff(1191,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(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.24/1.42 inference(transitivity,[status(thm)],[1190, 1188])).
% 1.24/1.42 tff(1192,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(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(1193,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(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[1192, 1191])).
% 1.24/1.42 tff(1194,plain,
% 1.24/1.42 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[1193, 45, 28, 1187, 1186])).
% 1.24/1.42 tff(1195,plain,
% 1.24/1.42 ((s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[971, 21, 1194])).
% 1.24/1.42 tff(1196,plain,
% 1.24/1.42 (b(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[1195, 921])).
% 1.24/1.42 tff(1197,assumption,(r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))), introduced(assumption)).
% 1.24/1.42 tff(1198,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(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(1199,plain,
% 1.24/1.42 (((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(1200,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(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[1199])).
% 1.24/1.42 tff(1201,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(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.24/1.42 inference(transitivity,[status(thm)],[1200, 1198])).
% 1.24/1.42 tff(1202,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(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(1203,plain,
% 1.24/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[1202, 1201])).
% 1.24/1.42 tff(1204,plain,
% 1.24/1.42 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[1203, 45, 1186, 1197])).
% 1.24/1.42 tff(1205,assumption,(s(s(s(s(s(s(z)))))) = s(s(s(s(z))))), introduced(assumption)).
% 1.24/1.42 tff(1206,plain,
% 1.24/1.42 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(s(s(z)))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[1205])).
% 1.24/1.42 tff(1207,plain,
% 1.24/1.42 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.24/1.42 inference(symmetry,[status(thm)],[1206])).
% 1.24/1.42 tff(1208,plain,
% 1.24/1.42 (s(s(s(z))) = s(s(s(s(s(z)))))),
% 1.24/1.42 inference(transitivity,[status(thm)],[218, 1207, 207])).
% 1.24/1.42 tff(1209,plain,
% 1.24/1.42 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(z))))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[1208])).
% 1.24/1.42 tff(1210,plain,
% 1.24/1.42 (s(s(z)) = s(s(s(s(z))))),
% 1.24/1.42 inference(transitivity,[status(thm)],[223, 1209, 163])).
% 1.24/1.42 tff(1211,plain,
% 1.24/1.42 ($false),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[607, 1210])).
% 1.24/1.42 tff(1212,plain,(~(s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.42 tff(1213,plain,
% 1.24/1.42 (((~![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))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(1214,plain,
% 1.24/1.42 ((~![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))))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(1215,plain,
% 1.24/1.42 ((~![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)))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[1214, 1213])).
% 1.24/1.42 tff(1216,plain,
% 1.24/1.42 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[1215, 21, 1212, 1204])).
% 1.24/1.42 tff(1217,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(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(1218,plain,
% 1.24/1.42 (((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(1219,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(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[1218])).
% 1.24/1.42 tff(1220,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(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 1.24/1.42 inference(transitivity,[status(thm)],[1219, 1217])).
% 1.24/1.42 tff(1221,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(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(1222,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(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[1221, 1220])).
% 1.24/1.42 tff(1223,plain,
% 1.24/1.42 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[1222, 45, 28, 1187, 1197])).
% 1.24/1.42 tff(1224,plain,
% 1.24/1.42 ((s(s(s(s(s(s(z)))))) = s(s(z))) | b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[1134, 21, 1223])).
% 1.24/1.42 tff(1225,plain,
% 1.24/1.42 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[1224, 1124])).
% 1.24/1.42 tff(1226,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(elem!1))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(1227,plain,
% 1.24/1.42 (((~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(1228,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(s(z)))))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~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(elem!1))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[1227])).
% 1.24/1.42 tff(1229,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(s(z)))))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~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(elem!1))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 1.24/1.42 inference(transitivity,[status(thm)],[1228, 1226])).
% 1.24/1.42 tff(1230,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(s(z)))))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(1231,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(elem!1))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[1230, 1229])).
% 1.24/1.42 tff(1232,plain,
% 1.24/1.42 (~r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[1231, 45, 1187, 1197])).
% 1.24/1.42 tff(1233,plain,
% 1.24/1.42 (b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[1176, 21, 1123, 1232])).
% 1.24/1.42 tff(1234,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(1235,plain,
% 1.24/1.42 (((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(1236,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[1235])).
% 1.24/1.42 tff(1237,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.24/1.42 inference(transitivity,[status(thm)],[1236, 1234])).
% 1.24/1.42 tff(1238,plain,
% 1.24/1.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(1239,plain,
% 1.24/1.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[1238, 1237])).
% 1.24/1.42 tff(1240,plain,
% 1.24/1.42 ($false),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[1239, 128, 1233, 1225, 1216, 1196])).
% 1.24/1.43 tff(1241,plain,((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.43 tff(1242,plain,
% 1.24/1.43 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1241, 1185, 1108, 1099])).
% 1.24/1.43 tff(1243,plain,
% 1.24/1.43 (r(s(s(s(s(z)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), elem!1)),
% 1.24/1.43 inference(monotonicity,[status(thm)],[986])).
% 1.24/1.43 tff(1244,plain,
% 1.24/1.43 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.24/1.43 inference(symmetry,[status(thm)],[1243])).
% 1.24/1.43 tff(1245,assumption,(r(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 1.24/1.43 tff(1246,plain,
% 1.24/1.43 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[1245, 1244])).
% 1.24/1.43 tff(1247,assumption,(~r(s(s(s(s(z)))), s(s(s(elem!1))))), introduced(assumption)).
% 1.24/1.43 tff(1248,plain,
% 1.24/1.43 ($false),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1247, 1246])).
% 1.24/1.43 tff(1249,plain,((~r(s(s(s(s(z)))), elem!1)) | r(s(s(s(s(z)))), s(s(s(elem!1)))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.43 tff(1250,plain,
% 1.24/1.43 (~r(s(s(s(s(z)))), elem!1)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1249, 1242, 307, 199])).
% 1.24/1.43 tff(1251,plain,
% 1.24/1.43 (b(s(s(s(s(z)))), elem!1)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[632, 1250, 243])).
% 1.24/1.43 tff(1252,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(1253,plain,
% 1.24/1.43 (((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, 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, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(1254,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z))))))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[1253])).
% 1.24/1.43 tff(1255,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.24/1.43 inference(transitivity,[status(thm)],[1254, 1252])).
% 1.24/1.43 tff(1256,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(1257,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z))))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[1256, 1255])).
% 1.24/1.43 tff(1258,plain,
% 1.24/1.43 (~b(s(z), s(s(s(s(z)))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1257, 128, 498, 1009, 922, 1251])).
% 1.24/1.43 tff(1259,plain,
% 1.24/1.43 (r(s(z), s(s(s(s(z)))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[684, 21, 681, 1258])).
% 1.24/1.43 tff(1260,plain,
% 1.24/1.43 (~b(s(s(s(s(z)))), z)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[583, 128, 498, 1009, 1251])).
% 1.24/1.43 tff(1261,plain,
% 1.24/1.43 (r(s(s(s(s(z)))), z)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[589, 21, 586, 1260])).
% 1.24/1.43 tff(1262,plain,
% 1.24/1.43 ($false),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[948, 1261, 1259, 272])).
% 1.24/1.43 tff(1263,plain,((~r(z, s(s(z)))) | (~r(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~(s(s(elem!1)) = elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.43 tff(1264,plain,
% 1.24/1.43 (~r(z, s(s(z)))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1263, 922, 498, 272, 307, 199, 297, 273])).
% 1.24/1.43 tff(1265,plain,
% 1.24/1.43 (b(z, s(s(z)))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[516, 1264])).
% 1.24/1.43 tff(1266,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(1267,plain,
% 1.24/1.43 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(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)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(1268,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[1267])).
% 1.24/1.43 tff(1269,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.24/1.43 inference(transitivity,[status(thm)],[1268, 1266])).
% 1.24/1.43 tff(1270,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(1271,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z))))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[1270, 1269])).
% 1.24/1.43 tff(1272,plain,
% 1.24/1.43 (~b(s(s(s(s(z)))), z)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1271, 128, 1265, 981, 973])).
% 1.24/1.43 tff(1273,plain,
% 1.24/1.43 (r(s(s(s(s(z)))), z)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[589, 21, 586, 1272])).
% 1.24/1.43 tff(1274,plain,
% 1.24/1.43 (~r(s(z), s(s(s(s(z)))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[948, 1273, 272])).
% 1.24/1.43 tff(1275,plain,
% 1.24/1.43 (b(s(z), s(s(s(s(z)))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[684, 21, 681, 1274])).
% 1.24/1.43 tff(1276,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), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(1277,plain,
% 1.24/1.43 (((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(1278,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), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[1277])).
% 1.24/1.43 tff(1279,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), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.24/1.43 inference(transitivity,[status(thm)],[1278, 1276])).
% 1.24/1.43 tff(1280,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), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(1281,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), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[1280, 1279])).
% 1.24/1.43 tff(1282,plain,
% 1.24/1.43 (~r(s(s(s(s(z)))), s(z))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1281, 45, 272, 1273])).
% 1.24/1.43 tff(1283,plain,
% 1.24/1.43 (b(s(s(s(s(z)))), s(z))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[784, 1282])).
% 1.24/1.43 tff(1284,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(1285,plain,
% 1.24/1.43 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(1286,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[1285])).
% 1.24/1.43 tff(1287,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.24/1.43 inference(transitivity,[status(thm)],[1286, 1284])).
% 1.24/1.43 tff(1288,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), 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))))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(1289,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[1288, 1287])).
% 1.24/1.43 tff(1290,plain,
% 1.24/1.43 ($false),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1289, 128, 273, 1283, 981, 1275])).
% 1.24/1.43 tff(1291,plain,((~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~r(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.43 tff(1292,plain,
% 1.24/1.43 (~b(s(z), elem!1)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1291, 917, 272, 273, 807, 916, 199])).
% 1.24/1.43 tff(1293,plain,
% 1.24/1.43 (r(s(z), elem!1)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[665, 1292, 257])).
% 1.24/1.43 tff(1294,plain,
% 1.24/1.43 (s(s(s(elem!1))) = elem!1),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[916, 984])).
% 1.24/1.43 tff(1295,plain,
% 1.24/1.43 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.24/1.43 inference(symmetry,[status(thm)],[916])).
% 1.24/1.43 tff(1296,plain,
% 1.24/1.43 (s(s(s(elem!1))) = elem!1),
% 1.24/1.43 inference(transitivity,[status(thm)],[1295, 199])).
% 1.24/1.43 tff(1297,plain,
% 1.24/1.43 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), elem!1)),
% 1.24/1.43 inference(monotonicity,[status(thm)],[1296])).
% 1.24/1.43 tff(1298,plain,
% 1.24/1.43 (r(s(z), elem!1) <=> r(s(z), s(s(s(elem!1))))),
% 1.24/1.43 inference(symmetry,[status(thm)],[1297])).
% 1.24/1.43 tff(1299,plain,
% 1.24/1.43 (r(s(z), s(s(s(elem!1))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[1293, 1298])).
% 1.24/1.43 tff(1300,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), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(1301,plain,
% 1.24/1.43 (((~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(1302,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(elem!1))), z)) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1)))))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[1301])).
% 1.24/1.43 tff(1303,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(elem!1))), z)) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.24/1.43 inference(transitivity,[status(thm)],[1302, 1300])).
% 1.24/1.43 tff(1304,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(elem!1))), z)) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(1305,plain,
% 1.24/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1)))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[1304, 1303])).
% 1.24/1.43 tff(1306,plain,
% 1.24/1.43 ($false),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1305, 45, 272, 323, 520])).
% 1.24/1.43 tff(1307,plain,((~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.43 tff(1308,plain,
% 1.24/1.43 (~r(s(s(s(elem!1))), z)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1307, 1299, 272])).
% 1.24/1.43 tff(1309,plain,
% 1.24/1.43 (~r(elem!1, z)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1007, 1308, 1294])).
% 1.24/1.43 tff(1310,plain,
% 1.24/1.43 (b(elem!1, z)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[574, 1309, 462])).
% 1.24/1.43 tff(1311,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(1312,plain,
% 1.24/1.43 (((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(1313,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[1312])).
% 1.24/1.43 tff(1314,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.24/1.43 inference(transitivity,[status(thm)],[1313, 1311])).
% 1.24/1.43 tff(1315,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(1316,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[1315, 1314])).
% 1.24/1.43 tff(1317,plain,
% 1.24/1.43 ((~b(s(s(z)), z)) | (~b(s(s(z)), elem!1))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1316, 128, 498, 577, 297, 273])).
% 1.24/1.43 tff(1318,plain,
% 1.24/1.43 (~b(s(s(z)), z)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1317, 591])).
% 1.24/1.43 tff(1319,plain,
% 1.24/1.43 (r(s(s(z)), z)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[25, 1318])).
% 1.24/1.43 tff(1320,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), 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)))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(1321,plain,
% 1.24/1.43 (((~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)))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(1322,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(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))))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[1321])).
% 1.24/1.43 tff(1323,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(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)))))),
% 1.24/1.43 inference(transitivity,[status(thm)],[1322, 1320])).
% 1.24/1.43 tff(1324,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(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(1325,plain,
% 1.24/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[1324, 1323])).
% 1.24/1.43 tff(1326,plain,
% 1.24/1.43 ($false),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1325, 45, 272, 634, 28])).
% 1.24/1.43 tff(1327,plain,((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.43 tff(1328,plain,
% 1.24/1.43 (~r(s(z), s(s(z)))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[1327, 1319, 272])).
% 1.24/1.43 tff(1329,plain,
% 1.24/1.43 (b(s(z), s(s(z)))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[648, 1328])).
% 1.24/1.43 tff(1330,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(1331,plain,
% 1.24/1.43 (((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), 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(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(1332,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[1331])).
% 1.24/1.43 tff(1333,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 1.24/1.44 inference(transitivity,[status(thm)],[1332, 1330])).
% 1.24/1.44 tff(1334,plain,
% 1.24/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(1335,plain,
% 1.24/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[1334, 1333])).
% 1.24/1.44 tff(1336,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1335, 128, 297, 591, 1329, 273])).
% 1.24/1.44 tff(1337,plain,((~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~r(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(1338,plain,
% 1.24/1.44 (~b(s(s(z)), elem!1)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1337, 917, 273, 272, 807, 1310])).
% 1.24/1.44 tff(1339,plain,
% 1.24/1.44 (r(s(s(z)), elem!1)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[370, 1338, 959])).
% 1.24/1.44 tff(1340,assumption,(r(s(z), elem!1)), introduced(assumption)).
% 1.24/1.44 tff(1341,plain,
% 1.24/1.44 (~r(s(s(s(s(z)))), s(z))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[772, 45, 272, 1340, 1245])).
% 1.24/1.44 tff(1342,plain,
% 1.24/1.44 (b(s(s(s(s(z)))), s(z))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[782, 21, 779, 1341])).
% 1.24/1.44 tff(1343,plain,
% 1.24/1.44 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[979, 45, 1103, 1245])).
% 1.24/1.44 tff(1344,plain,
% 1.24/1.44 (b(s(s(z)), s(s(s(s(z)))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[610, 21, 607, 1343])).
% 1.24/1.44 tff(1345,plain,
% 1.24/1.44 (~r(s(z), s(s(s(s(z)))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[672, 45, 1340, 1245])).
% 1.24/1.44 tff(1346,plain,
% 1.24/1.44 (b(s(z), s(s(s(s(z)))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[684, 21, 681, 1345])).
% 1.24/1.44 tff(1347,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), elem!1)) | (~r(s(z), z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(1348,plain,
% 1.24/1.44 (((~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), z)) | (~r(s(s(z)), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(1349,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), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z)))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[1348])).
% 1.24/1.44 tff(1350,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), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))),
% 1.24/1.44 inference(transitivity,[status(thm)],[1349, 1347])).
% 1.24/1.44 tff(1351,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), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), z)) | (~r(s(s(z)), s(z))))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(1352,plain,
% 1.24/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z)))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[1351, 1350])).
% 1.24/1.44 tff(1353,plain,
% 1.24/1.44 (~r(s(s(z)), s(z))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1352, 45, 272, 1340, 1103])).
% 1.24/1.44 tff(1354,plain,
% 1.24/1.44 (b(s(s(z)), s(z))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[86, 1353])).
% 1.24/1.44 tff(1355,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1289, 128, 1354, 1346, 1344, 1342])).
% 1.24/1.44 tff(1356,plain,((~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(1357,plain,
% 1.24/1.44 (~r(s(s(s(s(z)))), elem!1)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1356, 1339, 272, 1293])).
% 1.24/1.44 tff(1358,plain,
% 1.24/1.44 (b(s(s(s(s(z)))), elem!1)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[632, 1357, 243])).
% 1.24/1.44 tff(1359,plain,
% 1.24/1.44 (~b(s(s(s(s(z)))), z)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[583, 128, 917, 1310, 1358])).
% 1.24/1.44 tff(1360,plain,
% 1.24/1.44 (r(s(s(s(s(z)))), z)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[589, 21, 586, 1359])).
% 1.24/1.44 tff(1361,plain,
% 1.24/1.44 (~r(s(z), s(s(s(s(z)))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[948, 1360, 272])).
% 1.24/1.44 tff(1362,plain,
% 1.24/1.44 (b(s(z), s(s(s(s(z)))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[684, 21, 681, 1361])).
% 1.24/1.44 tff(1363,plain,
% 1.24/1.44 (~r(s(s(s(s(z)))), s(z))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1281, 45, 272, 1360])).
% 1.24/1.44 tff(1364,plain,
% 1.24/1.44 (b(s(s(s(s(z)))), s(z))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[784, 1363])).
% 1.24/1.44 tff(1365,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(1366,plain,
% 1.24/1.44 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(1367,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[1366])).
% 1.24/1.44 tff(1368,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.24/1.44 inference(transitivity,[status(thm)],[1367, 1365])).
% 1.24/1.44 tff(1369,plain,
% 1.24/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(1370,plain,
% 1.24/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[1369, 1368])).
% 1.24/1.44 tff(1371,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1370, 128, 807, 1358, 1364, 1362])).
% 1.24/1.44 tff(1372,plain,((~b(z, s(s(elem!1)))) | (~r(s(z), z)) | (~b(s(s(z)), s(z))) | (~(s(s(elem!1)) = elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | b(s(s(elem!1)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(1373,plain,
% 1.24/1.44 (~b(z, s(s(elem!1)))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1372, 273, 272, 199, 794, 263, 198])).
% 1.24/1.44 tff(1374,plain,
% 1.24/1.44 (r(z, s(s(elem!1)))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[160, 1373])).
% 1.24/1.44 tff(1375,plain,
% 1.24/1.44 (r(z, elem!1)),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[1374, 796])).
% 1.24/1.44 tff(1376,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(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(1377,plain,
% 1.24/1.44 (((~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(1378,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(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1))))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[1377])).
% 1.24/1.44 tff(1379,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(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))),
% 1.24/1.44 inference(transitivity,[status(thm)],[1378, 1376])).
% 1.24/1.44 tff(1380,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(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(1381,plain,
% 1.24/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[1380, 1379])).
% 1.24/1.44 tff(1382,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1381, 45, 88, 272, 89])).
% 1.24/1.44 tff(1383,plain,((~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(1384,plain,
% 1.24/1.44 (~r(s(z), s(s(elem!1)))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1383, 1374, 272])).
% 1.24/1.44 tff(1385,plain,
% 1.24/1.44 (b(s(z), s(s(elem!1)))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[117, 1384])).
% 1.24/1.44 tff(1386,plain,
% 1.24/1.44 (b(s(z), elem!1)),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[1385, 860])).
% 1.24/1.44 tff(1387,plain,
% 1.24/1.44 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 1.24/1.44 inference(symmetry,[status(thm)],[983])).
% 1.24/1.44 tff(1388,plain,
% 1.24/1.44 ((elem!1 = s(elem!1)) <=> (elem!1 = s(s(s(elem!1))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[354])).
% 1.24/1.44 tff(1389,plain,
% 1.24/1.44 ((elem!1 = s(elem!1)) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 1.24/1.44 inference(transitivity,[status(thm)],[1388, 1387])).
% 1.24/1.44 tff(1390,plain,
% 1.24/1.44 (~b(s(elem!1), s(s(z)))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[912, 128, 297, 922, 273, 263])).
% 1.24/1.44 tff(1391,plain,
% 1.24/1.44 (r(s(elem!1), s(s(z)))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[473, 21, 284, 1390])).
% 1.24/1.44 tff(1392,plain,
% 1.24/1.44 (r(elem!1, s(s(z)))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[493, 998, 653])).
% 1.24/1.44 tff(1393,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(elem!1, s(elem!1))) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), s(s(z)))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(1394,plain,
% 1.24/1.44 (((~r(s(elem!1), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), s(s(z)))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(1395,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(elem!1), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), s(s(z))))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[1394])).
% 1.24/1.44 tff(1396,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(elem!1), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), s(s(z)))))),
% 1.24/1.44 inference(transitivity,[status(thm)],[1395, 1393])).
% 1.24/1.44 tff(1397,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(elem!1), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(elem!1, s(elem!1))))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(1398,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(elem!1, s(elem!1))) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), s(s(z))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[1397, 1396])).
% 1.24/1.44 tff(1399,plain,
% 1.24/1.44 (~r(elem!1, s(elem!1))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1398, 45, 1392, 1391])).
% 1.24/1.44 tff(1400,assumption,(~b(elem!1, s(elem!1))), introduced(assumption)).
% 1.24/1.44 tff(1401,plain,
% 1.24/1.44 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1)))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(1402,plain,
% 1.24/1.44 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1)))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(1403,plain,
% 1.24/1.44 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[1402, 1401])).
% 1.24/1.44 tff(1404,plain,
% 1.24/1.44 ((elem!1 = s(elem!1)) | r(elem!1, s(elem!1))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1403, 21, 1400])).
% 1.24/1.44 tff(1405,plain,
% 1.24/1.44 (elem!1 = s(elem!1)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1404, 1399])).
% 1.24/1.44 tff(1406,plain,
% 1.24/1.44 (s(s(elem!1)) = s(s(s(elem!1)))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[1405, 1389])).
% 1.24/1.44 tff(1407,plain,
% 1.24/1.44 (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))),
% 1.24/1.44 inference(transitivity,[status(thm)],[203, 1100, 307])).
% 1.24/1.44 tff(1408,plain,
% 1.24/1.44 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(s(elem!1))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[1407])).
% 1.24/1.44 tff(1409,plain,
% 1.24/1.44 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 1.24/1.44 inference(transitivity,[status(thm)],[208, 1408, 186, 307])).
% 1.24/1.44 tff(1410,plain,
% 1.24/1.44 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(elem!1))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[1409])).
% 1.24/1.44 tff(1411,plain,
% 1.24/1.44 (s(s(s(s(z)))) = elem!1),
% 1.24/1.44 inference(transitivity,[status(thm)],[211, 1410, 186, 1090])).
% 1.24/1.44 tff(1412,plain,
% 1.24/1.44 (~(s(s(s(s(z)))) = elem!1)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[242, 1090])).
% 1.24/1.44 tff(1413,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1412, 1411])).
% 1.24/1.44 tff(1414,plain,((~(s(s(s(s(s(s(z)))))) = elem!1)) | (~(s(s(elem!1)) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(1415,plain,
% 1.24/1.44 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1414, 1406])).
% 1.24/1.44 tff(1416,assumption,(r(z, elem!1)), introduced(assumption)).
% 1.24/1.44 tff(1417,plain,
% 1.24/1.44 (r(s(s(z)), elem!1)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[370, 960, 240])).
% 1.24/1.44 tff(1418,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, elem!1)) | (~r(s(s(s(s(s(s(z)))))), 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(z, elem!1)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(1419,plain,
% 1.24/1.44 (((~r(z, elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(z)))))), z))) <=> ((~r(z, elem!1)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(1420,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, elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(z, elem!1)) | (~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, elem!1)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), elem!1))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[1419])).
% 1.24/1.44 tff(1421,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, elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(z, elem!1)) | (~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, elem!1)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.24/1.44 inference(transitivity,[status(thm)],[1420, 1418])).
% 1.24/1.44 tff(1422,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, elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(1423,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, elem!1)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), elem!1))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[1422, 1421])).
% 1.24/1.44 tff(1424,plain,
% 1.24/1.44 (~r(s(s(s(s(s(s(z)))))), z)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1423, 45, 1416, 1094])).
% 1.24/1.44 tff(1425,plain,
% 1.24/1.44 (b(s(s(s(s(s(s(z)))))), z)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1022, 21, 1019, 1424])).
% 1.24/1.44 tff(1426,plain,
% 1.24/1.44 (~r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1172, 45, 1103, 1094])).
% 1.24/1.44 tff(1427,plain,
% 1.24/1.44 (b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1176, 21, 1123, 1426])).
% 1.24/1.44 tff(1428,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, 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)))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(1429,plain,
% 1.24/1.44 (((~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)))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(1430,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, 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))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[1429])).
% 1.24/1.44 tff(1431,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, 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)))),
% 1.24/1.44 inference(transitivity,[status(thm)],[1430, 1428])).
% 1.24/1.44 tff(1432,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, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(z)), z)))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(1433,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, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[1432, 1431])).
% 1.24/1.44 tff(1434,plain,
% 1.24/1.44 (~r(s(s(z)), z)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1433, 45, 1416, 1103])).
% 1.24/1.44 tff(1435,plain,
% 1.24/1.44 (b(s(s(z)), z)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[25, 1434])).
% 1.24/1.44 tff(1436,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, elem!1)) | (~r(z, s(s(z)))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(z)))) | (~r(s(s(z)), elem!1)))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(1437,plain,
% 1.24/1.44 (((~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(z, s(s(z)))) | (~r(s(s(z)), elem!1)))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(1438,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)), 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(z, s(s(z)))) | (~r(s(s(z)), elem!1))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[1437])).
% 1.24/1.44 tff(1439,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)), 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(z, s(s(z)))) | (~r(s(s(z)), elem!1)))),
% 1.24/1.44 inference(transitivity,[status(thm)],[1438, 1436])).
% 1.24/1.44 tff(1440,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)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(1441,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, elem!1)) | (~r(z, s(s(z)))) | (~r(s(s(z)), elem!1))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[1440, 1439])).
% 1.24/1.44 tff(1442,plain,
% 1.24/1.44 (~r(z, s(s(z)))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1441, 45, 1416, 1103])).
% 1.24/1.44 tff(1443,plain,
% 1.24/1.44 (b(z, s(s(z)))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[516, 1442])).
% 1.24/1.44 tff(1444,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(1445,plain,
% 1.24/1.45 (((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(1446,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), 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(X0, 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)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[1445])).
% 1.24/1.45 tff(1447,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), 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(X0, 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)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 1.24/1.45 inference(transitivity,[status(thm)],[1446, 1444])).
% 1.24/1.45 tff(1448,plain,
% 1.24/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(1449,plain,
% 1.24/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[1448, 1447])).
% 1.24/1.45 tff(1450,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1449, 128, 1443, 1435, 1427, 1425])).
% 1.24/1.45 tff(1451,plain,((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(1452,plain,
% 1.24/1.45 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1451, 1417, 1416])).
% 1.24/1.45 tff(1453,plain,
% 1.24/1.45 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1055, 1452, 1415])).
% 1.24/1.45 tff(1454,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(z, elem!1)) | (~r(s(s(s(s(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)))), elem!1)) | (~r(s(s(s(s(z)))), z)))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(1455,plain,
% 1.24/1.45 (((~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)))), elem!1)) | (~r(s(s(s(s(z)))), z)))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(1456,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(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)))), elem!1)) | (~r(s(s(s(s(z)))), z))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[1455])).
% 1.24/1.45 tff(1457,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(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)))), elem!1)) | (~r(s(s(s(s(z)))), z)))),
% 1.24/1.45 inference(transitivity,[status(thm)],[1456, 1454])).
% 1.24/1.45 tff(1458,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(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(1459,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(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[1458, 1457])).
% 1.24/1.45 tff(1460,plain,
% 1.24/1.45 (~r(s(s(s(s(z)))), z)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1459, 45, 1416, 1245])).
% 1.24/1.45 tff(1461,plain,
% 1.24/1.45 (b(s(s(s(s(z)))), z)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[589, 21, 586, 1460])).
% 1.24/1.45 tff(1462,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(s(s(s(z)))))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(1463,plain,
% 1.24/1.45 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(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(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(1464,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(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(X0, 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)), s(s(s(s(z))))))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[1463])).
% 1.24/1.45 tff(1465,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(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(X0, 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)), s(s(s(s(z)))))))),
% 1.24/1.45 inference(transitivity,[status(thm)],[1464, 1462])).
% 1.24/1.45 tff(1466,plain,
% 1.24/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(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)))))))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(1467,plain,
% 1.24/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z))))))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[1466, 1465])).
% 1.24/1.45 tff(1468,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1467, 128, 1443, 1435, 1344, 1461])).
% 1.24/1.45 tff(1469,plain,((~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(1470,plain,
% 1.24/1.45 (~r(s(s(s(s(z)))), elem!1)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1469, 1417, 1416])).
% 1.24/1.45 tff(1471,plain,
% 1.24/1.45 (b(s(s(s(s(z)))), elem!1)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[632, 1470, 243])).
% 1.24/1.45 tff(1472,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(1473,plain,
% 1.24/1.45 (((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(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(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(1474,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[1473])).
% 1.24/1.45 tff(1475,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.24/1.45 inference(transitivity,[status(thm)],[1474, 1472])).
% 1.24/1.45 tff(1476,plain,
% 1.24/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(1477,plain,
% 1.24/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[1476, 1475])).
% 1.24/1.45 tff(1478,plain,
% 1.24/1.45 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1477, 128, 297, 922, 1471, 1453])).
% 1.24/1.45 tff(1479,plain,
% 1.24/1.45 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1215, 21, 1212, 1478])).
% 1.24/1.45 tff(1480,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(1481,plain,
% 1.24/1.45 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(z))))))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(1482,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(z))))))))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[1481])).
% 1.24/1.45 tff(1483,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 1.24/1.45 inference(transitivity,[status(thm)],[1482, 1480])).
% 1.24/1.45 tff(1484,plain,
% 1.24/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(1485,plain,
% 1.24/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(z))))))))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[1484, 1483])).
% 1.24/1.45 tff(1486,plain,
% 1.24/1.45 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1485, 128, 297, 922, 1453])).
% 1.24/1.45 tff(1487,plain,
% 1.24/1.45 (r(s(z), s(s(s(s(s(s(z)))))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1041, 21, 1038, 1486])).
% 1.24/1.45 tff(1488,plain,
% 1.24/1.45 (~b(s(z), s(s(s(s(z)))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[928, 128, 297, 922, 1471])).
% 1.24/1.45 tff(1489,plain,
% 1.24/1.45 (r(s(z), s(s(s(s(z)))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[684, 21, 681, 1488])).
% 1.24/1.45 tff(1490,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(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(1491,plain,
% 1.24/1.45 (((~r(s(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(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(z))))))))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(1492,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(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(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(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[1491])).
% 1.24/1.45 tff(1493,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(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(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(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.24/1.45 inference(transitivity,[status(thm)],[1492, 1490])).
% 1.24/1.45 tff(1494,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(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(1495,plain,
% 1.24/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[1494, 1493])).
% 1.24/1.45 tff(1496,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1495, 45, 1489, 1487, 1479])).
% 1.24/1.45 tff(1497,plain,((~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~r(z, elem!1)) | (~(s(s(elem!1)) = elem!1)) | b(elem!1, s(elem!1)) | (~b(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(1498,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1497, 1386, 1375, 273, 795, 199, 269, 263])).
% 1.24/1.45 tff(1499,plain,((~b(s(s(z)), s(z))) | (~(s(s(elem!1)) = elem!1)) | (~b(s(elem!1), s(z))) | (~r(s(z), z)) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(elem!1), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(1500,plain,
% 1.24/1.45 (~b(s(s(z)), s(z))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1499, 199, 262, 171, 198, 260])).
% 1.24/1.45 tff(1501,plain,
% 1.24/1.45 (r(s(s(z)), s(z))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[86, 1500])).
% 1.24/1.45 tff(1502,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(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(1503,plain,
% 1.24/1.45 (((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(1504,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(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[1503])).
% 1.24/1.45 tff(1505,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(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 1.24/1.45 inference(transitivity,[status(thm)],[1504, 1502])).
% 1.24/1.45 tff(1506,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(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(z))))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(1507,plain,
% 1.24/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[1506, 1505])).
% 1.24/1.45 tff(1508,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1507, 45, 272, 35, 28])).
% 1.24/1.45 tff(1509,plain,((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(1510,plain,
% 1.24/1.45 (~r(s(s(z)), z)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1509, 35, 272])).
% 1.24/1.45 tff(1511,plain,
% 1.24/1.45 (b(s(s(z)), z)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[25, 1510])).
% 1.24/1.45 tff(1512,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1352, 45, 272, 1340, 1103, 35])).
% 1.24/1.45 tff(1513,plain,((~r(s(s(z)), elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(1514,plain,
% 1.24/1.45 (~r(s(s(z)), elem!1)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1513, 1340, 272, 35])).
% 1.24/1.45 tff(1515,plain,
% 1.24/1.45 (b(s(s(z)), elem!1)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[370, 1514, 959])).
% 1.24/1.45 tff(1516,plain,
% 1.24/1.45 (r(s(z), s(s(elem!1))) <=> r(s(z), elem!1)),
% 1.24/1.45 inference(monotonicity,[status(thm)],[199])).
% 1.24/1.45 tff(1517,plain,
% 1.24/1.45 (r(s(z), elem!1) <=> r(s(z), s(s(elem!1)))),
% 1.24/1.45 inference(symmetry,[status(thm)],[1516])).
% 1.24/1.45 tff(1518,plain,
% 1.24/1.45 (r(s(z), s(s(elem!1)))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[1340, 1517])).
% 1.24/1.45 tff(1519,assumption,(r(s(s(elem!1)), z)), introduced(assumption)).
% 1.24/1.45 tff(1520,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(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)))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(1521,plain,
% 1.24/1.45 (((~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)))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(1522,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)), 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))))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[1521])).
% 1.24/1.45 tff(1523,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)), 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)))))),
% 1.24/1.45 inference(transitivity,[status(thm)],[1522, 1520])).
% 1.24/1.45 tff(1524,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)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(1525,plain,
% 1.24/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1))))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[1524, 1523])).
% 1.24/1.45 tff(1526,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1525, 45, 272, 89, 1519])).
% 1.24/1.45 tff(1527,plain,((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(1528,plain,
% 1.24/1.45 (~r(s(s(elem!1)), z)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[1527, 1518, 272])).
% 1.24/1.45 tff(1529,plain,
% 1.24/1.45 (r(s(s(elem!1)), z) <=> r(elem!1, z)),
% 1.24/1.45 inference(monotonicity,[status(thm)],[199])).
% 1.24/1.45 tff(1530,plain,
% 1.24/1.45 (r(elem!1, z) <=> r(s(s(elem!1)), z)),
% 1.24/1.45 inference(symmetry,[status(thm)],[1529])).
% 1.24/1.45 tff(1531,plain,
% 1.24/1.45 (r(s(s(elem!1)), z)),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[1004, 1530])).
% 1.24/1.46 tff(1532,assumption,(~r(s(s(elem!1)), z)), introduced(assumption)).
% 1.24/1.46 tff(1533,plain,
% 1.24/1.46 ($false),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1532, 1531])).
% 1.24/1.46 tff(1534,plain,((~r(elem!1, z)) | r(s(s(elem!1)), z) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.46 tff(1535,plain,
% 1.24/1.46 (~r(elem!1, z)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1534, 1528, 199])).
% 1.24/1.46 tff(1536,plain,
% 1.24/1.46 (b(elem!1, z)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[574, 1535, 462])).
% 1.24/1.46 tff(1537,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, 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)))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(1538,plain,
% 1.24/1.46 (((~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)))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(1539,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, 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))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[1538])).
% 1.24/1.46 tff(1540,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, 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)))),
% 1.24/1.46 inference(transitivity,[status(thm)],[1539, 1537])).
% 1.24/1.46 tff(1541,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, elem!1)) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(z), z)))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(1542,plain,
% 1.24/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[1541, 1540])).
% 1.24/1.46 tff(1543,plain,
% 1.24/1.46 ($false),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1542, 45, 1416, 272, 1340])).
% 1.24/1.46 tff(1544,plain,((~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.46 tff(1545,plain,
% 1.24/1.46 (~r(z, elem!1)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1544, 1340, 272])).
% 1.24/1.46 tff(1546,plain,
% 1.24/1.46 (((~![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))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(1547,plain,
% 1.24/1.46 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = elem!1) | b(z, elem!1) | r(z, elem!1))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(1548,plain,
% 1.24/1.46 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = elem!1) | b(z, elem!1) | r(z, elem!1)),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[1547, 1546])).
% 1.24/1.46 tff(1549,plain,
% 1.24/1.46 ((z = elem!1) | b(z, elem!1) | r(z, elem!1)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1548, 21])).
% 1.24/1.46 tff(1550,plain,
% 1.24/1.46 (b(z, elem!1)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1549, 1545, 251])).
% 1.24/1.46 tff(1551,plain,
% 1.24/1.46 (((~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(1552,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(z)), 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(X0, 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(z)), elem!1))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[1551])).
% 1.24/1.46 tff(1553,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(z)), 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(X0, 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(z)), elem!1)))),
% 1.24/1.46 inference(transitivity,[status(thm)],[1552, 612])).
% 1.24/1.46 tff(1554,plain,
% 1.24/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(z)), 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(1555,plain,
% 1.24/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[1554, 1553])).
% 1.24/1.46 tff(1556,plain,
% 1.24/1.46 ($false),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1555, 128, 1550, 1536, 1515, 1511])).
% 1.24/1.46 tff(1557,plain,((~r(s(z), elem!1)) | (~(s(s(elem!1)) = elem!1)) | (~r(s(z), z)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.46 tff(1558,plain,
% 1.24/1.46 (~r(s(z), elem!1)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1557, 199, 171, 1501])).
% 1.24/1.46 tff(1559,plain,
% 1.24/1.46 (b(s(z), elem!1)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[665, 1558, 257])).
% 1.24/1.46 tff(1560,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, 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(z)), s(z))) | (~r(elem!1, s(s(z)))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(1561,plain,
% 1.24/1.46 (((~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(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(1562,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(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(s(s(z)), s(z))) | (~r(elem!1, s(s(z))))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[1561])).
% 1.24/1.46 tff(1563,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(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(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))))),
% 1.24/1.46 inference(transitivity,[status(thm)],[1562, 1560])).
% 1.24/1.46 tff(1564,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(z)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(1565,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, s(s(z))))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[1564, 1563])).
% 1.24/1.46 tff(1566,plain,
% 1.24/1.46 (~r(elem!1, s(s(z)))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1565, 45, 313, 35])).
% 1.24/1.46 tff(1567,plain,
% 1.24/1.46 (b(elem!1, s(s(z)))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[493, 1566, 653])).
% 1.24/1.46 tff(1568,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)), elem!1)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(1569,plain,
% 1.24/1.46 (((~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1))) <=> ((~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(1570,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, 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(z))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z)))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[1569])).
% 1.24/1.46 tff(1571,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, 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(z))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))),
% 1.24/1.46 inference(transitivity,[status(thm)],[1570, 1568])).
% 1.24/1.46 tff(1572,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, s(z))) | (~r(s(s(z)), elem!1)))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(1573,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)), elem!1)) | (~r(s(s(z)), s(z)))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[1572, 1571])).
% 1.24/1.46 tff(1574,plain,
% 1.24/1.46 (~r(s(s(z)), elem!1)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1573, 45, 313, 35])).
% 1.24/1.46 tff(1575,plain,
% 1.24/1.46 (b(s(s(z)), elem!1)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[370, 1574, 240])).
% 1.24/1.46 tff(1576,plain,
% 1.24/1.46 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[316, 313, 271, 199])).
% 1.24/1.46 tff(1577,plain,
% 1.24/1.46 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[321, 1576, 198])).
% 1.24/1.46 tff(1578,plain,
% 1.24/1.46 (r(s(s(elem!1)), s(z)) <=> r(elem!1, s(z))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[199])).
% 1.24/1.46 tff(1579,plain,
% 1.24/1.46 (r(elem!1, s(z)) <=> r(s(s(elem!1)), s(z))),
% 1.24/1.46 inference(symmetry,[status(thm)],[1578])).
% 1.24/1.46 tff(1580,plain,
% 1.24/1.46 (r(s(s(elem!1)), s(z))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[313, 1579])).
% 1.24/1.46 tff(1581,plain,
% 1.24/1.46 (~r(z, s(s(elem!1)))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[438, 1580, 1577])).
% 1.24/1.46 tff(1582,plain,
% 1.24/1.46 (b(z, s(s(elem!1)))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[160, 1581])).
% 1.24/1.46 tff(1583,plain,
% 1.24/1.46 (b(z, elem!1)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[457, 1582, 378])).
% 1.24/1.46 tff(1584,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(1585,plain,
% 1.24/1.46 (((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~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)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(1586,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[1585])).
% 1.24/1.46 tff(1587,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 1.24/1.46 inference(transitivity,[status(thm)],[1586, 1584])).
% 1.24/1.46 tff(1588,plain,
% 1.24/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, 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(1589,plain,
% 1.24/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[1588, 1587])).
% 1.24/1.46 tff(1590,plain,
% 1.24/1.46 (~b(s(s(z)), z)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1589, 128, 1583, 1575, 1567])).
% 1.24/1.46 tff(1591,plain,
% 1.24/1.46 (r(s(s(z)), z)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[25, 1590])).
% 1.24/1.46 tff(1592,plain,
% 1.24/1.46 (~b(z, s(s(z)))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[506, 1583, 240, 1566, 1574])).
% 1.24/1.46 tff(1593,plain,
% 1.24/1.46 (r(z, s(s(z)))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[516, 1592])).
% 1.24/1.46 tff(1594,plain,
% 1.24/1.46 (~r(s(z), s(s(z)))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[642, 1593, 272])).
% 1.24/1.46 tff(1595,plain,
% 1.24/1.46 (b(s(z), s(s(z)))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[648, 1594])).
% 1.24/1.46 tff(1596,plain,
% 1.24/1.46 (~b(s(z), elem!1)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[660, 128, 1575, 1567, 1595])).
% 1.24/1.46 tff(1597,plain,
% 1.24/1.46 (r(s(z), elem!1)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[665, 1596, 257])).
% 1.24/1.46 tff(1598,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), elem!1)) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(1599,plain,
% 1.24/1.46 (((~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)), s(z))) | (~r(s(s(z)), z)))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(1600,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(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)), s(z))) | (~r(s(s(z)), z))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[1599])).
% 1.24/1.46 tff(1601,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(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)), s(z))) | (~r(s(s(z)), z)))),
% 1.24/1.46 inference(transitivity,[status(thm)],[1600, 1598])).
% 1.24/1.46 tff(1602,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(s(s(z)), z)) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(1603,plain,
% 1.24/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[1602, 1601])).
% 1.24/1.46 tff(1604,plain,
% 1.24/1.46 ($false),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1603, 45, 272, 1597, 35, 1591])).
% 1.24/1.46 tff(1605,plain,((~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~(s(s(elem!1)) = elem!1)) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(elem!1), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.46 tff(1606,plain,
% 1.24/1.46 (~r(elem!1, s(z))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1605, 1501, 171, 199, 198, 260])).
% 1.24/1.46 tff(1607,plain,
% 1.24/1.46 (b(elem!1, s(z))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[305, 1606, 295])).
% 1.24/1.46 tff(1608,assumption,(~(z = elem!1)), introduced(assumption)).
% 1.24/1.46 tff(1609,plain,
% 1.24/1.46 (r(z, elem!1)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1549, 455, 1608])).
% 1.24/1.46 tff(1610,assumption,(~(s(z) = elem!1)), introduced(assumption)).
% 1.24/1.46 tff(1611,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z, s(z))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(1612,plain,
% 1.24/1.46 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(z, s(z))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(1613,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z, s(z)))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[1612])).
% 1.24/1.46 tff(1614,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z, s(z))))),
% 1.24/1.46 inference(transitivity,[status(thm)],[1613, 1611])).
% 1.24/1.46 tff(1615,plain,
% 1.24/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(1616,plain,
% 1.24/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(z, s(z)))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[1615, 1614])).
% 1.24/1.46 tff(1617,plain,
% 1.24/1.46 ($false),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1616, 128, 577, 297, 550, 922])).
% 1.24/1.46 tff(1618,plain,((~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.46 tff(1619,plain,
% 1.24/1.46 (~b(s(z), elem!1)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1618, 297, 577, 550])).
% 1.24/1.46 tff(1620,plain,
% 1.24/1.46 (r(s(z), elem!1)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[665, 1619, 1610])).
% 1.24/1.46 tff(1621,plain,
% 1.24/1.46 (~r(s(z), z)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1542, 45, 1416, 1620])).
% 1.24/1.46 tff(1622,plain,
% 1.24/1.46 (b(s(z), z)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[170, 1621])).
% 1.24/1.46 tff(1623,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(1624,plain,
% 1.24/1.46 (((~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(1625,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z)))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[1624])).
% 1.24/1.46 tff(1626,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))))),
% 1.24/1.46 inference(transitivity,[status(thm)],[1625, 1623])).
% 1.24/1.46 tff(1627,plain,
% 1.24/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(1628,plain,
% 1.24/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z)))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[1627, 1626])).
% 1.24/1.46 tff(1629,plain,
% 1.24/1.46 ($false),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1628, 128, 577, 297, 550, 1622])).
% 1.24/1.46 tff(1630,plain,((~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(z, s(z))) | (~r(z, elem!1)) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.24/1.46 tff(1631,plain,
% 1.24/1.46 (~b(elem!1, z)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1630, 550, 297, 1416, 1610])).
% 1.24/1.46 tff(1632,assumption,(~b(elem!1, z)), introduced(assumption)).
% 1.24/1.46 tff(1633,assumption,(elem!1 = s(z)), introduced(assumption)).
% 1.24/1.46 tff(1634,plain,
% 1.24/1.46 (b(z, elem!1) <=> b(z, s(z))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[1633])).
% 1.24/1.46 tff(1635,plain,
% 1.24/1.46 (b(z, s(z)) <=> b(z, elem!1)),
% 1.24/1.46 inference(symmetry,[status(thm)],[1634])).
% 1.24/1.46 tff(1636,plain,
% 1.24/1.46 (b(z, elem!1)),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[550, 1635])).
% 1.24/1.46 tff(1637,plain,
% 1.24/1.46 ($false),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[455, 1636])).
% 1.24/1.46 tff(1638,plain,((~(elem!1 = s(z))) | b(z, elem!1) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.46 tff(1639,plain,
% 1.24/1.46 (~(elem!1 = s(z))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1638, 550, 455])).
% 1.24/1.46 tff(1640,assumption,(s(z) = elem!1), introduced(assumption)).
% 1.24/1.46 tff(1641,plain,
% 1.24/1.46 (elem!1 = s(z)),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[1640, 252])).
% 1.24/1.46 tff(1642,assumption,(~(elem!1 = s(z))), introduced(assumption)).
% 1.24/1.46 tff(1643,plain,
% 1.24/1.46 ($false),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1642, 1641])).
% 1.24/1.46 tff(1644,plain,((~(s(z) = elem!1)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.46 tff(1645,plain,
% 1.24/1.46 (~(s(z) = elem!1)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1644, 1639])).
% 1.24/1.46 tff(1646,plain,
% 1.24/1.46 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1089, 1086])).
% 1.24/1.46 tff(1647,assumption,(z = elem!1), introduced(assumption)).
% 1.24/1.46 tff(1648,plain,
% 1.24/1.46 (s(z) = s(elem!1)),
% 1.24/1.46 inference(monotonicity,[status(thm)],[1647])).
% 1.24/1.46 tff(1649,plain,
% 1.24/1.46 (s(elem!1) = s(z)),
% 1.24/1.46 inference(symmetry,[status(thm)],[1648])).
% 1.24/1.46 tff(1650,plain,
% 1.24/1.46 (b(s(elem!1), s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[1649])).
% 1.24/1.46 tff(1651,plain,
% 1.24/1.46 (b(s(z), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.24/1.46 inference(symmetry,[status(thm)],[1650])).
% 1.24/1.46 tff(1652,plain,
% 1.24/1.46 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[1647])).
% 1.24/1.46 tff(1653,plain,
% 1.24/1.46 (b(elem!1, s(s(elem!1)))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[453, 1652])).
% 1.24/1.46 tff(1654,plain,
% 1.24/1.46 (b(s(z), z) <=> b(s(z), elem!1)),
% 1.24/1.46 inference(monotonicity,[status(thm)],[1647])).
% 1.24/1.46 tff(1655,plain,
% 1.24/1.46 (b(s(z), elem!1) <=> b(s(z), z)),
% 1.24/1.46 inference(symmetry,[status(thm)],[1654])).
% 1.24/1.46 tff(1656,plain,
% 1.24/1.46 (b(s(z), z)),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[922, 1655])).
% 1.24/1.46 tff(1657,plain,
% 1.24/1.46 ($false),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[164, 1656])).
% 1.24/1.46 tff(1658,plain,((~(z = elem!1)) | b(s(z), z) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.46 tff(1659,plain,
% 1.24/1.46 (~b(s(z), elem!1)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1658, 1647, 164])).
% 1.24/1.46 tff(1660,plain,
% 1.24/1.46 (r(s(z), elem!1)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[665, 1659, 1610])).
% 1.24/1.46 tff(1661,plain,
% 1.24/1.46 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 1.24/1.46 inference(monotonicity,[status(thm)],[1647])).
% 1.24/1.46 tff(1662,plain,
% 1.24/1.46 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), z)),
% 1.24/1.46 inference(symmetry,[status(thm)],[1661])).
% 1.24/1.46 tff(1663,assumption,(b(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.24/1.46 tff(1664,plain,
% 1.24/1.46 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1073, 1646])).
% 1.24/1.46 tff(1665,plain,
% 1.24/1.46 (r(s(elem!1), s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[1649])).
% 1.24/1.46 tff(1666,plain,
% 1.24/1.46 (r(s(z), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.24/1.46 inference(symmetry,[status(thm)],[1665])).
% 1.24/1.46 tff(1667,plain,
% 1.24/1.46 (r(s(elem!1), s(s(elem!1)))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[89, 1666])).
% 1.24/1.46 tff(1668,plain,
% 1.24/1.46 (elem!1 = z),
% 1.24/1.46 inference(symmetry,[status(thm)],[1647])).
% 1.24/1.46 tff(1669,plain,
% 1.24/1.46 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(elem!1)))), z)),
% 1.24/1.46 inference(monotonicity,[status(thm)],[1668])).
% 1.24/1.46 tff(1670,plain,
% 1.24/1.46 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.24/1.46 inference(symmetry,[status(thm)],[1669])).
% 1.24/1.46 tff(1671,plain,
% 1.24/1.46 (s(s(z)) = s(s(elem!1))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[1648])).
% 1.24/1.46 tff(1672,plain,
% 1.24/1.46 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[1671])).
% 1.24/1.46 tff(1673,plain,
% 1.24/1.46 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[1672])).
% 1.24/1.46 tff(1674,plain,
% 1.24/1.46 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(elem!1)))), z)),
% 1.24/1.46 inference(monotonicity,[status(thm)],[1673, 1668])).
% 1.24/1.46 tff(1675,plain,
% 1.24/1.46 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 1.24/1.46 inference(monotonicity,[status(thm)],[1647])).
% 1.24/1.46 tff(1676,plain,
% 1.24/1.46 ((~(s(s(s(s(z)))) = z)) <=> (~(s(s(s(s(z)))) = elem!1))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[1675])).
% 1.24/1.46 tff(1677,plain,
% 1.24/1.46 (~(s(s(s(s(z)))) = elem!1)),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[586, 1676])).
% 1.24/1.46 tff(1678,plain,
% 1.24/1.46 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[1065, 1063])).
% 1.24/1.46 tff(1679,plain,
% 1.24/1.46 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[803, 1678])).
% 1.24/1.46 tff(1680,plain,
% 1.24/1.46 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[693, 1678])).
% 1.24/1.46 tff(1681,assumption,(b(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.24/1.46 tff(1682,plain,
% 1.24/1.46 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1647])).
% 1.24/1.47 tff(1683,plain,
% 1.24/1.47 (r(elem!1, s(s(s(elem!1)))) <=> r(z, s(s(s(elem!1))))),
% 1.24/1.47 inference(symmetry,[status(thm)],[1682])).
% 1.24/1.47 tff(1684,plain,
% 1.24/1.47 ((~r(elem!1, s(s(s(elem!1))))) <=> (~r(z, s(s(s(elem!1)))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1683])).
% 1.24/1.47 tff(1685,plain,
% 1.24/1.47 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[700, 698])).
% 1.24/1.47 tff(1686,plain,
% 1.24/1.47 (r(s(s(s(s(elem!1)))), z) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1647])).
% 1.24/1.47 tff(1687,plain,
% 1.24/1.47 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(elem!1)))), z)),
% 1.24/1.47 inference(symmetry,[status(thm)],[1686])).
% 1.24/1.47 tff(1688,plain,
% 1.24/1.47 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1673])).
% 1.24/1.47 tff(1689,plain,
% 1.24/1.47 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(elem!1)))), z)),
% 1.24/1.47 inference(transitivity,[status(thm)],[1688, 1687])).
% 1.24/1.47 tff(1690,plain,
% 1.24/1.47 (r(s(s(s(s(elem!1)))), z)),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[1245, 1689])).
% 1.24/1.47 tff(1691,assumption,(~(s(s(s(elem!1))) = s(s(elem!1)))), introduced(assumption)).
% 1.24/1.47 tff(1692,plain,
% 1.24/1.47 (r(z, s(s(s(s(elem!1))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1647])).
% 1.24/1.47 tff(1693,plain,
% 1.24/1.47 (r(elem!1, s(s(s(s(elem!1))))) <=> r(z, s(s(s(s(elem!1)))))),
% 1.24/1.47 inference(symmetry,[status(thm)],[1692])).
% 1.24/1.47 tff(1694,plain,
% 1.24/1.47 ((z = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = z)),
% 1.24/1.47 inference(commutativity,[status(thm)],[])).
% 1.24/1.47 tff(1695,plain,
% 1.24/1.47 ((elem!1 = s(s(s(s(elem!1))))) <=> (z = s(s(s(s(elem!1)))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1668])).
% 1.24/1.47 tff(1696,plain,
% 1.24/1.47 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = z)),
% 1.24/1.47 inference(transitivity,[status(thm)],[1695, 1694])).
% 1.24/1.47 tff(1697,plain,
% 1.24/1.47 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.24/1.47 inference(symmetry,[status(thm)],[1696])).
% 1.24/1.47 tff(1698,plain,
% 1.24/1.47 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1697])).
% 1.24/1.47 tff(1699,plain,
% 1.24/1.47 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[176, 1698])).
% 1.24/1.47 tff(1700,plain,
% 1.24/1.47 (r(s(elem!1), elem!1) <=> r(s(z), elem!1)),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1649])).
% 1.24/1.47 tff(1701,plain,
% 1.24/1.47 (r(s(z), elem!1) <=> r(s(elem!1), elem!1)),
% 1.24/1.47 inference(symmetry,[status(thm)],[1700])).
% 1.24/1.47 tff(1702,plain,
% 1.24/1.47 (r(s(elem!1), elem!1)),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[1340, 1701])).
% 1.24/1.47 tff(1703,plain,
% 1.24/1.47 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[1245, 1688])).
% 1.24/1.47 tff(1704,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(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(1705,plain,
% 1.24/1.47 (((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(1706,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(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1705])).
% 1.24/1.47 tff(1707,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(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.24/1.47 inference(transitivity,[status(thm)],[1706, 1704])).
% 1.24/1.47 tff(1708,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(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(1709,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(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1))))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[1708, 1707])).
% 1.24/1.47 tff(1710,plain,
% 1.24/1.47 ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1))))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1709, 45, 1703])).
% 1.24/1.47 tff(1711,plain,
% 1.24/1.47 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1710, 1702])).
% 1.24/1.47 tff(1712,plain,
% 1.24/1.47 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 1.24/1.47 inference(commutativity,[status(thm)],[])).
% 1.24/1.47 tff(1713,plain,
% 1.24/1.47 ((s(s(s(s(elem!1)))) = s(z)) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1648])).
% 1.24/1.47 tff(1714,plain,
% 1.24/1.47 ((s(s(s(s(elem!1)))) = s(z)) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 1.24/1.47 inference(transitivity,[status(thm)],[1713, 1712])).
% 1.24/1.47 tff(1715,plain,
% 1.24/1.47 ((~(s(s(s(s(elem!1)))) = s(z))) <=> (~(s(elem!1) = s(s(s(s(elem!1))))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1714])).
% 1.24/1.47 tff(1716,assumption,(s(s(s(s(elem!1)))) = s(z)), introduced(assumption)).
% 1.24/1.47 tff(1717,plain,
% 1.24/1.47 (s(z) = s(s(s(s(elem!1))))),
% 1.24/1.47 inference(symmetry,[status(thm)],[1716])).
% 1.24/1.47 tff(1718,plain,
% 1.24/1.47 (inj_0(s(z)) = inj_0(s(s(s(s(elem!1)))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1717])).
% 1.24/1.47 tff(1719,plain,
% 1.24/1.47 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(z))),
% 1.24/1.47 inference(symmetry,[status(thm)],[1718])).
% 1.24/1.47 tff(1720,plain,
% 1.24/1.47 (s(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 1.24/1.47 inference(symmetry,[status(thm)],[233])).
% 1.24/1.47 tff(1721,plain,
% 1.24/1.47 (s(s(s(elem!1))) = z),
% 1.24/1.47 inference(transitivity,[status(thm)],[1720, 1719, 64])).
% 1.24/1.47 tff(1722,plain,
% 1.24/1.47 ($false),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[382, 1721])).
% 1.24/1.47 tff(1723,plain,(~(s(s(s(s(elem!1)))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.47 tff(1724,plain,
% 1.24/1.47 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[1723, 1715])).
% 1.24/1.47 tff(1725,plain,
% 1.24/1.47 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), s(s(s(s(elem!1))))) | r(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), s(s(s(s(elem!1))))) | r(s(elem!1), s(s(s(s(elem!1))))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(1726,plain,
% 1.24/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), s(s(s(s(elem!1))))) | r(s(elem!1), s(s(s(s(elem!1))))))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(1727,plain,
% 1.24/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), s(s(s(s(elem!1))))) | r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[1726, 1725])).
% 1.24/1.47 tff(1728,plain,
% 1.24/1.47 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1727, 21, 1724, 1711])).
% 1.24/1.47 tff(1729,plain,
% 1.24/1.47 (b(elem!1, s(elem!1)) <=> b(elem!1, s(z))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1649])).
% 1.24/1.47 tff(1730,plain,
% 1.24/1.47 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 1.24/1.47 inference(symmetry,[status(thm)],[1729])).
% 1.24/1.47 tff(1731,plain,
% 1.24/1.47 (b(z, s(z)) <=> b(elem!1, s(z))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1647])).
% 1.24/1.47 tff(1732,plain,
% 1.24/1.47 (b(elem!1, s(z))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[550, 1731])).
% 1.24/1.47 tff(1733,plain,
% 1.24/1.47 (b(elem!1, s(elem!1))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[1732, 1730])).
% 1.24/1.47 tff(1734,plain,
% 1.24/1.47 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1648])).
% 1.24/1.47 tff(1735,plain,
% 1.24/1.47 ((~r(s(s(s(s(elem!1)))), s(z))) <=> (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1734])).
% 1.24/1.47 tff(1736,assumption,(r(s(s(s(s(elem!1)))), z)), introduced(assumption)).
% 1.24/1.47 tff(1737,assumption,(r(s(s(s(s(elem!1)))), s(z))), introduced(assumption)).
% 1.24/1.47 tff(1738,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), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(1739,plain,
% 1.24/1.47 (((~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(1740,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), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(z)))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1739])).
% 1.24/1.47 tff(1741,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), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.24/1.47 inference(transitivity,[status(thm)],[1740, 1738])).
% 1.24/1.47 tff(1742,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), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(1743,plain,
% 1.24/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[1742, 1741])).
% 1.24/1.47 tff(1744,plain,
% 1.24/1.47 ($false),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1743, 45, 272, 1737, 1736])).
% 1.24/1.47 tff(1745,plain,((~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.47 tff(1746,plain,
% 1.24/1.47 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1745, 1690, 272])).
% 1.24/1.47 tff(1747,plain,
% 1.24/1.47 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[1746, 1735])).
% 1.24/1.47 tff(1748,plain,
% 1.24/1.47 ((s(elem!1) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 1.24/1.47 inference(symmetry,[status(thm)],[1712])).
% 1.24/1.47 tff(1749,plain,
% 1.24/1.47 ((s(s(s(s(elem!1)))) = s(z)) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 1.24/1.47 inference(transitivity,[status(thm)],[1714, 1748])).
% 1.24/1.47 tff(1750,plain,
% 1.24/1.47 ((~(s(s(s(s(elem!1)))) = s(z))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1749])).
% 1.24/1.47 tff(1751,plain,
% 1.24/1.47 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[1723, 1750])).
% 1.24/1.47 tff(1752,plain,
% 1.24/1.47 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(elem!1)) | b(s(s(s(s(elem!1)))), s(elem!1)) | r(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(elem!1)) | b(s(s(s(s(elem!1)))), s(elem!1)) | r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(1753,plain,
% 1.24/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(elem!1)) | b(s(s(s(s(elem!1)))), s(elem!1)) | r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(1754,plain,
% 1.24/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(elem!1)) | b(s(s(s(s(elem!1)))), s(elem!1)) | r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[1753, 1752])).
% 1.24/1.47 tff(1755,plain,
% 1.24/1.47 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1754, 21, 1751, 1747])).
% 1.24/1.47 tff(1756,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(1757,plain,
% 1.24/1.47 (((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1))))))) <=> ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(1758,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1)))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1757])).
% 1.24/1.47 tff(1759,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))))),
% 1.24/1.47 inference(transitivity,[status(thm)],[1758, 1756])).
% 1.24/1.47 tff(1760,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(1761,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1)))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[1760, 1759])).
% 1.24/1.47 tff(1762,plain,
% 1.24/1.47 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1761, 128, 1755, 1733, 1728])).
% 1.24/1.47 tff(1763,plain,
% 1.24/1.47 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(elem!1))))) | b(elem!1, s(s(s(s(elem!1))))) | r(elem!1, s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(elem!1))))) | b(elem!1, s(s(s(s(elem!1))))) | r(elem!1, s(s(s(s(elem!1))))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(1764,plain,
% 1.24/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(elem!1))))) | b(elem!1, s(s(s(s(elem!1))))) | r(elem!1, s(s(s(s(elem!1))))))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(1765,plain,
% 1.24/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(elem!1))))) | b(elem!1, s(s(s(s(elem!1))))) | r(elem!1, s(s(s(s(elem!1)))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[1764, 1763])).
% 1.24/1.47 tff(1766,plain,
% 1.24/1.47 ((elem!1 = s(s(s(s(elem!1))))) | b(elem!1, s(s(s(s(elem!1))))) | r(elem!1, s(s(s(s(elem!1)))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1765, 21])).
% 1.24/1.47 tff(1767,plain,
% 1.24/1.47 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1766, 1762, 1699])).
% 1.24/1.47 tff(1768,plain,
% 1.24/1.47 (r(z, s(s(s(s(elem!1)))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[1767, 1693])).
% 1.24/1.47 tff(1769,plain,
% 1.24/1.47 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1647])).
% 1.24/1.47 tff(1770,plain,
% 1.24/1.47 (b(elem!1, s(s(s(elem!1)))) <=> b(z, s(s(s(elem!1))))),
% 1.24/1.47 inference(symmetry,[status(thm)],[1769])).
% 1.24/1.47 tff(1771,plain,
% 1.24/1.47 ((~b(elem!1, s(s(s(elem!1))))) <=> (~b(z, s(s(s(elem!1)))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1770])).
% 1.24/1.47 tff(1772,assumption,(r(s(s(s(s(elem!1)))), s(s(s(elem!1))))), introduced(assumption)).
% 1.24/1.47 tff(1773,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(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(1774,plain,
% 1.24/1.47 (((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(1775,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(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1774])).
% 1.24/1.47 tff(1776,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(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.24/1.47 inference(transitivity,[status(thm)],[1775, 1773])).
% 1.24/1.47 tff(1777,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(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(1778,plain,
% 1.24/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[1777, 1776])).
% 1.24/1.47 tff(1779,plain,
% 1.24/1.47 ($false),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1778, 45, 1772, 1736, 520])).
% 1.24/1.47 tff(1780,plain,((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.47 tff(1781,plain,
% 1.24/1.47 (~r(s(s(s(elem!1))), z)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1780, 1772, 1736])).
% 1.24/1.47 tff(1782,assumption,(r(z, s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.24/1.47 tff(1783,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(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(1784,plain,
% 1.24/1.47 (((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1))))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(1785,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(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[1784])).
% 1.24/1.47 tff(1786,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(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.24/1.47 inference(transitivity,[status(thm)],[1785, 1783])).
% 1.24/1.47 tff(1787,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(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(1788,plain,
% 1.24/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[1787, 1786])).
% 1.24/1.47 tff(1789,plain,
% 1.24/1.47 ($false),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1788, 45, 1772, 424, 1782])).
% 1.24/1.47 tff(1790,plain,((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.47 tff(1791,plain,
% 1.24/1.47 (~r(z, s(s(s(elem!1))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[1790, 1772, 1782])).
% 1.24/1.47 tff(1792,plain,
% 1.24/1.47 (~b(s(z), s(s(s(elem!1))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[561, 1791, 550, 1781])).
% 1.24/1.47 tff(1793,plain,
% 1.24/1.47 (r(s(z), s(s(s(elem!1))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[339, 1792])).
% 1.24/1.47 tff(1794,assumption,(r(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 1.24/1.47 tff(1795,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(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(1796,plain,
% 1.24/1.47 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(1797,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(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1)))))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[1796])).
% 1.24/1.48 tff(1798,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(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.24/1.48 inference(transitivity,[status(thm)],[1797, 1795])).
% 1.24/1.48 tff(1799,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(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(1800,plain,
% 1.24/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1)))))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[1799, 1798])).
% 1.24/1.48 tff(1801,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1800, 45, 89, 323, 1794])).
% 1.24/1.48 tff(1802,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(1803,plain,
% 1.24/1.48 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1802, 1793, 89])).
% 1.24/1.48 tff(1804,plain,
% 1.24/1.48 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[889, 1803, 1691])).
% 1.24/1.48 tff(1805,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(1806,plain,
% 1.24/1.48 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(1807,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1)))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[1806])).
% 1.24/1.48 tff(1808,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))),
% 1.24/1.48 inference(transitivity,[status(thm)],[1807, 1805])).
% 1.24/1.48 tff(1809,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(1810,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1)))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[1809, 1808])).
% 1.24/1.48 tff(1811,plain,
% 1.24/1.48 (~b(elem!1, s(s(s(elem!1))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1810, 128, 1681, 1663, 1804, 1733])).
% 1.24/1.48 tff(1812,plain,
% 1.24/1.48 (~b(z, s(s(s(elem!1))))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[1811, 1771])).
% 1.24/1.48 tff(1813,plain,
% 1.24/1.48 (b(z, s(s(s(elem!1))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[858, 1791])).
% 1.24/1.48 tff(1814,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1813, 1812])).
% 1.24/1.48 tff(1815,plain,((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~(z = elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(1816,plain,
% 1.24/1.48 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1815, 1768, 1681, 1663, 1691, 89, 550, 1647, 1690])).
% 1.24/1.48 tff(1817,plain,
% 1.24/1.48 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(1818,plain,
% 1.24/1.48 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(1819,plain,
% 1.24/1.48 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[1818, 1817])).
% 1.24/1.48 tff(1820,plain,
% 1.24/1.48 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1819, 21])).
% 1.24/1.48 tff(1821,plain,
% 1.24/1.48 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1820, 1816, 1685])).
% 1.24/1.48 tff(1822,assumption,(~b(s(s(s(s(elem!1)))), s(z))), introduced(assumption)).
% 1.24/1.48 tff(1823,assumption,(~r(s(s(s(s(elem!1)))), s(z))), introduced(assumption)).
% 1.24/1.48 tff(1824,plain,
% 1.24/1.48 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z)))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(1825,plain,
% 1.24/1.48 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z)))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(1826,plain,
% 1.24/1.48 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[1825, 1824])).
% 1.24/1.48 tff(1827,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1826, 21, 1823, 1723, 1822])).
% 1.24/1.48 tff(1828,plain,(r(s(s(s(s(elem!1)))), s(z)) | b(s(s(s(s(elem!1)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(1829,plain,
% 1.24/1.48 (b(s(s(s(s(elem!1)))), s(z))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1828, 1746])).
% 1.24/1.48 tff(1830,assumption,(b(elem!1, s(elem!1))), introduced(assumption)).
% 1.24/1.48 tff(1831,plain,
% 1.24/1.48 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1802, 323, 89])).
% 1.24/1.48 tff(1832,plain,
% 1.24/1.48 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[889, 1831, 1691])).
% 1.24/1.48 tff(1833,plain,
% 1.24/1.48 (~b(elem!1, s(s(s(elem!1))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1810, 128, 1681, 1663, 1832, 1830])).
% 1.24/1.48 tff(1834,plain,
% 1.24/1.48 (~b(z, s(s(s(elem!1))))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[1833, 1771])).
% 1.24/1.48 tff(1835,plain,
% 1.24/1.48 (~r(z, s(s(s(elem!1))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[854, 323, 272])).
% 1.24/1.48 tff(1836,plain,
% 1.24/1.48 (b(z, s(s(s(elem!1))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[858, 1835])).
% 1.24/1.48 tff(1837,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1836, 1834])).
% 1.24/1.48 tff(1838,plain,((~r(s(z), s(s(s(elem!1))))) | (~(z = elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(1839,plain,
% 1.24/1.48 (~r(s(z), s(s(s(elem!1))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1838, 1733, 1681, 1663, 1647, 1691, 89, 272])).
% 1.24/1.48 tff(1840,plain,
% 1.24/1.48 (b(s(z), s(s(s(elem!1))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[339, 1839])).
% 1.24/1.48 tff(1841,assumption,(b(s(s(s(s(elem!1)))), s(z))), introduced(assumption)).
% 1.24/1.48 tff(1842,assumption,(b(s(s(s(s(elem!1)))), s(s(s(elem!1))))), introduced(assumption)).
% 1.24/1.48 tff(1843,assumption,(b(s(s(s(elem!1))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.24/1.48 tff(1844,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(1845,plain,
% 1.24/1.48 (((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z)))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(1846,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[1845])).
% 1.24/1.48 tff(1847,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.24/1.48 inference(transitivity,[status(thm)],[1846, 1844])).
% 1.24/1.48 tff(1848,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(1849,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[1848, 1847])).
% 1.24/1.48 tff(1850,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1849, 128, 549, 1843, 1842, 1841])).
% 1.24/1.48 tff(1851,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(1852,plain,
% 1.24/1.48 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1851, 1840, 1829, 1821])).
% 1.24/1.48 tff(1853,plain,
% 1.24/1.48 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(1854,plain,
% 1.24/1.48 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(1855,plain,
% 1.24/1.48 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[1854, 1853])).
% 1.24/1.48 tff(1856,plain,
% 1.24/1.48 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1855, 21])).
% 1.24/1.48 tff(1857,plain,
% 1.24/1.48 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1856, 1852, 698])).
% 1.24/1.48 tff(1858,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, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(1859,plain,
% 1.24/1.48 (((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(1860,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(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[1859])).
% 1.24/1.48 tff(1861,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(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.24/1.48 inference(transitivity,[status(thm)],[1860, 1858])).
% 1.24/1.48 tff(1862,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(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(1863,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, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[1862, 1861])).
% 1.24/1.48 tff(1864,plain,
% 1.24/1.48 (~r(elem!1, s(s(s(elem!1))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1863, 45, 1767, 1857])).
% 1.24/1.48 tff(1865,plain,
% 1.24/1.48 (~r(z, s(s(s(elem!1))))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[1864, 1684])).
% 1.24/1.48 tff(1866,assumption,(r(s(s(s(elem!1))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.24/1.48 tff(1867,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(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(1868,plain,
% 1.24/1.48 (((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(1869,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(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[1868])).
% 1.24/1.48 tff(1870,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(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.24/1.48 inference(transitivity,[status(thm)],[1869, 1867])).
% 1.24/1.48 tff(1871,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(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(1872,plain,
% 1.24/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[1871, 1870])).
% 1.24/1.48 tff(1873,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1872, 45, 1866, 520, 1736])).
% 1.24/1.48 tff(1874,plain,((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(1875,plain,
% 1.24/1.48 (~r(s(s(s(elem!1))), z)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1874, 1857, 1690])).
% 1.24/1.48 tff(1876,plain,
% 1.24/1.48 (r(z, s(s(s(elem!1))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[561, 1875, 550, 1840])).
% 1.24/1.48 tff(1877,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1876, 1865])).
% 1.24/1.48 tff(1878,plain,((~r(s(s(s(s(z)))), elem!1)) | (~(z = elem!1)) | (~b(z, s(z))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(1879,plain,
% 1.24/1.48 (~r(s(s(s(s(z)))), elem!1)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1878, 1681, 550, 1680, 1647, 1663, 1679, 89, 272, 1340])).
% 1.24/1.48 tff(1880,plain,
% 1.24/1.48 (b(s(s(s(s(z)))), elem!1)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[632, 1879, 1677])).
% 1.24/1.48 tff(1881,plain,
% 1.24/1.48 (b(s(s(s(s(elem!1)))), z)),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[1880, 1674])).
% 1.24/1.48 tff(1882,plain,
% 1.24/1.48 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[1881, 1670])).
% 1.24/1.48 tff(1883,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(1884,plain,
% 1.24/1.48 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(1885,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[1884])).
% 1.24/1.48 tff(1886,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.24/1.48 inference(transitivity,[status(thm)],[1885, 1883])).
% 1.24/1.48 tff(1887,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(1888,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[1887, 1886])).
% 1.24/1.48 tff(1889,plain,
% 1.24/1.48 ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1888, 128, 1681, 1663])).
% 1.24/1.48 tff(1890,plain,
% 1.24/1.48 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1889, 1882])).
% 1.24/1.48 tff(1891,assumption,(~b(s(s(s(s(elem!1)))), s(s(elem!1)))), introduced(assumption)).
% 1.24/1.48 tff(1892,assumption,(~r(s(s(s(s(elem!1)))), s(s(elem!1)))), introduced(assumption)).
% 1.24/1.48 tff(1893,plain,
% 1.24/1.48 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(elem!1))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(1894,plain,
% 1.24/1.48 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(elem!1))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(1895,plain,
% 1.24/1.48 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[1894, 1893])).
% 1.24/1.48 tff(1896,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1895, 21, 1892, 1063, 1891])).
% 1.24/1.48 tff(1897,plain,(b(s(s(s(s(elem!1)))), s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1))) | (s(s(s(s(elem!1)))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(1898,plain,
% 1.24/1.48 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1897, 1890, 1063])).
% 1.24/1.48 tff(1899,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(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(1900,plain,
% 1.24/1.48 (((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(1901,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(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1))))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[1900])).
% 1.24/1.48 tff(1902,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(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.24/1.49 inference(transitivity,[status(thm)],[1901, 1899])).
% 1.24/1.49 tff(1903,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(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(1904,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(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1))))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[1903, 1902])).
% 1.24/1.49 tff(1905,plain,
% 1.24/1.49 ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(elem!1))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1904, 45, 1898])).
% 1.24/1.49 tff(1906,plain,
% 1.24/1.49 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1905, 1667])).
% 1.24/1.49 tff(1907,plain,
% 1.24/1.49 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1727, 21, 1724, 1906])).
% 1.24/1.49 tff(1908,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(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1909,plain,
% 1.24/1.49 (((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1910,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(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[1909])).
% 1.24/1.49 tff(1911,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(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.24/1.49 inference(transitivity,[status(thm)],[1910, 1908])).
% 1.24/1.49 tff(1912,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(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(1913,plain,
% 1.24/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[1912, 1911])).
% 1.24/1.49 tff(1914,plain,
% 1.24/1.49 ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1913, 45, 1898])).
% 1.24/1.49 tff(1915,plain,
% 1.24/1.49 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1914, 1667, 1702])).
% 1.24/1.49 tff(1916,assumption,(~r(s(s(s(s(elem!1)))), s(elem!1))), introduced(assumption)).
% 1.24/1.49 tff(1917,assumption,(~b(s(s(s(s(elem!1)))), s(elem!1))), introduced(assumption)).
% 1.24/1.49 tff(1918,assumption,(~(s(s(s(s(elem!1)))) = s(elem!1))), introduced(assumption)).
% 1.24/1.49 tff(1919,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1754, 21, 1918, 1917, 1916])).
% 1.24/1.49 tff(1920,plain,(r(s(s(s(s(elem!1)))), s(elem!1)) | (s(s(s(s(elem!1)))) = s(elem!1)) | b(s(s(s(s(elem!1)))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(1921,plain,
% 1.24/1.49 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1920, 1915, 1751])).
% 1.24/1.49 tff(1922,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1923,plain,
% 1.24/1.49 (((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1))) <=> ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1924,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1)))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[1923])).
% 1.24/1.49 tff(1925,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))))),
% 1.24/1.49 inference(transitivity,[status(thm)],[1924, 1922])).
% 1.24/1.49 tff(1926,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(1927,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1)))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[1926, 1925])).
% 1.24/1.49 tff(1928,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1927, 128, 1921, 1733, 1882, 1907])).
% 1.24/1.49 tff(1929,plain,((~b(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~(z = elem!1)) | (~r(s(z), s(s(elem!1)))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(1930,plain,
% 1.24/1.49 (~b(s(s(elem!1)), elem!1)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1929, 89, 1647, 1340, 1664, 1663, 550, 272])).
% 1.24/1.49 tff(1931,plain,
% 1.24/1.49 (((~![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))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1932,plain,
% 1.24/1.49 ((~![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))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(1933,plain,
% 1.24/1.49 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1)),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[1932, 1931])).
% 1.24/1.49 tff(1934,plain,
% 1.24/1.49 ((s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1933, 21])).
% 1.24/1.49 tff(1935,plain,
% 1.24/1.49 (r(s(s(elem!1)), elem!1)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1934, 1930, 1086])).
% 1.24/1.49 tff(1936,plain,
% 1.24/1.49 (r(s(s(elem!1)), z)),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[1935, 1662])).
% 1.24/1.49 tff(1937,plain,
% 1.24/1.49 (~r(s(s(elem!1)), z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1527, 89, 272])).
% 1.24/1.49 tff(1938,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1937, 1936])).
% 1.24/1.49 tff(1939,plain,((~r(s(z), s(s(elem!1)))) | (~(z = elem!1)) | (s(s(elem!1)) = elem!1) | (~r(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(1940,plain,
% 1.24/1.49 (~r(s(z), s(s(elem!1)))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1939, 1647, 1086, 1660, 1653, 550, 171])).
% 1.24/1.49 tff(1941,plain,
% 1.24/1.49 (b(s(z), s(s(elem!1)))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[117, 1940])).
% 1.24/1.49 tff(1942,plain,
% 1.24/1.49 (b(s(elem!1), s(s(elem!1)))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[1941, 1651])).
% 1.24/1.49 tff(1943,plain,
% 1.24/1.49 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(z))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[1649])).
% 1.24/1.49 tff(1944,plain,
% 1.24/1.49 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), s(elem!1))),
% 1.24/1.49 inference(symmetry,[status(thm)],[1943])).
% 1.24/1.49 tff(1945,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1946,plain,
% 1.24/1.49 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1947,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1))))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[1946])).
% 1.24/1.49 tff(1948,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))))),
% 1.24/1.49 inference(transitivity,[status(thm)],[1947, 1945])).
% 1.24/1.49 tff(1949,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(1950,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1))))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[1949, 1948])).
% 1.24/1.49 tff(1951,plain,
% 1.24/1.49 ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1950, 128])).
% 1.24/1.49 tff(1952,plain,
% 1.24/1.49 (~b(s(s(elem!1)), elem!1)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1951, 1941, 1732, 1653])).
% 1.24/1.49 tff(1953,plain,
% 1.24/1.49 (r(s(s(elem!1)), elem!1)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1934, 1952, 1086])).
% 1.24/1.49 tff(1954,plain,
% 1.24/1.49 (r(s(s(elem!1)), z)),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[1953, 1662])).
% 1.24/1.49 tff(1955,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), 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))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1956,plain,
% 1.24/1.49 (((~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))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1957,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), 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)))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[1956])).
% 1.24/1.49 tff(1958,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), 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))))),
% 1.24/1.49 inference(transitivity,[status(thm)],[1957, 1955])).
% 1.24/1.49 tff(1959,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), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(1960,plain,
% 1.24/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z)))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[1959, 1958])).
% 1.24/1.49 tff(1961,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1960, 45, 325, 272, 1519])).
% 1.24/1.49 tff(1962,plain,((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(1963,plain,
% 1.24/1.49 (~r(s(s(elem!1)), s(z))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1962, 1954, 171])).
% 1.24/1.49 tff(1964,plain,
% 1.24/1.49 (b(s(s(elem!1)), s(z))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[292, 1963])).
% 1.24/1.49 tff(1965,plain,
% 1.24/1.49 (b(s(s(elem!1)), s(elem!1))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[1964, 1944])).
% 1.24/1.49 tff(1966,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, s(elem!1))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1967,plain,
% 1.24/1.49 (((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1968,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, s(elem!1)))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[1967])).
% 1.24/1.49 tff(1969,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, s(elem!1))))),
% 1.24/1.49 inference(transitivity,[status(thm)],[1968, 1966])).
% 1.24/1.49 tff(1970,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(1971,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1)))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[1970, 1969])).
% 1.24/1.49 tff(1972,plain,
% 1.24/1.49 ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1971, 128, 1653, 1733])).
% 1.24/1.49 tff(1973,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1972, 1965, 1942])).
% 1.24/1.49 tff(1974,plain,((~(z = elem!1)) | (s(s(elem!1)) = elem!1) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (s(z) = elem!1) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(1975,plain,
% 1.24/1.49 (~(z = elem!1)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1974, 453, 550, 1086, 1645, 164])).
% 1.24/1.49 tff(1976,plain,
% 1.24/1.49 (r(z, elem!1)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1549, 1975, 455])).
% 1.24/1.49 tff(1977,plain,
% 1.24/1.49 (~r(s(z), elem!1)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1544, 1976, 171])).
% 1.24/1.49 tff(1978,plain,
% 1.24/1.49 (b(s(z), elem!1)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[665, 1977, 1645])).
% 1.24/1.49 tff(1979,plain,
% 1.24/1.49 ((~(z = elem!1)) <=> (~(elem!1 = z))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[459])).
% 1.24/1.49 tff(1980,plain,
% 1.24/1.49 (~(elem!1 = z)),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[1975, 1979])).
% 1.24/1.49 tff(1981,plain,
% 1.24/1.49 (r(elem!1, z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[574, 1980, 1632])).
% 1.24/1.49 tff(1982,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), z)) | (~r(elem!1, s(z))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(elem!1, z)))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1983,plain,
% 1.24/1.49 (((~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z)))) <=> ((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(elem!1, z)))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1984,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), 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(s(z), z)) | (~r(elem!1, s(z))) | (~r(elem!1, z))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[1983])).
% 1.24/1.49 tff(1985,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), 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(s(z), z)) | (~r(elem!1, s(z))) | (~r(elem!1, z)))),
% 1.24/1.49 inference(transitivity,[status(thm)],[1984, 1982])).
% 1.24/1.49 tff(1986,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), z)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z))))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(1987,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), z)) | (~r(elem!1, s(z))) | (~r(elem!1, z))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[1986, 1985])).
% 1.24/1.49 tff(1988,plain,
% 1.24/1.49 (~r(elem!1, s(z))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1987, 45, 1981, 171])).
% 1.24/1.49 tff(1989,plain,
% 1.24/1.49 (b(elem!1, s(z))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[305, 1988, 1639])).
% 1.24/1.49 tff(1990,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(s(elem!1)))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1991,plain,
% 1.24/1.49 (((~b(s(z), elem!1)) | (~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), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1992,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~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(X0, 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), s(s(elem!1))))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[1991])).
% 1.24/1.49 tff(1993,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~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(X0, 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), s(s(elem!1)))))),
% 1.24/1.49 inference(transitivity,[status(thm)],[1992, 1990])).
% 1.24/1.49 tff(1994,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~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)))))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(1995,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(s(elem!1))))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[1994, 1993])).
% 1.24/1.49 tff(1996,plain,
% 1.24/1.49 ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1995, 128])).
% 1.24/1.49 tff(1997,plain,
% 1.24/1.49 (~b(s(s(elem!1)), elem!1)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1996, 876, 922, 297])).
% 1.24/1.49 tff(1998,plain,
% 1.24/1.49 (r(s(s(elem!1)), elem!1)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1934, 1997, 1086])).
% 1.24/1.49 tff(1999,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(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)))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(2000,plain,
% 1.24/1.49 (((~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)))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(2001,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(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))))),
% 1.24/1.50 inference(monotonicity,[status(thm)],[2000])).
% 1.24/1.50 tff(2002,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(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)))),
% 1.24/1.50 inference(transitivity,[status(thm)],[2001, 1999])).
% 1.24/1.50 tff(2003,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(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)))),
% 1.24/1.50 inference(quant_inst,[status(thm)],[])).
% 1.24/1.50 tff(2004,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(elem!1)), elem!1)) | (~r(s(s(elem!1)), z))),
% 1.24/1.50 inference(modus_ponens,[status(thm)],[2003, 2002])).
% 1.24/1.50 tff(2005,plain,
% 1.24/1.50 (~r(s(s(elem!1)), z)),
% 1.24/1.50 inference(unit_resolution,[status(thm)],[2004, 45, 1416, 1998])).
% 1.24/1.50 tff(2006,assumption,(b(s(s(elem!1)), z)), introduced(assumption)).
% 1.24/1.50 tff(2007,plain,
% 1.24/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(s(elem!1)))) | (~b(z, s(z))))),
% 1.24/1.50 inference(rewrite,[status(thm)],[])).
% 1.24/1.50 tff(2008,plain,
% 1.24/1.50 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z)))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(2009,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(s(elem!1)))) | (~b(z, s(z)))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[2008])).
% 1.34/1.50 tff(2010,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(s(elem!1)))) | (~b(z, s(z))))),
% 1.34/1.50 inference(transitivity,[status(thm)],[2009, 2007])).
% 1.34/1.50 tff(2011,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(2012,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z)))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[2011, 2010])).
% 1.34/1.50 tff(2013,plain,
% 1.34/1.50 ($false),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[2012, 128, 550, 453, 2006, 876])).
% 1.34/1.50 tff(2014,plain,((~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.50 tff(2015,plain,
% 1.34/1.50 (~b(s(s(elem!1)), z)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[2014, 876, 550, 453])).
% 1.34/1.50 tff(2016,plain,
% 1.34/1.50 (((~![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))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(2017,plain,
% 1.34/1.50 ((~![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))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(2018,plain,
% 1.34/1.50 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = z) | b(s(s(elem!1)), z) | r(s(s(elem!1)), z)),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[2017, 2016])).
% 1.34/1.50 tff(2019,plain,
% 1.34/1.50 ($false),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[2018, 21, 154, 2015, 2005])).
% 1.34/1.50 tff(2020,plain,((~b(s(z), s(s(elem!1)))) | (~r(z, elem!1)) | (s(s(elem!1)) = elem!1) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.50 tff(2021,plain,
% 1.34/1.50 (~b(s(z), s(s(elem!1)))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[2020, 1989, 1086, 550, 453, 1976, 1978])).
% 1.34/1.50 tff(2022,plain,
% 1.34/1.50 (r(s(z), s(s(elem!1)))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[117, 2021])).
% 1.34/1.50 tff(2023,plain,
% 1.34/1.50 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1073, 1069])).
% 1.34/1.50 tff(2024,plain,
% 1.34/1.50 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1065, 2023])).
% 1.34/1.50 tff(2025,plain,
% 1.34/1.50 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[803, 2024])).
% 1.34/1.50 tff(2026,plain,
% 1.34/1.50 (b(s(s(elem!1)), z)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[2018, 21, 154, 1937])).
% 1.34/1.50 tff(2027,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z, s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z, s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(2028,plain,
% 1.34/1.50 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(2029,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z, s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[2028])).
% 1.34/1.50 tff(2030,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z, s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 1.34/1.50 inference(transitivity,[status(thm)],[2029, 2027])).
% 1.34/1.50 tff(2031,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(2032,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[2031, 2030])).
% 1.34/1.50 tff(2033,plain,
% 1.34/1.50 ($false),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[2032, 128, 550, 453, 2026, 1832, 1836])).
% 1.34/1.50 tff(2034,plain,((~r(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.50 tff(2035,plain,
% 1.34/1.50 (~r(s(z), s(s(s(elem!1))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[2034, 453, 550, 2025, 89, 272])).
% 1.34/1.50 tff(2036,plain,
% 1.34/1.50 (b(s(z), s(s(s(elem!1))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[339, 2035])).
% 1.34/1.50 tff(2037,plain,
% 1.34/1.50 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[693, 2024])).
% 1.34/1.50 tff(2038,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(2039,plain,
% 1.34/1.50 (((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1))))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(2040,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[2039])).
% 1.34/1.50 tff(2041,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.34/1.50 inference(transitivity,[status(thm)],[2040, 2038])).
% 1.34/1.50 tff(2042,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(2043,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[2042, 2041])).
% 1.34/1.50 tff(2044,plain,
% 1.34/1.50 (~b(z, s(s(s(s(elem!1)))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[2043, 128, 297, 550, 922, 1841])).
% 1.34/1.50 tff(2045,plain,
% 1.34/1.50 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1))))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(2046,plain,
% 1.34/1.50 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1))))))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(2047,plain,
% 1.34/1.50 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1)))))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[2046, 2045])).
% 1.34/1.50 tff(2048,plain,
% 1.34/1.50 (r(z, s(s(s(s(elem!1)))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[2047, 21, 2044, 178])).
% 1.34/1.50 tff(2049,plain,
% 1.34/1.50 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1790, 2048, 424])).
% 1.34/1.50 tff(2050,plain,
% 1.34/1.50 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1820, 2049, 1685])).
% 1.34/1.50 tff(2051,plain,
% 1.34/1.50 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1851, 2050, 549, 1841])).
% 1.34/1.50 tff(2052,plain,
% 1.34/1.50 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1856, 2051, 698])).
% 1.34/1.50 tff(2053,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(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(2054,plain,
% 1.34/1.50 (((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(2055,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(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[2054])).
% 1.34/1.50 tff(2056,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(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.34/1.50 inference(transitivity,[status(thm)],[2055, 2053])).
% 1.34/1.50 tff(2057,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(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(2058,plain,
% 1.34/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[2057, 2056])).
% 1.34/1.50 tff(2059,plain,
% 1.34/1.50 ($false),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[2058, 45, 2052, 424, 2048])).
% 1.34/1.50 tff(2060,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.50 tff(2061,plain,
% 1.34/1.50 (~r(z, s(s(s(elem!1))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[2060, 1841, 2037, 2036, 297, 550, 922])).
% 1.34/1.50 tff(2062,plain,
% 1.34/1.50 (r(s(s(s(elem!1))), z)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[561, 2061, 550, 2036])).
% 1.34/1.50 tff(2063,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(2064,plain,
% 1.34/1.50 (((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(2065,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~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(X0, 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, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[2064])).
% 1.34/1.50 tff(2066,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~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(X0, 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, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 1.34/1.50 inference(transitivity,[status(thm)],[2065, 2063])).
% 1.34/1.50 tff(2067,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(2068,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[2067, 2066])).
% 1.34/1.50 tff(2069,plain,
% 1.34/1.50 ($false),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[2068, 128, 30, 297, 550, 453, 922])).
% 1.34/1.50 tff(2070,plain,((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.50 tff(2071,plain,
% 1.34/1.50 (~b(s(s(elem!1)), s(z))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[2070, 297, 550, 453, 922])).
% 1.34/1.50 tff(2072,plain,
% 1.34/1.50 (r(s(s(elem!1)), s(z))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[292, 2071])).
% 1.34/1.50 tff(2073,plain,
% 1.34/1.50 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[700, 2037])).
% 1.34/1.50 tff(2074,plain,
% 1.34/1.50 (~r(s(s(s(s(elem!1)))), z)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1780, 1772, 520])).
% 1.34/1.50 tff(2075,assumption,(~b(s(s(s(s(elem!1)))), z)), introduced(assumption)).
% 1.34/1.50 tff(2076,assumption,(~r(s(s(s(s(elem!1)))), z)), introduced(assumption)).
% 1.34/1.50 tff(2077,plain,
% 1.34/1.50 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = z) | b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = z) | b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(2078,plain,
% 1.34/1.50 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = z) | b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(2079,plain,
% 1.34/1.50 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = z) | b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z)),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[2078, 2077])).
% 1.34/1.50 tff(2080,plain,
% 1.34/1.50 ($false),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[2079, 21, 176, 2076, 2075])).
% 1.34/1.50 tff(2081,plain,(b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.50 tff(2082,plain,
% 1.34/1.50 (b(s(s(s(s(elem!1)))), z)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[2081, 2074])).
% 1.34/1.50 tff(2083,assumption,(b(s(s(s(s(elem!1)))), z)), introduced(assumption)).
% 1.34/1.50 tff(2084,assumption,(b(s(s(s(s(elem!1)))), s(s(elem!1)))), introduced(assumption)).
% 1.34/1.50 tff(2085,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(2086,plain,
% 1.34/1.51 (((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(2087,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[2086])).
% 1.34/1.51 tff(2088,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.34/1.51 inference(transitivity,[status(thm)],[2087, 2085])).
% 1.34/1.51 tff(2089,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(2090,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[2089, 2088])).
% 1.34/1.51 tff(2091,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[2090, 128, 453, 2006, 2084, 2083])).
% 1.34/1.51 tff(2092,plain,((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(2093,plain,
% 1.34/1.51 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[2092, 2082, 2026, 453])).
% 1.34/1.51 tff(2094,plain,
% 1.34/1.51 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1897, 2093, 1063])).
% 1.34/1.51 tff(2095,assumption,(r(s(s(s(s(elem!1)))), s(s(elem!1)))), introduced(assumption)).
% 1.34/1.51 tff(2096,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(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(2097,plain,
% 1.34/1.51 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(2098,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)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[2097])).
% 1.34/1.51 tff(2099,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)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.34/1.51 inference(transitivity,[status(thm)],[2098, 2096])).
% 1.34/1.51 tff(2100,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)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(2101,plain,
% 1.34/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[2100, 2099])).
% 1.34/1.51 tff(2102,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[2101, 45, 2095, 324, 1772])).
% 1.34/1.51 tff(2103,plain,((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(2104,plain,
% 1.34/1.51 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[2103, 2094, 1772])).
% 1.34/1.51 tff(2105,plain,
% 1.34/1.51 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[321, 2104, 1678])).
% 1.34/1.51 tff(2106,assumption,(b(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 1.34/1.51 tff(2107,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(2108,plain,
% 1.34/1.51 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(2109,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[2108])).
% 1.34/1.51 tff(2110,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.34/1.51 inference(transitivity,[status(thm)],[2109, 2107])).
% 1.34/1.51 tff(2111,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(2112,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[2111, 2110])).
% 1.34/1.51 tff(2113,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[2112, 128, 30, 2106, 549, 875])).
% 1.34/1.51 tff(2114,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(2115,plain,
% 1.34/1.51 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[2114, 2106, 30, 549])).
% 1.34/1.51 tff(2116,plain,
% 1.34/1.51 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[889, 2115, 1691])).
% 1.34/1.51 tff(2117,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(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(2118,plain,
% 1.34/1.51 (((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(2119,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(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z)))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[2118])).
% 1.34/1.51 tff(2120,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(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.34/1.51 inference(transitivity,[status(thm)],[2119, 2117])).
% 1.34/1.51 tff(2121,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(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(2122,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(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z)))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[2121, 2120])).
% 1.34/1.51 tff(2123,plain,
% 1.34/1.51 (~r(s(s(s(elem!1))), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[2122, 45, 272, 89, 2116])).
% 1.34/1.51 tff(2124,plain,
% 1.34/1.51 (b(s(s(s(elem!1))), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[195, 2123, 191])).
% 1.34/1.51 tff(2125,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(2126,plain,
% 1.34/1.51 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(2127,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[2126])).
% 1.34/1.51 tff(2128,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.34/1.51 inference(transitivity,[status(thm)],[2127, 2125])).
% 1.34/1.51 tff(2129,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(2130,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[2129, 2128])).
% 1.34/1.51 tff(2131,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[2130, 128, 30, 2106, 549, 2124])).
% 1.34/1.51 tff(2132,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(2133,plain,
% 1.34/1.51 (~b(s(s(elem!1)), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[2132, 2105, 272, 89, 549, 1679])).
% 1.34/1.51 tff(2134,plain,
% 1.34/1.51 (r(s(s(elem!1)), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[292, 2133])).
% 1.34/1.51 tff(2135,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)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(2136,plain,
% 1.34/1.51 (((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(2137,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)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[2136])).
% 1.34/1.51 tff(2138,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)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.34/1.51 inference(transitivity,[status(thm)],[2137, 2135])).
% 1.34/1.51 tff(2139,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)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(2140,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)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[2139, 2138])).
% 1.34/1.51 tff(2141,plain,
% 1.34/1.51 ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[2140, 45])).
% 1.34/1.51 tff(2142,plain,
% 1.34/1.51 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[2141, 2134, 2094])).
% 1.34/1.51 tff(2143,plain,
% 1.34/1.51 (b(s(s(s(s(elem!1)))), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1828, 2142])).
% 1.34/1.51 tff(2144,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(2145,plain,
% 1.34/1.51 (((~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(2146,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[2145])).
% 1.34/1.51 tff(2147,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.34/1.51 inference(transitivity,[status(thm)],[2146, 2144])).
% 1.34/1.51 tff(2148,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(2149,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[2148, 2147])).
% 1.34/1.51 tff(2150,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[2149, 128, 297, 550, 922, 2143, 2082])).
% 1.34/1.51 tff(2151,plain,((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(2152,plain,
% 1.34/1.51 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[2151, 2062, 550, 922, 272, 89, 2036, 2023, 453, 297])).
% 1.34/1.51 tff(2153,plain,
% 1.34/1.51 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1820, 2152, 2073])).
% 1.34/1.51 tff(2154,assumption,(~(s(z) = s(s(s(elem!1))))), introduced(assumption)).
% 1.34/1.51 tff(2155,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, s(z))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(2156,plain,
% 1.34/1.51 (((~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(2157,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, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(z)))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[2156])).
% 1.34/1.51 tff(2158,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, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.34/1.51 inference(transitivity,[status(thm)],[2157, 2155])).
% 1.34/1.51 tff(2159,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, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(2160,plain,
% 1.34/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[2159, 2158])).
% 1.34/1.52 tff(2161,plain,
% 1.34/1.52 (~r(s(s(s(s(elem!1)))), z)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2160, 45, 27, 1737])).
% 1.34/1.52 tff(2162,plain,
% 1.34/1.52 (b(s(s(s(s(elem!1)))), z)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2079, 21, 176, 2161])).
% 1.34/1.52 tff(2163,plain,
% 1.34/1.52 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2141, 1737, 325])).
% 1.34/1.52 tff(2164,plain,
% 1.34/1.52 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1895, 21, 2163, 1063])).
% 1.34/1.52 tff(2165,plain,
% 1.34/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(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(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(2166,plain,
% 1.34/1.52 (((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z))) <=> ((~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(2167,plain,
% 1.34/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z)))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[2166])).
% 1.34/1.52 tff(2168,plain,
% 1.34/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))),
% 1.34/1.52 inference(transitivity,[status(thm)],[2167, 2165])).
% 1.34/1.52 tff(2169,plain,
% 1.34/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(2170,plain,
% 1.34/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z)))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[2169, 2168])).
% 1.34/1.52 tff(2171,plain,
% 1.34/1.52 (~r(s(s(elem!1)), z)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2170, 45, 325, 27])).
% 1.34/1.52 tff(2172,plain,
% 1.34/1.52 (b(s(s(elem!1)), z)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2018, 21, 154, 2171])).
% 1.34/1.52 tff(2173,plain,
% 1.34/1.52 (~r(z, s(s(elem!1)))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[405, 27, 325])).
% 1.34/1.52 tff(2174,plain,
% 1.34/1.52 (b(z, s(s(elem!1)))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[160, 2173])).
% 1.34/1.52 tff(2175,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2090, 128, 2174, 2172, 2164, 2162])).
% 1.34/1.52 tff(2176,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(2177,plain,
% 1.34/1.52 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2176, 27, 1063, 325])).
% 1.34/1.52 tff(2178,plain,
% 1.34/1.52 (b(s(s(s(s(elem!1)))), s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1826, 21, 2177, 1723])).
% 1.34/1.52 tff(2179,plain,
% 1.34/1.52 (~b(s(z), s(s(s(elem!1))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1851, 2178, 1842, 1843])).
% 1.34/1.52 tff(2180,plain,
% 1.34/1.52 (r(s(z), s(s(s(elem!1))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[338, 2179, 2154])).
% 1.34/1.52 tff(2181,plain,
% 1.34/1.52 (~r(s(s(s(elem!1))), z)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1307, 2180, 272])).
% 1.34/1.52 tff(2182,plain,
% 1.34/1.52 (b(s(s(s(elem!1))), z)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[547, 21, 382, 2181])).
% 1.34/1.52 tff(2183,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(2184,plain,
% 1.34/1.52 (((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(2185,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[2184])).
% 1.34/1.52 tff(2186,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 1.34/1.52 inference(transitivity,[status(thm)],[2185, 2183])).
% 1.34/1.52 tff(2187,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(2188,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[2187, 2186])).
% 1.34/1.52 tff(2189,plain,
% 1.34/1.52 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2188, 128, 2174, 2172, 2182])).
% 1.34/1.52 tff(2190,plain,
% 1.34/1.52 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[321, 2189, 691])).
% 1.34/1.52 tff(2191,plain,
% 1.34/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(2192,plain,
% 1.34/1.52 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(2193,plain,
% 1.34/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~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)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[2192])).
% 1.34/1.52 tff(2194,plain,
% 1.34/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~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)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.34/1.52 inference(transitivity,[status(thm)],[2193, 2191])).
% 1.34/1.52 tff(2195,plain,
% 1.34/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(2196,plain,
% 1.34/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[2195, 2194])).
% 1.34/1.52 tff(2197,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2196, 45, 325, 272, 2190, 2180])).
% 1.34/1.52 tff(2198,plain,((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(z) = s(s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(2199,plain,
% 1.34/1.52 (~r(z, s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2198, 272, 325, 691, 2154, 1842, 1843, 1070])).
% 1.34/1.52 tff(2200,plain,
% 1.34/1.52 (b(z, s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[415, 2199])).
% 1.34/1.52 tff(2201,plain,
% 1.34/1.52 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1851, 549, 1842, 1843])).
% 1.34/1.52 tff(2202,plain,
% 1.34/1.52 (r(s(s(s(s(elem!1)))), s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1826, 21, 1723, 2201])).
% 1.34/1.52 tff(2203,plain,
% 1.34/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(2204,plain,
% 1.34/1.52 (((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(2205,plain,
% 1.34/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z)))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[2204])).
% 1.34/1.52 tff(2206,plain,
% 1.34/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.34/1.52 inference(transitivity,[status(thm)],[2205, 2203])).
% 1.34/1.52 tff(2207,plain,
% 1.34/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(2208,plain,
% 1.34/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[2207, 2206])).
% 1.34/1.52 tff(2209,plain,
% 1.34/1.52 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2208, 45, 325, 2202])).
% 1.34/1.52 tff(2210,plain,
% 1.34/1.52 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(s(elem!1))))) | r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(s(elem!1))))) | r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(2211,plain,
% 1.34/1.52 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(s(elem!1))))) | r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(2212,plain,
% 1.34/1.52 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(s(elem!1))))) | r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[2211, 2210])).
% 1.34/1.52 tff(2213,plain,
% 1.34/1.52 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2212, 21, 2209, 1069])).
% 1.34/1.52 tff(2214,plain,
% 1.34/1.52 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2141, 2202, 325])).
% 1.34/1.52 tff(2215,plain,
% 1.34/1.52 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1895, 21, 2214, 1070])).
% 1.34/1.52 tff(2216,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(2217,plain,
% 1.34/1.52 (((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(2218,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[2217])).
% 1.34/1.52 tff(2219,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.34/1.52 inference(transitivity,[status(thm)],[2218, 2216])).
% 1.34/1.52 tff(2220,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(2221,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[2220, 2219])).
% 1.34/1.52 tff(2222,plain,
% 1.34/1.52 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2221, 128, 1843, 1842, 2213])).
% 1.34/1.52 tff(2223,plain,
% 1.34/1.52 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[321, 2222, 691])).
% 1.34/1.52 tff(2224,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(2225,plain,
% 1.34/1.52 (((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(2226,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[2225])).
% 1.34/1.52 tff(2227,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.34/1.52 inference(transitivity,[status(thm)],[2226, 2224])).
% 1.34/1.52 tff(2228,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(2229,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[2228, 2227])).
% 1.34/1.52 tff(2230,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2229, 128, 550, 549, 1843, 1842, 874])).
% 1.34/1.52 tff(2231,plain,((~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(2232,plain,
% 1.34/1.52 (~b(z, s(s(s(elem!1))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2231, 549, 550, 1843, 1842])).
% 1.34/1.52 tff(2233,plain,
% 1.34/1.52 ((z = s(s(s(elem!1)))) | r(z, s(s(s(elem!1))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[436, 21, 2232])).
% 1.34/1.52 tff(2234,plain,
% 1.34/1.52 (r(z, s(s(s(elem!1))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2233, 543])).
% 1.34/1.52 tff(2235,plain,
% 1.34/1.52 (~r(z, s(s(elem!1)))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[432, 2234, 325, 2223])).
% 1.34/1.52 tff(2236,plain,
% 1.34/1.52 (b(z, s(s(elem!1)))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[160, 2235])).
% 1.34/1.52 tff(2237,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(2238,plain,
% 1.34/1.52 (((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(2239,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[2238])).
% 1.34/1.52 tff(2240,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.34/1.52 inference(transitivity,[status(thm)],[2239, 2237])).
% 1.34/1.52 tff(2241,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(2242,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[2241, 2240])).
% 1.34/1.52 tff(2243,plain,
% 1.34/1.52 (~b(s(s(s(s(elem!1)))), z)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2242, 128, 2236, 1842, 2215, 2213])).
% 1.34/1.52 tff(2244,plain,
% 1.34/1.52 (r(s(s(s(s(elem!1)))), z)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[2079, 21, 176, 2243])).
% 1.34/1.52 tff(2245,plain,
% 1.34/1.52 ((s(z) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(z))),
% 1.34/1.52 inference(commutativity,[status(thm)],[])).
% 1.34/1.52 tff(2246,plain,
% 1.34/1.52 ((s(s(s(s(elem!1)))) = s(z)) <=> (s(z) = s(s(s(s(elem!1)))))),
% 1.34/1.52 inference(symmetry,[status(thm)],[2245])).
% 1.34/1.52 tff(2247,plain,
% 1.34/1.52 ((~(s(s(s(s(elem!1)))) = s(z))) <=> (~(s(z) = s(s(s(s(elem!1))))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[2246])).
% 1.34/1.52 tff(2248,plain,
% 1.34/1.52 (~(s(z) = s(s(s(s(elem!1)))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[1723, 2247])).
% 1.34/1.52 tff(2249,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(2250,plain,
% 1.34/1.52 (((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1))))))) <=> ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(2251,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[2250])).
% 1.34/1.52 tff(2252,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[2251, 2249])).
% 1.34/1.53 tff(2253,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(2254,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[2253, 2252])).
% 1.34/1.53 tff(2255,plain,
% 1.34/1.53 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2254, 128, 549, 1843, 1842])).
% 1.34/1.53 tff(2256,plain,
% 1.34/1.53 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(elem!1))))) | b(s(z), s(s(s(s(elem!1))))) | r(s(z), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(elem!1))))) | b(s(z), s(s(s(s(elem!1))))) | r(s(z), s(s(s(s(elem!1))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(2257,plain,
% 1.34/1.53 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(elem!1))))) | b(s(z), s(s(s(s(elem!1))))) | r(s(z), s(s(s(s(elem!1))))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(2258,plain,
% 1.34/1.53 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(elem!1))))) | b(s(z), s(s(s(s(elem!1))))) | r(s(z), s(s(s(s(elem!1)))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[2257, 2256])).
% 1.34/1.53 tff(2259,plain,
% 1.34/1.53 ((s(z) = s(s(s(s(elem!1))))) | r(s(z), s(s(s(s(elem!1)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2258, 21, 2255])).
% 1.34/1.53 tff(2260,plain,
% 1.34/1.53 (r(s(z), s(s(s(s(elem!1)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2259, 2248])).
% 1.34/1.53 tff(2261,plain,
% 1.34/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(2262,plain,
% 1.34/1.53 (((~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), s(s(s(s(elem!1))))))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(2263,plain,
% 1.34/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[2262])).
% 1.34/1.53 tff(2264,plain,
% 1.34/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.34/1.53 inference(transitivity,[status(thm)],[2263, 2261])).
% 1.34/1.53 tff(2265,plain,
% 1.34/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(2266,plain,
% 1.34/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[2265, 2264])).
% 1.34/1.53 tff(2267,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2266, 45, 272, 2260, 2244])).
% 1.34/1.53 tff(2268,plain,((~b(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(2269,plain,
% 1.34/1.53 (~b(s(z), s(s(s(elem!1))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2268, 272, 1842, 325, 2200, 1843, 691, 1069])).
% 1.34/1.53 tff(2270,plain,
% 1.34/1.53 (r(s(z), s(s(s(elem!1))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[338, 2269, 2154])).
% 1.34/1.53 tff(2271,plain,
% 1.34/1.53 (~r(z, s(s(s(elem!1))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[854, 272, 2270])).
% 1.34/1.53 tff(2272,plain,
% 1.34/1.53 ((z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[436, 21, 2271])).
% 1.34/1.53 tff(2273,plain,
% 1.34/1.53 (b(z, s(s(s(elem!1))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2272, 543])).
% 1.34/1.53 tff(2274,plain,
% 1.34/1.53 ((s(s(s(s(elem!1)))) = z) <=> (z = s(s(s(s(elem!1)))))),
% 1.34/1.53 inference(symmetry,[status(thm)],[1694])).
% 1.34/1.53 tff(2275,plain,
% 1.34/1.53 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(z = s(s(s(s(elem!1))))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[2274])).
% 1.34/1.53 tff(2276,plain,
% 1.34/1.53 (~(z = s(s(s(s(elem!1)))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[176, 2275])).
% 1.34/1.53 tff(2277,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(2278,plain,
% 1.34/1.53 (((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(2279,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[2278])).
% 1.34/1.53 tff(2280,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[2279, 2277])).
% 1.34/1.53 tff(2281,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(2282,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[2281, 2280])).
% 1.34/1.53 tff(2283,plain,
% 1.34/1.53 (~b(z, s(s(s(s(elem!1)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2282, 128, 1843, 1842, 874])).
% 1.34/1.53 tff(2284,plain,
% 1.34/1.53 ((z = s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2047, 21, 2283])).
% 1.34/1.53 tff(2285,plain,
% 1.34/1.53 (r(z, s(s(s(s(elem!1)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2284, 2276])).
% 1.34/1.53 tff(2286,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(2287,plain,
% 1.34/1.53 (((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(2288,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[2287])).
% 1.34/1.53 tff(2289,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[2288, 2286])).
% 1.34/1.53 tff(2290,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(2291,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[2290, 2289])).
% 1.34/1.53 tff(2292,plain,
% 1.34/1.53 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2291, 128, 2106, 1843, 1842])).
% 1.34/1.53 tff(2293,plain,
% 1.34/1.53 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1895, 21, 1063, 2292])).
% 1.34/1.53 tff(2294,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(2295,plain,
% 1.34/1.53 (((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(2296,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[2295])).
% 1.34/1.53 tff(2297,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[2296, 2294])).
% 1.34/1.53 tff(2298,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(2299,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[2298, 2297])).
% 1.34/1.53 tff(2300,plain,
% 1.34/1.53 (~b(z, s(s(elem!1)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2299, 128, 2106, 1843, 1842, 874])).
% 1.34/1.53 tff(2301,plain,
% 1.34/1.53 (r(z, s(s(elem!1)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[160, 2300])).
% 1.34/1.53 tff(2302,plain,
% 1.34/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(2303,plain,
% 1.34/1.53 (((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1))))))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(2304,plain,
% 1.34/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1))))))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[2303])).
% 1.34/1.53 tff(2305,plain,
% 1.34/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[2304, 2302])).
% 1.34/1.53 tff(2306,plain,
% 1.34/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(2307,plain,
% 1.34/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1))))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[2306, 2305])).
% 1.34/1.53 tff(2308,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2307, 45, 2301, 2293, 2285])).
% 1.34/1.53 tff(2309,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(2310,plain,
% 1.34/1.53 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2309, 2273, 1843, 1842, 1070])).
% 1.34/1.53 tff(2311,plain,
% 1.34/1.53 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[321, 2310, 691])).
% 1.34/1.53 tff(2312,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2196, 45, 325, 272, 2311, 2270])).
% 1.34/1.53 tff(2313,plain,((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (s(z) = s(s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(2314,plain,
% 1.34/1.53 ((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2313, 190])).
% 1.34/1.53 tff(2315,plain,
% 1.34/1.53 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2314, 2153, 272, 1069, 2024, 2072])).
% 1.34/1.53 tff(2316,plain,
% 1.34/1.53 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1856, 2315, 2037])).
% 1.34/1.53 tff(2317,plain,
% 1.34/1.53 (~r(s(s(s(s(elem!1)))), z)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1874, 2316, 2062])).
% 1.34/1.53 tff(2318,plain,
% 1.34/1.53 (b(s(s(s(s(elem!1)))), z)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2081, 2317])).
% 1.34/1.53 tff(2319,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2149, 128, 297, 550, 922, 1841, 2318])).
% 1.34/1.53 tff(2320,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~r(s(z), z)) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(2321,plain,
% 1.34/1.53 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2320, 1989, 550, 1978, 171, 1646, 2022, 453])).
% 1.34/1.53 tff(2322,plain,
% 1.34/1.53 (r(s(s(s(s(elem!1)))), s(z))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1828, 2321])).
% 1.34/1.53 tff(2323,plain,
% 1.34/1.53 (~b(s(s(elem!1)), s(z))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2070, 1989, 550, 453, 1978])).
% 1.34/1.53 tff(2324,plain,
% 1.34/1.53 (r(s(s(elem!1)), s(z))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[292, 2323])).
% 1.34/1.53 tff(2325,plain,
% 1.34/1.53 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2208, 45, 2324, 2322])).
% 1.34/1.53 tff(2326,plain,
% 1.34/1.53 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2212, 21, 2325, 1646])).
% 1.34/1.53 tff(2327,plain,
% 1.34/1.53 (~r(s(s(s(s(elem!1)))), z)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1745, 2322, 171])).
% 1.34/1.53 tff(2328,plain,
% 1.34/1.53 (b(s(s(s(s(elem!1)))), z)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2081, 2327])).
% 1.34/1.53 tff(2329,plain,
% 1.34/1.53 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[2141, 2322, 2324])).
% 1.34/1.53 tff(2330,plain,
% 1.34/1.53 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1897, 2329, 1664])).
% 1.34/1.53 tff(2331,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(2332,plain,
% 1.34/1.53 (((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(2333,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[2332])).
% 1.34/1.54 tff(2334,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.34/1.54 inference(transitivity,[status(thm)],[2333, 2331])).
% 1.34/1.54 tff(2335,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(2336,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[2335, 2334])).
% 1.34/1.54 tff(2337,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2336, 128, 453, 2330, 2328, 2326])).
% 1.34/1.54 tff(2338,plain,((~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (s(s(elem!1)) = elem!1) | b(elem!1, z) | b(z, elem!1) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(2339,plain,
% 1.34/1.54 (~b(z, s(s(elem!1)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2338, 1086, 550, 1632, 455, 164])).
% 1.34/1.54 tff(2340,plain,
% 1.34/1.54 (r(z, s(s(elem!1)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[160, 2339])).
% 1.34/1.54 tff(2341,plain,
% 1.34/1.54 (s(s(elem!1)) = elem!1),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[450, 372])).
% 1.34/1.54 tff(2342,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1086, 2341])).
% 1.34/1.54 tff(2343,plain,((~(elem!1 = s(s(elem!1)))) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(2344,plain,
% 1.34/1.54 (~(elem!1 = s(s(elem!1)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2343, 1086])).
% 1.34/1.54 tff(2345,plain,
% 1.34/1.54 (~r(s(z), s(s(elem!1)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1383, 88, 171])).
% 1.34/1.54 tff(2346,plain,
% 1.34/1.54 (b(s(z), s(s(elem!1)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[117, 2345])).
% 1.34/1.54 tff(2347,plain,
% 1.34/1.54 (~(z = elem!1)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1658, 922, 164])).
% 1.34/1.54 tff(2348,plain,
% 1.34/1.54 (r(z, elem!1)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1549, 2347, 455])).
% 1.34/1.54 tff(2349,assumption,(r(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.34/1.54 tff(2350,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(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(2351,plain,
% 1.34/1.54 (((~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(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(2352,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(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(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[2351])).
% 1.34/1.54 tff(2353,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(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(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 1.34/1.54 inference(transitivity,[status(thm)],[2352, 2350])).
% 1.34/1.54 tff(2354,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(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(2355,plain,
% 1.34/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[2354, 2353])).
% 1.34/1.54 tff(2356,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2355, 45, 1416, 88, 2349])).
% 1.34/1.54 tff(2357,plain,((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(2358,plain,
% 1.34/1.54 (~r(s(s(elem!1)), elem!1)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2357, 2348, 88])).
% 1.34/1.54 tff(2359,plain,
% 1.34/1.54 (b(s(s(elem!1)), elem!1)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1934, 2358, 1086])).
% 1.34/1.54 tff(2360,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(2361,plain,
% 1.34/1.54 (((~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(2362,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1))))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[2361])).
% 1.34/1.54 tff(2363,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[2362, 2360])).
% 1.34/1.54 tff(2364,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(2365,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[2364, 2363])).
% 1.34/1.54 tff(2366,plain,
% 1.34/1.54 ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2365, 128])).
% 1.34/1.54 tff(2367,plain,
% 1.34/1.54 (~b(elem!1, s(s(elem!1)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2366, 2359, 922, 2346])).
% 1.34/1.54 tff(2368,plain,
% 1.34/1.54 (((~![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))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(2369,plain,
% 1.34/1.54 ((~![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))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(2370,plain,
% 1.34/1.54 ((~![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)))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[2369, 2368])).
% 1.34/1.54 tff(2371,plain,
% 1.34/1.54 ((elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2370, 21])).
% 1.34/1.54 tff(2372,plain,
% 1.34/1.54 (r(elem!1, s(s(elem!1)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2371, 2367, 2344])).
% 1.34/1.54 tff(2373,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(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(2374,plain,
% 1.34/1.54 (((~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(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(2375,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(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(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[2374])).
% 1.34/1.54 tff(2376,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(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(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[2375, 2373])).
% 1.34/1.54 tff(2377,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(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(2378,plain,
% 1.34/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[2377, 2376])).
% 1.34/1.54 tff(2379,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2378, 45, 2348, 88, 2372])).
% 1.34/1.54 tff(2380,plain,((~b(s(z), elem!1)) | (~r(z, s(s(elem!1)))) | (s(s(elem!1)) = elem!1) | b(z, elem!1) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(2381,plain,
% 1.34/1.54 (~b(s(z), elem!1)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2380, 2340, 1086, 455, 164])).
% 1.34/1.54 tff(2382,plain,
% 1.34/1.54 (r(s(z), elem!1)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[665, 2381, 1645])).
% 1.34/1.54 tff(2383,plain,
% 1.34/1.54 (~r(z, elem!1)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1544, 2382, 171])).
% 1.34/1.54 tff(2384,plain,
% 1.34/1.54 (z = elem!1),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1549, 2383, 455])).
% 1.34/1.54 tff(2385,plain,
% 1.34/1.54 (s(z) = s(elem!1)),
% 1.34/1.54 inference(monotonicity,[status(thm)],[2384])).
% 1.34/1.54 tff(2386,plain,
% 1.34/1.54 (s(elem!1) = s(z)),
% 1.34/1.54 inference(symmetry,[status(thm)],[2385])).
% 1.34/1.54 tff(2387,plain,
% 1.34/1.54 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(z), s(s(s(elem!1))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[2386])).
% 1.34/1.54 tff(2388,plain,
% 1.34/1.54 (b(s(z), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.34/1.54 inference(symmetry,[status(thm)],[2387])).
% 1.34/1.54 tff(2389,plain,
% 1.34/1.54 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(z), s(s(s(elem!1))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[1649])).
% 1.34/1.54 tff(2390,plain,
% 1.34/1.54 (r(s(z), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 1.34/1.54 inference(symmetry,[status(thm)],[2389])).
% 1.34/1.54 tff(2391,plain,
% 1.34/1.54 (r(s(elem!1), s(s(s(elem!1))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[323, 2390])).
% 1.34/1.54 tff(2392,plain,
% 1.34/1.54 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[700, 1680])).
% 1.34/1.54 tff(2393,plain,
% 1.34/1.54 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 1.34/1.54 inference(monotonicity,[status(thm)],[1647])).
% 1.34/1.54 tff(2394,plain,
% 1.34/1.54 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), z)),
% 1.34/1.54 inference(symmetry,[status(thm)],[2393])).
% 1.34/1.54 tff(2395,plain,
% 1.34/1.54 (b(s(s(z)), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.34/1.54 inference(monotonicity,[status(thm)],[1671])).
% 1.34/1.54 tff(2396,plain,
% 1.34/1.54 (b(s(s(z)), elem!1) <=> b(s(s(elem!1)), z)),
% 1.34/1.54 inference(transitivity,[status(thm)],[2395, 2394])).
% 1.34/1.54 tff(2397,plain,
% 1.34/1.54 ((s(s(z)) = z) <=> (s(s(z)) = elem!1)),
% 1.34/1.54 inference(monotonicity,[status(thm)],[1647])).
% 1.34/1.54 tff(2398,plain,
% 1.34/1.54 ((~(s(s(z)) = z)) <=> (~(s(s(z)) = elem!1))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[2397])).
% 1.34/1.54 tff(2399,plain,
% 1.34/1.54 (~(s(s(z)) = elem!1)),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[11, 2398])).
% 1.34/1.54 tff(2400,plain,
% 1.34/1.54 (b(s(s(s(s(elem!1)))), z)),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[576, 1674])).
% 1.34/1.54 tff(2401,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2075, 2400])).
% 1.34/1.54 tff(2402,plain,((~b(s(s(s(s(z)))), elem!1)) | b(s(s(s(s(elem!1)))), z) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(2403,plain,
% 1.34/1.54 (~b(s(s(s(s(z)))), elem!1)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2402, 2075, 1647])).
% 1.34/1.54 tff(2404,plain,
% 1.34/1.54 (r(s(s(s(s(z)))), elem!1)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[632, 2403, 1677])).
% 1.34/1.54 tff(2405,plain,
% 1.34/1.54 (~r(s(s(z)), elem!1)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1356, 2404, 272, 1340])).
% 1.34/1.54 tff(2406,plain,
% 1.34/1.54 (b(s(s(z)), elem!1)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[370, 2405, 2399])).
% 1.34/1.54 tff(2407,plain,
% 1.34/1.54 (b(s(s(elem!1)), z)),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[2406, 2396])).
% 1.34/1.54 tff(2408,plain,
% 1.34/1.54 (~r(s(z), s(s(elem!1)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1383, 88, 272])).
% 1.34/1.54 tff(2409,plain,
% 1.34/1.54 (b(s(z), s(s(elem!1)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[117, 2408])).
% 1.34/1.54 tff(2410,plain,
% 1.34/1.54 (r(s(s(s(s(elem!1)))), z)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2081, 2075])).
% 1.34/1.54 tff(2411,plain,
% 1.34/1.54 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1745, 2410, 272])).
% 1.34/1.54 tff(2412,plain,
% 1.34/1.54 (b(s(s(s(s(elem!1)))), s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1828, 2411])).
% 1.34/1.54 tff(2413,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(2414,plain,
% 1.34/1.54 (((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z)))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(2415,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[2414])).
% 1.34/1.54 tff(2416,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[2415, 2413])).
% 1.34/1.54 tff(2417,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(2418,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[2417, 2416])).
% 1.34/1.54 tff(2419,plain,
% 1.34/1.54 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2418, 128, 550, 2006, 876, 1841])).
% 1.34/1.54 tff(2420,plain,
% 1.34/1.54 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1897, 2419, 1063])).
% 1.34/1.54 tff(2421,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(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(2422,plain,
% 1.34/1.54 (((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(2423,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(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[2422])).
% 1.34/1.54 tff(2424,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(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[2423, 2421])).
% 1.34/1.54 tff(2425,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(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(2426,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(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[2425, 2424])).
% 1.34/1.54 tff(2427,plain,
% 1.34/1.54 (~r(s(s(s(s(elem!1)))), z)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2426, 45, 88, 2420])).
% 1.34/1.54 tff(2428,plain,
% 1.34/1.54 (b(s(s(s(s(elem!1)))), z)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2079, 21, 176, 2427])).
% 1.34/1.54 tff(2429,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(2430,plain,
% 1.34/1.54 (((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(2431,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[2430])).
% 1.34/1.54 tff(2432,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[2431, 2429])).
% 1.34/1.54 tff(2433,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(2434,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[2433, 2432])).
% 1.34/1.54 tff(2435,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2434, 128, 550, 2006, 876, 1841, 2428])).
% 1.34/1.54 tff(2436,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (s(s(s(s(elem!1)))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(2437,plain,
% 1.34/1.54 (~b(s(s(elem!1)), z)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2436, 2412, 88, 550, 2409, 1063])).
% 1.34/1.54 tff(2438,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2437, 2407])).
% 1.34/1.54 tff(2439,plain,(b(s(s(s(s(elem!1)))), z) | (~(z = elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(z, s(s(elem!1)))) | (~b(z, s(z))) | (s(s(s(s(elem!1)))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(2440,plain,
% 1.34/1.54 (b(s(s(s(s(elem!1)))), z)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2439, 1647, 272, 1340, 88, 550, 1063])).
% 1.34/1.54 tff(2441,plain,
% 1.34/1.54 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[2440, 1670])).
% 1.34/1.54 tff(2442,plain,
% 1.34/1.54 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 1.34/1.54 inference(monotonicity,[status(thm)],[1647])).
% 1.34/1.54 tff(2443,plain,
% 1.34/1.54 ((s(s(s(elem!1))) = z) <=> (elem!1 = s(s(s(elem!1))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[2442, 705])).
% 1.34/1.54 tff(2444,plain,
% 1.34/1.54 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 1.34/1.54 inference(transitivity,[status(thm)],[2443, 982])).
% 1.34/1.54 tff(2445,plain,
% 1.34/1.54 ((~(s(s(s(elem!1))) = z)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[2444])).
% 1.34/1.54 tff(2446,plain,
% 1.34/1.54 (~(s(s(s(elem!1))) = elem!1)),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[382, 2445])).
% 1.34/1.54 tff(2447,plain,
% 1.34/1.54 (~r(s(s(s(elem!1))), z)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1307, 323, 272])).
% 1.34/1.54 tff(2448,plain,
% 1.34/1.54 (r(s(s(s(elem!1))), z) <=> r(s(s(s(elem!1))), elem!1)),
% 1.34/1.54 inference(monotonicity,[status(thm)],[1647])).
% 1.34/1.54 tff(2449,plain,
% 1.34/1.54 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), z)),
% 1.34/1.54 inference(symmetry,[status(thm)],[2448])).
% 1.34/1.54 tff(2450,assumption,(r(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.34/1.54 tff(2451,plain,
% 1.34/1.54 (r(s(s(s(elem!1))), z)),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[2450, 2449])).
% 1.34/1.54 tff(2452,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[544, 2451])).
% 1.34/1.54 tff(2453,plain,((~r(s(s(s(elem!1))), elem!1)) | r(s(s(s(elem!1))), z) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(2454,plain,
% 1.34/1.54 (~r(s(s(s(elem!1))), elem!1)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2453, 2447, 1647])).
% 1.34/1.54 tff(2455,plain,
% 1.34/1.54 (b(s(s(s(elem!1))), elem!1)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[742, 2454, 2446])).
% 1.34/1.54 tff(2456,plain,
% 1.34/1.54 ((~(s(s(s(elem!1))) = z)) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[2443])).
% 1.34/1.54 tff(2457,plain,
% 1.34/1.54 (~(elem!1 = s(s(s(elem!1))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[382, 2456])).
% 1.34/1.54 tff(2458,assumption,(r(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 1.34/1.54 tff(2459,plain,
% 1.34/1.54 (r(z, s(s(s(elem!1))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[2458, 1683])).
% 1.34/1.54 tff(2460,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[558, 2459])).
% 1.34/1.54 tff(2461,plain,((~r(elem!1, s(s(s(elem!1))))) | r(z, s(s(s(elem!1)))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(2462,plain,
% 1.34/1.54 (~r(elem!1, s(s(s(elem!1))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[2461, 1835, 1647])).
% 1.34/1.54 tff(2463,plain,
% 1.34/1.54 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1)))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(2464,plain,
% 1.34/1.54 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1)))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(2465,plain,
% 1.34/1.54 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[2464, 2463])).
% 1.34/1.55 tff(2466,plain,
% 1.34/1.55 ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2465, 21])).
% 1.34/1.55 tff(2467,plain,
% 1.34/1.55 (b(elem!1, s(s(s(elem!1))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2466, 2462, 2457])).
% 1.34/1.55 tff(2468,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(2469,plain,
% 1.34/1.55 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(2470,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[2469])).
% 1.34/1.55 tff(2471,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[2470, 2468])).
% 1.34/1.55 tff(2472,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(2473,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[2472, 2471])).
% 1.34/1.55 tff(2474,plain,
% 1.34/1.55 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2473, 128, 2467, 2455, 2441])).
% 1.34/1.55 tff(2475,plain,
% 1.34/1.55 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1820, 2474, 2392])).
% 1.34/1.55 tff(2476,plain,
% 1.34/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(2477,plain,
% 1.34/1.55 (((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(2478,plain,
% 1.34/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[2477])).
% 1.34/1.55 tff(2479,plain,
% 1.34/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[2478, 2476])).
% 1.34/1.55 tff(2480,plain,
% 1.34/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(2481,plain,
% 1.34/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[2480, 2479])).
% 1.34/1.55 tff(2482,plain,
% 1.34/1.55 ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(elem!1))))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2481, 45, 2475])).
% 1.34/1.55 tff(2483,plain,
% 1.34/1.55 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2482, 2391])).
% 1.34/1.55 tff(2484,plain,
% 1.34/1.55 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1727, 21, 1724, 2483])).
% 1.34/1.55 tff(2485,plain,
% 1.34/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(2486,plain,
% 1.34/1.55 (((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(2487,plain,
% 1.34/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[2486])).
% 1.34/1.55 tff(2488,plain,
% 1.34/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[2487, 2485])).
% 1.34/1.55 tff(2489,plain,
% 1.34/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(2490,plain,
% 1.34/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[2489, 2488])).
% 1.34/1.55 tff(2491,plain,
% 1.34/1.55 ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2490, 45, 2475])).
% 1.34/1.55 tff(2492,plain,
% 1.34/1.55 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2491, 2391, 1702])).
% 1.34/1.55 tff(2493,plain,
% 1.34/1.55 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1920, 2492, 1751])).
% 1.34/1.55 tff(2494,plain,
% 1.34/1.55 (~r(s(z), s(s(elem!1)))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1383, 272, 88])).
% 1.34/1.55 tff(2495,plain,
% 1.34/1.55 (b(s(z), s(s(elem!1)))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[117, 2494])).
% 1.34/1.55 tff(2496,plain,
% 1.34/1.55 (~r(s(s(elem!1)), z)),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1962, 272, 325])).
% 1.34/1.55 tff(2497,plain,
% 1.34/1.55 (b(s(s(elem!1)), z)),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2018, 21, 154, 2496])).
% 1.34/1.55 tff(2498,plain,
% 1.34/1.55 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2436, 2497, 416, 2495, 88, 1063])).
% 1.34/1.55 tff(2499,plain,
% 1.34/1.55 (r(s(s(s(s(elem!1)))), s(z))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1828, 2498])).
% 1.34/1.55 tff(2500,plain,
% 1.34/1.55 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2141, 2499, 325])).
% 1.34/1.55 tff(2501,plain,
% 1.34/1.55 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 1.34/1.55 inference(symmetry,[status(thm)],[227])).
% 1.34/1.55 tff(2502,plain,
% 1.34/1.55 (elem!1 = s(s(s(s(elem!1))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[202, 2501])).
% 1.34/1.55 tff(2503,plain,
% 1.34/1.55 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[202])).
% 1.34/1.55 tff(2504,plain,
% 1.34/1.55 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.34/1.55 inference(transitivity,[status(thm)],[2503, 1067])).
% 1.34/1.55 tff(2505,plain,
% 1.34/1.55 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.34/1.55 inference(symmetry,[status(thm)],[2504])).
% 1.34/1.55 tff(2506,plain,
% 1.34/1.55 ((~(s(s(s(s(elem!1)))) = s(s(elem!1)))) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[2505])).
% 1.34/1.55 tff(2507,plain,
% 1.34/1.55 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[1063, 2506])).
% 1.34/1.55 tff(2508,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2507, 2502])).
% 1.34/1.55 tff(2509,plain,((~(s(s(elem!1)) = elem!1)) | (s(s(s(s(elem!1)))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.55 tff(2510,plain,
% 1.34/1.55 (~(s(s(elem!1)) = elem!1)),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2509, 1063])).
% 1.34/1.55 tff(2511,plain,
% 1.34/1.55 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1089, 2510])).
% 1.34/1.55 tff(2512,plain,
% 1.34/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(2513,plain,
% 1.34/1.55 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(2514,plain,
% 1.34/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[2513])).
% 1.34/1.55 tff(2515,plain,
% 1.34/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[2514, 2512])).
% 1.34/1.55 tff(2516,plain,
% 1.34/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(2517,plain,
% 1.34/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[2516, 2515])).
% 1.34/1.55 tff(2518,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2517, 45, 272, 1737, 323, 1772])).
% 1.34/1.55 tff(2519,plain,((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.55 tff(2520,plain,
% 1.34/1.55 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2519, 1737, 272, 323])).
% 1.34/1.55 tff(2521,plain,
% 1.34/1.55 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1820, 2520, 809])).
% 1.34/1.55 tff(2522,plain,
% 1.34/1.55 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2313, 2521, 691, 1069, 272, 190, 325])).
% 1.34/1.55 tff(2523,plain,
% 1.34/1.55 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1856, 2522, 808])).
% 1.34/1.55 tff(2524,plain,
% 1.34/1.55 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2208, 45, 325, 1737])).
% 1.34/1.55 tff(2525,plain,
% 1.34/1.55 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2212, 21, 2524, 1069])).
% 1.34/1.55 tff(2526,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(2527,plain,
% 1.34/1.55 (((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1))))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(2528,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[2527])).
% 1.34/1.55 tff(2529,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[2528, 2526])).
% 1.34/1.55 tff(2530,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(2531,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[2530, 2529])).
% 1.34/1.55 tff(2532,plain,
% 1.34/1.55 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2531, 128, 876, 2084, 2525])).
% 1.34/1.55 tff(2533,plain,
% 1.34/1.55 ((s(z) = s(s(s(s(elem!1))))) | r(s(z), s(s(s(s(elem!1)))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2258, 21, 2532])).
% 1.34/1.55 tff(2534,plain,
% 1.34/1.55 (r(s(z), s(s(s(s(elem!1)))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2533, 2248])).
% 1.34/1.55 tff(2535,plain,
% 1.34/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(2536,plain,
% 1.34/1.55 (((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(2537,plain,
% 1.34/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(elem!1)))))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[2536])).
% 1.34/1.55 tff(2538,plain,
% 1.34/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[2537, 2535])).
% 1.34/1.55 tff(2539,plain,
% 1.34/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(2540,plain,
% 1.34/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(elem!1)))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[2539, 2538])).
% 1.34/1.55 tff(2541,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2540, 45, 2534, 323, 2523])).
% 1.34/1.55 tff(2542,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.55 tff(2543,plain,
% 1.34/1.55 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2542, 2499, 2495, 323, 2511, 325, 1678, 272])).
% 1.34/1.55 tff(2544,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1897, 2543, 2500, 1063])).
% 1.34/1.55 tff(2545,plain,((~r(s(z), z)) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.55 tff(2546,plain,
% 1.34/1.55 (~r(s(s(elem!1)), s(z))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2545, 323, 272, 1063, 88])).
% 1.34/1.55 tff(2547,plain,
% 1.34/1.55 (b(s(s(elem!1)), s(z))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[292, 2546])).
% 1.34/1.55 tff(2548,plain,
% 1.34/1.55 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[2083, 1670])).
% 1.34/1.55 tff(2549,plain,
% 1.34/1.55 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(z))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[1649])).
% 1.34/1.55 tff(2550,plain,
% 1.34/1.55 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.55 inference(symmetry,[status(thm)],[2549])).
% 1.34/1.55 tff(2551,plain,
% 1.34/1.55 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(z))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[1649])).
% 1.34/1.55 tff(2552,plain,
% 1.34/1.55 ((~r(s(s(s(elem!1))), s(elem!1))) <=> (~r(s(s(s(elem!1))), s(z)))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[2551])).
% 1.34/1.55 tff(2553,plain,
% 1.34/1.55 (r(s(s(s(elem!1))), z)),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[561, 549, 550, 558])).
% 1.34/1.55 tff(2554,plain,
% 1.34/1.55 ((~r(s(s(s(elem!1))), elem!1)) <=> (~r(s(s(s(elem!1))), z))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[2449])).
% 1.34/1.55 tff(2555,assumption,(~r(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.34/1.55 tff(2556,plain,
% 1.34/1.55 (~r(s(s(s(elem!1))), z)),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[2555, 2554])).
% 1.34/1.55 tff(2557,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[520, 2556])).
% 1.34/1.55 tff(2558,plain,(r(s(s(s(elem!1))), elem!1) | (~r(s(s(s(elem!1))), z)) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.55 tff(2559,plain,
% 1.34/1.55 (r(s(s(s(elem!1))), elem!1)),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[2558, 2553, 1647])).
% 1.34/1.55 tff(2560,plain,
% 1.34/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(2561,plain,
% 1.34/1.55 (((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(2562,plain,
% 1.34/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[2561])).
% 1.34/1.56 tff(2563,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(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.34/1.56 inference(transitivity,[status(thm)],[2562, 2560])).
% 1.34/1.56 tff(2564,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(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(2565,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(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[2564, 2563])).
% 1.34/1.56 tff(2566,plain,
% 1.34/1.56 ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2565, 45, 2559])).
% 1.34/1.56 tff(2567,plain,
% 1.34/1.56 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2566, 1702])).
% 1.34/1.56 tff(2568,plain,
% 1.34/1.56 (~r(s(s(s(elem!1))), s(z))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[2567, 2552])).
% 1.34/1.56 tff(2569,plain,
% 1.34/1.56 (b(s(s(s(elem!1))), s(z))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[196, 2568])).
% 1.34/1.56 tff(2570,plain,
% 1.34/1.56 (b(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[2569, 2550])).
% 1.34/1.56 tff(2571,plain,
% 1.34/1.56 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(z), s(s(s(elem!1))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[1649])).
% 1.34/1.56 tff(2572,plain,
% 1.34/1.56 (b(s(z), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.34/1.56 inference(symmetry,[status(thm)],[2571])).
% 1.34/1.56 tff(2573,plain,
% 1.34/1.56 (b(s(elem!1), s(s(s(elem!1))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[549, 2572])).
% 1.34/1.56 tff(2574,plain,
% 1.34/1.56 (~r(elem!1, s(s(s(elem!1))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2461, 558, 1647])).
% 1.34/1.56 tff(2575,plain,
% 1.34/1.56 (b(elem!1, s(s(s(elem!1))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2466, 2574, 2457])).
% 1.34/1.56 tff(2576,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(2577,plain,
% 1.34/1.56 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(2578,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1)))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[2577])).
% 1.34/1.56 tff(2579,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[2578, 2576])).
% 1.34/1.56 tff(2580,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(2581,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1)))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[2580, 2579])).
% 1.34/1.56 tff(2582,plain,
% 1.34/1.56 ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2581, 128, 2575, 1733])).
% 1.34/1.56 tff(2583,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2582, 2573, 2570])).
% 1.34/1.56 tff(2584,plain,((~b(s(z), s(s(s(elem!1))))) | (~(z = elem!1)) | (~r(s(z), elem!1)) | (~b(z, s(z))) | r(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(2585,plain,
% 1.34/1.56 (~b(s(z), s(s(s(elem!1))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2584, 558, 1340, 550, 1647])).
% 1.34/1.56 tff(2586,plain,
% 1.34/1.56 (r(s(z), s(s(s(elem!1))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[339, 2585])).
% 1.34/1.56 tff(2587,plain,
% 1.34/1.56 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2519, 2586, 272, 1737])).
% 1.34/1.56 tff(2588,plain,
% 1.34/1.56 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1820, 2587, 712])).
% 1.34/1.56 tff(2589,plain,
% 1.34/1.56 (~r(s(s(s(elem!1))), z)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1307, 2586, 272])).
% 1.34/1.56 tff(2590,plain,
% 1.34/1.56 (~r(s(s(s(elem!1))), elem!1)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2453, 2589, 1647])).
% 1.34/1.56 tff(2591,plain,
% 1.34/1.56 (b(s(s(s(elem!1))), elem!1)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[742, 2590, 2446])).
% 1.34/1.56 tff(2592,plain,
% 1.34/1.56 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1))) <=> ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(2593,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[2592])).
% 1.34/1.56 tff(2594,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[2593, 2468])).
% 1.34/1.56 tff(2595,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(2596,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[2595, 2594])).
% 1.34/1.56 tff(2597,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2596, 128, 2575, 2591, 2588, 2548])).
% 1.34/1.56 tff(2598,plain,(r(z, s(s(s(elem!1)))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~(z = elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(2599,plain,
% 1.34/1.56 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2598, 1835, 1647, 272, 2392, 1340, 550, 2440])).
% 1.34/1.56 tff(2600,plain,
% 1.34/1.56 (b(s(s(s(s(elem!1)))), s(z))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1828, 2599])).
% 1.34/1.56 tff(2601,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(2602,plain,
% 1.34/1.56 (((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z)))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(2603,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[2602])).
% 1.34/1.56 tff(2604,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[2603, 2601])).
% 1.34/1.56 tff(2605,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(2606,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[2605, 2604])).
% 1.34/1.56 tff(2607,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2606, 128, 30, 876, 1841, 2084])).
% 1.34/1.56 tff(2608,plain,((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(2609,plain,
% 1.34/1.56 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2608, 2600, 2409, 2547])).
% 1.34/1.56 tff(2610,plain,
% 1.34/1.56 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1897, 2609, 1063])).
% 1.34/1.56 tff(2611,plain,
% 1.34/1.56 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[1647])).
% 1.34/1.56 tff(2612,plain,
% 1.34/1.56 (r(elem!1, s(s(elem!1)))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[88, 2611])).
% 1.34/1.56 tff(2613,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(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(2614,plain,
% 1.34/1.56 (((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1))))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(2615,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(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[2614])).
% 1.34/1.56 tff(2616,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(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[2615, 2613])).
% 1.34/1.56 tff(2617,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(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(2618,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(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[2617, 2616])).
% 1.34/1.56 tff(2619,plain,
% 1.34/1.56 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2618, 45, 2612, 2610])).
% 1.34/1.56 tff(2620,plain,
% 1.34/1.56 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1766, 2619, 1699])).
% 1.34/1.56 tff(2621,plain,
% 1.34/1.56 (((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(2622,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1)))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[2621])).
% 1.34/1.56 tff(2623,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[2622, 1756])).
% 1.34/1.56 tff(2624,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(2625,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1)))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[2624, 2623])).
% 1.34/1.56 tff(2626,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2625, 128, 2620, 2493, 1733, 2484])).
% 1.34/1.56 tff(2627,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~(z = elem!1)) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~r(s(z), z)) | (~b(z, s(z))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(2628,plain,
% 1.34/1.56 (~r(s(z), s(s(s(elem!1))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2627, 2382, 2384, 1664, 171, 550, 2340])).
% 1.34/1.56 tff(2629,plain,
% 1.34/1.56 (b(s(z), s(s(s(elem!1))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[339, 2628])).
% 1.34/1.56 tff(2630,plain,
% 1.34/1.56 (b(s(elem!1), s(s(s(elem!1))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[2629, 2388])).
% 1.34/1.56 tff(2631,plain,
% 1.34/1.56 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(z))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[2386])).
% 1.34/1.56 tff(2632,plain,
% 1.34/1.56 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.56 inference(symmetry,[status(thm)],[2631])).
% 1.34/1.56 tff(2633,plain,
% 1.34/1.56 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(z))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[2386])).
% 1.34/1.56 tff(2634,plain,
% 1.34/1.56 ((~r(s(s(s(elem!1))), s(elem!1))) <=> (~r(s(s(s(elem!1))), s(z)))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[2633])).
% 1.34/1.56 tff(2635,plain,
% 1.34/1.56 (r(s(elem!1), elem!1) <=> r(s(z), elem!1)),
% 1.34/1.56 inference(monotonicity,[status(thm)],[2386])).
% 1.34/1.56 tff(2636,plain,
% 1.34/1.56 (r(s(z), elem!1) <=> r(s(elem!1), elem!1)),
% 1.34/1.56 inference(symmetry,[status(thm)],[2635])).
% 1.34/1.56 tff(2637,plain,
% 1.34/1.56 (r(s(elem!1), elem!1)),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[2382, 2636])).
% 1.34/1.56 tff(2638,plain,
% 1.34/1.56 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 1.34/1.56 inference(monotonicity,[status(thm)],[2384])).
% 1.34/1.56 tff(2639,plain,
% 1.34/1.56 ((s(s(s(elem!1))) = z) <=> (elem!1 = s(s(s(elem!1))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[2638, 705])).
% 1.34/1.56 tff(2640,plain,
% 1.34/1.56 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 1.34/1.56 inference(transitivity,[status(thm)],[2639, 982])).
% 1.34/1.56 tff(2641,plain,
% 1.34/1.56 ((~(s(s(s(elem!1))) = z)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[2640])).
% 1.34/1.56 tff(2642,plain,
% 1.34/1.56 (~(s(s(s(elem!1))) = elem!1)),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[382, 2641])).
% 1.34/1.56 tff(2643,plain,
% 1.34/1.56 (b(elem!1, s(elem!1)) <=> b(elem!1, s(z))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[2386])).
% 1.34/1.56 tff(2644,plain,
% 1.34/1.56 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 1.34/1.56 inference(symmetry,[status(thm)],[2643])).
% 1.34/1.56 tff(2645,plain,
% 1.34/1.56 (b(z, s(z)) <=> b(elem!1, s(z))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[2384])).
% 1.34/1.56 tff(2646,plain,
% 1.34/1.56 (b(elem!1, s(z))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[550, 2645])).
% 1.34/1.56 tff(2647,plain,
% 1.34/1.56 (b(elem!1, s(elem!1))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[2646, 2644])).
% 1.34/1.56 tff(2648,plain,
% 1.34/1.56 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1065, 1664])).
% 1.34/1.56 tff(2649,plain,
% 1.34/1.56 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[693, 2648])).
% 1.34/1.56 tff(2650,plain,
% 1.34/1.56 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[700, 2649])).
% 1.34/1.56 tff(2651,plain,
% 1.34/1.56 (elem!1 = z),
% 1.34/1.56 inference(symmetry,[status(thm)],[2384])).
% 1.34/1.56 tff(2652,plain,
% 1.34/1.56 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(elem!1)))), z)),
% 1.34/1.56 inference(monotonicity,[status(thm)],[2651])).
% 1.34/1.56 tff(2653,plain,
% 1.34/1.56 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.34/1.56 inference(symmetry,[status(thm)],[2652])).
% 1.34/1.56 tff(2654,plain,
% 1.34/1.56 (b(s(s(s(s(elem!1)))), z)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2439, 2384, 171, 2382, 2340, 550, 1664])).
% 1.34/1.56 tff(2655,plain,
% 1.34/1.56 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[2654, 2653])).
% 1.34/1.56 tff(2656,assumption,(b(s(s(s(s(elem!1)))), elem!1)), introduced(assumption)).
% 1.34/1.56 tff(2657,plain,
% 1.34/1.56 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.56 inference(symmetry,[status(thm)],[2551])).
% 1.34/1.56 tff(2658,plain,
% 1.34/1.56 ((~b(s(s(s(elem!1))), s(elem!1))) <=> (~b(s(s(s(elem!1))), s(z)))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[2549])).
% 1.34/1.56 tff(2659,assumption,(b(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.34/1.56 tff(2660,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(2661,plain,
% 1.34/1.56 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(2662,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1)))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[2661])).
% 1.34/1.56 tff(2663,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[2662, 2660])).
% 1.34/1.56 tff(2664,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(2665,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1)))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[2664, 2663])).
% 1.34/1.56 tff(2666,plain,
% 1.34/1.56 ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2665, 128, 2659, 1830])).
% 1.34/1.56 tff(2667,plain,
% 1.34/1.56 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[2666, 2573])).
% 1.34/1.56 tff(2668,plain,
% 1.34/1.56 (~b(s(s(s(elem!1))), s(z))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[2667, 2658])).
% 1.34/1.56 tff(2669,plain,
% 1.34/1.56 (r(s(s(s(elem!1))), s(z))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[196, 2668])).
% 1.34/1.56 tff(2670,plain,
% 1.34/1.56 (r(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[2669, 2657])).
% 1.34/1.56 tff(2671,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(2672,plain,
% 1.34/1.56 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1))) <=> ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2673,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1)))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2672])).
% 1.34/1.57 tff(2674,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[2673, 2671])).
% 1.34/1.57 tff(2675,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(2676,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1)))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2675, 2674])).
% 1.34/1.57 tff(2677,plain,
% 1.34/1.57 ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2676, 128, 2659, 1830, 2656])).
% 1.34/1.57 tff(2678,plain,
% 1.34/1.57 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2677, 2573])).
% 1.34/1.57 tff(2679,plain,
% 1.34/1.57 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1920, 2678, 1751])).
% 1.34/1.57 tff(2680,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(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2681,plain,
% 1.34/1.57 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2682,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(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2681])).
% 1.34/1.57 tff(2683,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(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[2682, 2680])).
% 1.34/1.57 tff(2684,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(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(2685,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(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2684, 2683])).
% 1.34/1.57 tff(2686,plain,
% 1.34/1.57 ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2685, 45, 2679])).
% 1.34/1.57 tff(2687,plain,
% 1.34/1.57 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2686, 2670])).
% 1.34/1.57 tff(2688,plain,
% 1.34/1.57 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1820, 2687, 712])).
% 1.34/1.57 tff(2689,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2690,plain,
% 1.34/1.57 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2691,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1)))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2690])).
% 1.34/1.57 tff(2692,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[2691, 2689])).
% 1.34/1.57 tff(2693,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(2694,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1)))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2693, 2692])).
% 1.34/1.57 tff(2695,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2694, 128, 2659, 2688, 1830, 2656, 2573])).
% 1.34/1.57 tff(2696,plain,((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~(z = elem!1)) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(2697,plain,
% 1.34/1.57 (~b(s(s(s(elem!1))), elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2696, 2629, 2655, 2650, 2384, 2647])).
% 1.34/1.57 tff(2698,plain,
% 1.34/1.57 (r(s(s(s(elem!1))), elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[742, 2697, 2642])).
% 1.34/1.57 tff(2699,plain,
% 1.34/1.57 ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2565, 45, 2698])).
% 1.34/1.57 tff(2700,plain,
% 1.34/1.57 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2699, 2637])).
% 1.34/1.57 tff(2701,plain,
% 1.34/1.57 (~r(s(s(s(elem!1))), s(z))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2700, 2634])).
% 1.34/1.57 tff(2702,plain,
% 1.34/1.57 (b(s(s(s(elem!1))), s(z))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[196, 2701])).
% 1.34/1.57 tff(2703,plain,
% 1.34/1.57 (b(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2702, 2632])).
% 1.34/1.57 tff(2704,plain,
% 1.34/1.57 (~r(s(z), s(s(elem!1)))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1383, 2340, 171])).
% 1.34/1.57 tff(2705,plain,
% 1.34/1.57 (b(s(z), s(s(elem!1)))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[117, 2704])).
% 1.34/1.57 tff(2706,plain,
% 1.34/1.57 (b(s(elem!1), s(s(elem!1)))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[876, 1651])).
% 1.34/1.57 tff(2707,assumption,(~b(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 1.34/1.57 tff(2708,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2707, 2706])).
% 1.34/1.57 tff(2709,plain,(b(s(elem!1), s(s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(2710,plain,
% 1.34/1.57 (b(s(elem!1), s(s(elem!1)))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2709, 2705, 2384])).
% 1.34/1.57 tff(2711,plain,
% 1.34/1.57 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2384])).
% 1.34/1.57 tff(2712,plain,
% 1.34/1.57 (r(elem!1, s(s(elem!1)))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2340, 2711])).
% 1.34/1.57 tff(2713,plain,
% 1.34/1.57 ((~(s(s(s(elem!1))) = z)) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2639])).
% 1.34/1.57 tff(2714,plain,
% 1.34/1.57 (~(elem!1 = s(s(s(elem!1))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[382, 2713])).
% 1.34/1.57 tff(2715,plain,
% 1.34/1.57 ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2581, 128, 2647])).
% 1.34/1.57 tff(2716,plain,
% 1.34/1.57 (~b(elem!1, s(s(s(elem!1))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2715, 2703, 2630])).
% 1.34/1.57 tff(2717,plain,
% 1.34/1.57 (r(elem!1, s(s(s(elem!1))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2466, 2716, 2714])).
% 1.34/1.57 tff(2718,assumption,(b(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 1.34/1.57 tff(2719,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2720,plain,
% 1.34/1.57 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(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(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2721,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2720])).
% 1.34/1.57 tff(2722,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[2721, 2719])).
% 1.34/1.57 tff(2723,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(2724,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2723, 2722])).
% 1.34/1.57 tff(2725,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2724, 128, 30, 876, 2106, 2718])).
% 1.34/1.57 tff(2726,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(2727,plain,
% 1.34/1.57 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2726, 30, 2718, 876])).
% 1.34/1.57 tff(2728,plain,
% 1.34/1.57 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[321, 2727, 2648])).
% 1.34/1.57 tff(2729,assumption,(r(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.34/1.57 tff(2730,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2731,plain,
% 1.34/1.57 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2732,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~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(X0, 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(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2731])).
% 1.34/1.57 tff(2733,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~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(X0, 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(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[2732, 2730])).
% 1.34/1.57 tff(2734,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(2735,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2734, 2733])).
% 1.34/1.57 tff(2736,plain,
% 1.34/1.57 ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2735, 128])).
% 1.34/1.57 tff(2737,plain,
% 1.34/1.57 (~b(s(s(elem!1)), elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2736, 30, 297, 876])).
% 1.34/1.57 tff(2738,plain,
% 1.34/1.57 (r(s(s(elem!1)), elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1934, 2737, 1086])).
% 1.34/1.57 tff(2739,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(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2740,plain,
% 1.34/1.57 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2741,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)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2740])).
% 1.34/1.57 tff(2742,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)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[2741, 2739])).
% 1.34/1.57 tff(2743,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)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(2744,plain,
% 1.34/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2743, 2742])).
% 1.34/1.57 tff(2745,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2744, 45, 2738, 2729, 2458, 2728])).
% 1.34/1.57 tff(2746,plain,((~b(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (s(s(elem!1)) = elem!1) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(2747,plain,
% 1.34/1.57 (~b(s(s(elem!1)), s(z))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2746, 2717, 2712, 1086, 2702, 2705, 2646])).
% 1.34/1.57 tff(2748,plain,
% 1.34/1.57 (r(s(s(elem!1)), s(z))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[292, 2747])).
% 1.34/1.57 tff(2749,plain,
% 1.34/1.57 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[438, 2748, 2340])).
% 1.34/1.57 tff(2750,plain,
% 1.34/1.57 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[321, 2749, 2648])).
% 1.34/1.57 tff(2751,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2752,plain,
% 1.34/1.57 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2753,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1)))))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2752])).
% 1.34/1.57 tff(2754,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[2753, 2751])).
% 1.34/1.57 tff(2755,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(2756,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2755, 2754])).
% 1.34/1.57 tff(2757,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2756, 128, 2750, 2710, 2703, 2630])).
% 1.34/1.57 tff(2758,plain,((s(s(elem!1)) = elem!1) | (~b(z, s(z))) | b(z, elem!1) | b(s(z), z) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(2759,plain,
% 1.34/1.57 (s(s(elem!1)) = elem!1),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2758, 550, 455, 164, 1632])).
% 1.34/1.57 tff(2760,plain,
% 1.34/1.57 (~(s(s(s(s(z)))) = elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[242, 2759])).
% 1.34/1.57 tff(2761,plain,
% 1.34/1.57 (elem!1 = s(s(elem!1))),
% 1.34/1.57 inference(symmetry,[status(thm)],[2759])).
% 1.34/1.57 tff(2762,plain,
% 1.34/1.57 (s(elem!1) = s(s(s(elem!1)))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2761])).
% 1.34/1.57 tff(2763,plain,
% 1.34/1.57 (s(s(s(elem!1))) = s(elem!1)),
% 1.34/1.57 inference(symmetry,[status(thm)],[2762])).
% 1.34/1.57 tff(2764,plain,
% 1.34/1.57 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2763])).
% 1.34/1.57 tff(2765,plain,
% 1.34/1.57 (s(s(s(s(elem!1)))) = elem!1),
% 1.34/1.57 inference(transitivity,[status(thm)],[2764, 2759])).
% 1.34/1.57 tff(2766,plain,
% 1.34/1.57 (r(s(s(s(s(elem!1)))), s(z)) <=> r(elem!1, s(z))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2765])).
% 1.34/1.57 tff(2767,plain,
% 1.34/1.57 ((~r(s(s(s(s(elem!1)))), s(z))) <=> (~r(elem!1, s(z)))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2766])).
% 1.34/1.57 tff(2768,plain,
% 1.34/1.57 (b(s(s(s(s(elem!1)))), z) <=> b(elem!1, z)),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2765])).
% 1.34/1.57 tff(2769,plain,
% 1.34/1.57 (b(elem!1, z) <=> b(s(s(s(s(elem!1)))), z)),
% 1.34/1.57 inference(symmetry,[status(thm)],[2768])).
% 1.34/1.57 tff(2770,plain,
% 1.34/1.57 ((~b(elem!1, z)) <=> (~b(s(s(s(s(elem!1)))), z))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2769])).
% 1.34/1.57 tff(2771,plain,
% 1.34/1.57 (~b(s(s(s(s(elem!1)))), z)),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[1632, 2770])).
% 1.34/1.57 tff(2772,plain,
% 1.34/1.57 (r(s(s(s(s(elem!1)))), z)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2081, 2771])).
% 1.34/1.57 tff(2773,plain,
% 1.34/1.57 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1745, 2772, 171])).
% 1.34/1.57 tff(2774,plain,
% 1.34/1.57 (~r(elem!1, s(z))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2773, 2767])).
% 1.34/1.57 tff(2775,plain,
% 1.34/1.57 (b(elem!1, s(z))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[305, 2774, 1639])).
% 1.34/1.57 tff(2776,plain,
% 1.34/1.57 ((s(s(elem!1)) = z) <=> (elem!1 = z)),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2759])).
% 1.34/1.57 tff(2777,plain,
% 1.34/1.57 ((s(s(elem!1)) = z) <=> (z = elem!1)),
% 1.34/1.57 inference(transitivity,[status(thm)],[2776, 247])).
% 1.34/1.57 tff(2778,plain,
% 1.34/1.57 ((~(s(s(elem!1)) = z)) <=> (~(z = elem!1))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2777])).
% 1.34/1.57 tff(2779,plain,
% 1.34/1.57 (~(z = elem!1)),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[154, 2778])).
% 1.34/1.57 tff(2780,plain,
% 1.34/1.57 (r(z, elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1549, 2779, 455])).
% 1.34/1.57 tff(2781,plain,
% 1.34/1.57 (~r(s(z), elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1544, 2780, 171])).
% 1.34/1.57 tff(2782,plain,
% 1.34/1.57 (b(s(z), elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[665, 2781, 1645])).
% 1.34/1.58 tff(2783,plain,
% 1.34/1.58 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2765])).
% 1.34/1.58 tff(2784,plain,
% 1.34/1.58 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 1.34/1.58 inference(transitivity,[status(thm)],[2783, 225])).
% 1.34/1.58 tff(2785,plain,
% 1.34/1.58 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2784])).
% 1.34/1.58 tff(2786,plain,
% 1.34/1.58 (~(s(s(z)) = elem!1)),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[239, 2785])).
% 1.34/1.58 tff(2787,plain,
% 1.34/1.58 (~r(s(s(s(s(z)))), z)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[948, 930, 272])).
% 1.34/1.58 tff(2788,plain,
% 1.34/1.58 (b(s(s(s(s(z)))), z)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[589, 21, 586, 2787])).
% 1.34/1.58 tff(2789,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, 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(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(2790,plain,
% 1.34/1.58 (((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, 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(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(2791,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(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(X0, 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(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2790])).
% 1.34/1.58 tff(2792,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(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(X0, 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(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 1.34/1.58 inference(transitivity,[status(thm)],[2791, 2789])).
% 1.34/1.58 tff(2793,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(2794,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[2793, 2792])).
% 1.34/1.58 tff(2795,plain,
% 1.34/1.58 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2794, 128, 297, 922, 591, 576])).
% 1.34/1.58 tff(2796,plain,
% 1.34/1.58 (r(s(s(z)), s(s(s(s(z)))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[610, 21, 607, 2795])).
% 1.34/1.58 tff(2797,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(z)))), s(z))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(2798,plain,
% 1.34/1.58 (((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(2799,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(z)))), s(z)))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2798])).
% 1.34/1.58 tff(2800,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(z)))), s(z))))),
% 1.34/1.58 inference(transitivity,[status(thm)],[2799, 2797])).
% 1.34/1.58 tff(2801,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(2802,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(z)))), s(z)))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[2801, 2800])).
% 1.34/1.58 tff(2803,plain,
% 1.34/1.58 (~b(s(s(s(s(z)))), s(z))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2802, 128, 297, 922, 576])).
% 1.34/1.58 tff(2804,plain,
% 1.34/1.58 (r(s(s(s(s(z)))), s(z))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[782, 21, 779, 2803])).
% 1.34/1.58 tff(2805,plain,
% 1.34/1.58 (((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(2806,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(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(X0, 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(s(z)), elem!1))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2805])).
% 1.34/1.58 tff(2807,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(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(X0, 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(s(z)), elem!1)))),
% 1.34/1.58 inference(transitivity,[status(thm)],[2806, 892])).
% 1.34/1.58 tff(2808,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(2809,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)), elem!1))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[2808, 2807])).
% 1.34/1.58 tff(2810,plain,
% 1.34/1.58 (~b(s(s(z)), s(z))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2809, 128, 297, 922, 591])).
% 1.34/1.58 tff(2811,plain,
% 1.34/1.58 (r(s(s(z)), s(z))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[86, 2810])).
% 1.34/1.58 tff(2812,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(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(2813,plain,
% 1.34/1.58 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(2814,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(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2813])).
% 1.34/1.58 tff(2815,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(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.34/1.58 inference(transitivity,[status(thm)],[2814, 2812])).
% 1.34/1.58 tff(2816,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(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(2817,plain,
% 1.34/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[2816, 2815])).
% 1.34/1.58 tff(2818,plain,
% 1.34/1.58 ($false),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2817, 45, 2811, 2804, 2796])).
% 1.34/1.58 tff(2819,plain,((~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.58 tff(2820,plain,
% 1.34/1.58 (~b(s(s(z)), elem!1)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2819, 576, 922, 297])).
% 1.34/1.58 tff(2821,plain,
% 1.34/1.58 (r(s(s(z)), elem!1)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[370, 2820, 484])).
% 1.34/1.58 tff(2822,plain,
% 1.34/1.58 (~r(s(s(z)), z)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1433, 45, 1416, 2821])).
% 1.34/1.58 tff(2823,plain,
% 1.34/1.58 (b(s(s(z)), z)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[25, 2822])).
% 1.34/1.58 tff(2824,plain,
% 1.34/1.58 (~r(z, s(s(z)))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1441, 45, 1416, 2821])).
% 1.34/1.58 tff(2825,plain,
% 1.34/1.58 (b(z, s(s(z)))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[516, 2824])).
% 1.34/1.58 tff(2826,plain,
% 1.34/1.58 (((~b(s(s(z)), z)) | (~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(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(2827,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~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(X0, 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)), s(s(s(s(z))))))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2826])).
% 1.34/1.58 tff(2828,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~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(X0, 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)), s(s(s(s(z)))))))),
% 1.34/1.58 inference(transitivity,[status(thm)],[2827, 1462])).
% 1.34/1.58 tff(2829,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~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)))))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(2830,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(s(s(s(z))))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[2829, 2828])).
% 1.34/1.58 tff(2831,plain,
% 1.34/1.58 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2830, 128, 2825, 2823, 2788])).
% 1.34/1.58 tff(2832,plain,
% 1.34/1.58 (r(s(s(z)), s(s(s(s(z)))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[610, 21, 607, 2831])).
% 1.34/1.58 tff(2833,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(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(2834,plain,
% 1.34/1.58 (((~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(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(2835,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(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(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2834])).
% 1.34/1.58 tff(2836,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(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(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.34/1.58 inference(transitivity,[status(thm)],[2835, 2833])).
% 1.34/1.58 tff(2837,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(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))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(2838,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(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[2837, 2836])).
% 1.34/1.58 tff(2839,plain,
% 1.34/1.58 (~r(s(s(z)), s(z))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2838, 45, 272, 930, 2832])).
% 1.34/1.58 tff(2840,plain,
% 1.34/1.58 (b(s(s(z)), s(z))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[86, 2839])).
% 1.34/1.58 tff(2841,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(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(2842,plain,
% 1.34/1.58 (((~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(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(2843,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(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(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2842])).
% 1.34/1.58 tff(2844,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(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(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.34/1.58 inference(transitivity,[status(thm)],[2843, 2841])).
% 1.34/1.58 tff(2845,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(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)))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(2846,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(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[2845, 2844])).
% 1.34/1.58 tff(2847,plain,
% 1.34/1.58 (~r(s(z), s(s(z)))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2846, 45, 930, 2832])).
% 1.34/1.58 tff(2848,plain,
% 1.34/1.58 (b(s(z), s(s(z)))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[648, 2847])).
% 1.34/1.58 tff(2849,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), s(s(z)))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), s(s(z)))) | (~b(z, s(s(z)))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(2850,plain,
% 1.34/1.58 (((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(2851,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(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(X0, 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(z), s(s(z)))) | (~b(z, s(s(z))))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2850])).
% 1.34/1.58 tff(2852,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(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(X0, 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(z), s(s(z)))) | (~b(z, s(s(z)))))),
% 1.34/1.58 inference(transitivity,[status(thm)],[2851, 2849])).
% 1.34/1.58 tff(2853,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(2854,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[2853, 2852])).
% 1.34/1.58 tff(2855,plain,
% 1.34/1.58 ($false),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2854, 128, 550, 2825, 2848, 2840])).
% 1.34/1.58 tff(2856,plain,((~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(z))) | (~r(s(z), z)) | (~r(z, elem!1)) | (s(s(z)) = elem!1) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.58 tff(2857,plain,
% 1.34/1.58 (~b(s(s(s(s(z)))), elem!1)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2856, 550, 171, 2780, 2786, 2782, 2775])).
% 1.34/1.58 tff(2858,plain,
% 1.34/1.58 (r(s(s(s(s(z)))), elem!1)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[632, 2857, 2760])).
% 1.34/1.58 tff(2859,plain,
% 1.34/1.58 (~r(s(s(s(s(z)))), z)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1459, 45, 2780, 2858])).
% 1.34/1.58 tff(2860,plain,
% 1.34/1.58 (b(s(s(s(s(z)))), z)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[589, 21, 586, 2859])).
% 1.34/1.58 tff(2861,plain,
% 1.34/1.58 (~r(s(s(z)), elem!1)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1469, 2858, 2780])).
% 1.34/1.58 tff(2862,plain,
% 1.34/1.58 (b(s(s(z)), elem!1)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[370, 2861, 2786])).
% 1.34/1.58 tff(2863,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z)))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z)))) | (~b(s(s(z)), elem!1)))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(2864,plain,
% 1.34/1.58 (((~b(s(z), elem!1)) | (~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(z), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(2865,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~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(X0, 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(z)))) | (~b(s(s(z)), elem!1))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2864])).
% 1.34/1.58 tff(2866,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~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(X0, 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(z)))) | (~b(s(s(z)), elem!1)))),
% 1.34/1.59 inference(transitivity,[status(thm)],[2865, 2863])).
% 1.34/1.59 tff(2867,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~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)))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(2868,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z)))) | (~b(s(s(z)), elem!1))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[2867, 2866])).
% 1.34/1.59 tff(2869,plain,
% 1.34/1.59 (~b(s(z), s(s(z)))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2868, 128, 2775, 2782, 2862])).
% 1.34/1.59 tff(2870,plain,
% 1.34/1.59 (r(s(z), s(s(z)))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[648, 2869])).
% 1.34/1.59 tff(2871,plain,
% 1.34/1.59 (~r(s(s(z)), z)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1327, 2870, 171])).
% 1.34/1.59 tff(2872,plain,
% 1.34/1.59 (b(s(s(z)), z)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[25, 2871])).
% 1.34/1.59 tff(2873,plain,
% 1.34/1.59 (~r(z, s(s(z)))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[642, 2870, 171])).
% 1.34/1.59 tff(2874,plain,
% 1.34/1.59 (b(z, s(s(z)))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[516, 2873])).
% 1.34/1.59 tff(2875,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2876,plain,
% 1.34/1.59 (((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2877,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(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(X0, 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)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[2876])).
% 1.34/1.59 tff(2878,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(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(X0, 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)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 1.34/1.59 inference(transitivity,[status(thm)],[2877, 2875])).
% 1.34/1.59 tff(2879,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(2880,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[2879, 2878])).
% 1.34/1.59 tff(2881,plain,
% 1.34/1.59 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2880, 128, 2874, 2872, 2860])).
% 1.34/1.59 tff(2882,plain,
% 1.34/1.59 ((s(s(s(s(z)))) = s(s(z))) | r(s(s(s(s(z)))), s(s(z)))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[971, 21, 2881])).
% 1.34/1.59 tff(2883,plain,
% 1.34/1.59 (r(s(s(s(s(z)))), s(s(z)))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2882, 921])).
% 1.34/1.59 tff(2884,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(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2885,plain,
% 1.34/1.59 (((~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(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2886,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)))), 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(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[2885])).
% 1.34/1.59 tff(2887,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)))), 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(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[2886, 2884])).
% 1.34/1.59 tff(2888,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)))), 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)))))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(2889,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(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[2888, 2887])).
% 1.34/1.59 tff(2890,plain,
% 1.34/1.59 (~r(s(z), s(s(s(s(z)))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2889, 45, 2870, 2883])).
% 1.34/1.59 tff(2891,plain,
% 1.34/1.59 (b(s(z), s(s(s(s(z)))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[684, 21, 681, 2890])).
% 1.34/1.59 tff(2892,plain,
% 1.34/1.59 ((z = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = z)),
% 1.34/1.59 inference(commutativity,[status(thm)],[])).
% 1.34/1.59 tff(2893,plain,
% 1.34/1.59 ((s(s(s(s(z)))) = z) <=> (z = s(s(s(s(z)))))),
% 1.34/1.59 inference(symmetry,[status(thm)],[2892])).
% 1.34/1.59 tff(2894,plain,
% 1.34/1.59 ((~(s(s(s(s(z)))) = z)) <=> (~(z = s(s(s(s(z))))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[2893])).
% 1.34/1.59 tff(2895,plain,
% 1.34/1.59 (~(z = s(s(s(s(z)))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[586, 2894])).
% 1.34/1.59 tff(2896,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(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)))))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2897,plain,
% 1.34/1.59 (((~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)))))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2898,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(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))))))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[2897])).
% 1.34/1.59 tff(2899,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(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)))))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[2898, 2896])).
% 1.34/1.59 tff(2900,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(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(2901,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(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z))))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[2900, 2899])).
% 1.34/1.59 tff(2902,plain,
% 1.34/1.59 (~r(z, s(s(s(s(z)))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2901, 45, 2780, 2858])).
% 1.34/1.59 tff(2903,plain,
% 1.34/1.59 (((~![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))))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2904,plain,
% 1.34/1.59 ((~![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))))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(2905,plain,
% 1.34/1.59 ((~![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)))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[2904, 2903])).
% 1.34/1.59 tff(2906,plain,
% 1.34/1.59 ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z)))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2905, 21, 2902])).
% 1.34/1.59 tff(2907,plain,
% 1.34/1.59 (b(z, s(s(s(s(z)))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2906, 2895])).
% 1.34/1.59 tff(2908,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2909,plain,
% 1.34/1.59 (((~b(z, s(z))) | (~b(z, 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(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2910,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[2909])).
% 1.34/1.59 tff(2911,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[2910, 2908])).
% 1.34/1.59 tff(2912,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, 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))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(2913,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[2912, 2911])).
% 1.34/1.59 tff(2914,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2913, 128, 550, 2907, 2860, 2891])).
% 1.34/1.59 tff(2915,plain,((~b(z, s(z))) | b(z, elem!1) | b(elem!1, z) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(2916,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2915, 1631, 550, 164, 455])).
% 1.34/1.59 tff(2917,plain,((~b(z, s(z))) | b(s(z), z) | b(z, elem!1) | (~b(elem!1, s(z))) | (~r(z, elem!1)) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(2918,plain,
% 1.34/1.59 (~b(z, s(z))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2917, 455, 164, 297, 1609, 1610])).
% 1.34/1.59 tff(2919,plain,
% 1.34/1.59 (r(z, s(z))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[415, 2918])).
% 1.34/1.59 tff(2920,assumption,(r(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.34/1.59 tff(2921,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(z, elem!1)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2922,plain,
% 1.34/1.59 (((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2923,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(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[2922])).
% 1.34/1.59 tff(2924,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(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.34/1.59 inference(transitivity,[status(thm)],[2923, 2921])).
% 1.34/1.59 tff(2925,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(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(2926,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(z, elem!1)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[2925, 2924])).
% 1.34/1.59 tff(2927,plain,
% 1.34/1.59 (~r(s(s(s(s(z)))), z)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2926, 45, 1416, 27, 2920])).
% 1.34/1.59 tff(2928,plain,
% 1.34/1.59 (b(s(s(s(s(z)))), z)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[589, 21, 586, 2927])).
% 1.34/1.59 tff(2929,plain,
% 1.34/1.59 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2817, 45, 35, 2920])).
% 1.34/1.59 tff(2930,plain,
% 1.34/1.59 (b(s(s(z)), s(s(s(s(z)))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[610, 21, 607, 2929])).
% 1.34/1.59 tff(2931,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(z, elem!1)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2932,plain,
% 1.34/1.59 (((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, elem!1)) | (~r(s(s(z)), z))) <=> ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2933,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(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, elem!1)) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[2932])).
% 1.34/1.59 tff(2934,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(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, elem!1)) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 1.34/1.59 inference(transitivity,[status(thm)],[2933, 2931])).
% 1.34/1.59 tff(2935,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(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, elem!1)) | (~r(s(s(z)), z)))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(2936,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(z, elem!1)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[2935, 2934])).
% 1.34/1.59 tff(2937,plain,
% 1.34/1.59 (~r(s(s(z)), z)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2936, 45, 1416, 27, 35])).
% 1.34/1.59 tff(2938,plain,
% 1.34/1.59 (b(s(s(z)), z)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[25, 2937])).
% 1.34/1.59 tff(2939,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(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))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2940,plain,
% 1.34/1.59 (((~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))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2941,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(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)))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[2940])).
% 1.34/1.59 tff(2942,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(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))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[2941, 2939])).
% 1.34/1.59 tff(2943,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(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))),
% 1.34/1.60 inference(quant_inst,[status(thm)],[])).
% 1.34/1.60 tff(2944,plain,
% 1.34/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z)))),
% 1.34/1.60 inference(modus_ponens,[status(thm)],[2943, 2942])).
% 1.34/1.60 tff(2945,plain,
% 1.34/1.60 ($false),
% 1.34/1.60 inference(unit_resolution,[status(thm)],[2944, 45, 27, 519, 35])).
% 1.34/1.60 tff(2946,plain,((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.60 tff(2947,plain,
% 1.34/1.60 (~r(z, s(s(z)))),
% 1.34/1.60 inference(unit_resolution,[status(thm)],[2946, 35, 27])).
% 1.34/1.60 tff(2948,plain,
% 1.34/1.60 (b(z, s(s(z)))),
% 1.34/1.60 inference(unit_resolution,[status(thm)],[516, 2947])).
% 1.34/1.60 tff(2949,plain,
% 1.34/1.60 ($false),
% 1.34/1.60 inference(unit_resolution,[status(thm)],[1467, 128, 2948, 2938, 2930, 2928])).
% 1.34/1.60 tff(2950,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.60 tff(2951,plain,
% 1.34/1.60 (~r(s(s(s(s(z)))), s(z))),
% 1.34/1.60 inference(unit_resolution,[status(thm)],[2950, 2919, 1609, 35])).
% 1.34/1.60 tff(2952,plain,
% 1.34/1.60 (b(s(s(s(s(z)))), s(z))),
% 1.34/1.60 inference(unit_resolution,[status(thm)],[784, 2951])).
% 1.34/1.60 tff(2953,assumption,(~(s(s(s(s(z)))) = elem!1)), introduced(assumption)).
% 1.34/1.60 tff(2954,plain,
% 1.34/1.60 (~r(s(s(z)), z)),
% 1.34/1.60 inference(unit_resolution,[status(thm)],[1509, 35, 171])).
% 1.34/1.60 tff(2955,plain,
% 1.34/1.60 (b(s(s(z)), z)),
% 1.34/1.60 inference(unit_resolution,[status(thm)],[25, 2954])).
% 1.34/1.60 tff(2956,assumption,(~(s(s(s(s(s(s(z)))))) = elem!1)), introduced(assumption)).
% 1.34/1.60 tff(2957,plain,
% 1.34/1.60 (~r(z, s(s(z)))),
% 1.34/1.60 inference(unit_resolution,[status(thm)],[2946, 2919, 35])).
% 1.34/1.60 tff(2958,plain,
% 1.34/1.60 (b(z, s(s(z)))),
% 1.34/1.60 inference(unit_resolution,[status(thm)],[516, 2957])).
% 1.34/1.60 tff(2959,plain,
% 1.34/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(s(z)))))))) | (~b(s(s(z)), 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(X0, 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(s(s(s(s(s(z)))))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.34/1.60 inference(rewrite,[status(thm)],[])).
% 1.34/1.60 tff(2960,plain,
% 1.34/1.60 (((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.34/1.60 inference(rewrite,[status(thm)],[])).
% 1.34/1.60 tff(2961,plain,
% 1.34/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~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(X0, 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(s(s(s(s(s(z)))))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1))))),
% 1.34/1.60 inference(monotonicity,[status(thm)],[2960])).
% 1.34/1.60 tff(2962,plain,
% 1.34/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~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(X0, 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(s(s(s(s(s(z)))))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.44/1.60 inference(transitivity,[status(thm)],[2961, 2959])).
% 1.44/1.60 tff(2963,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(2964,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(s(z)))))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[2963, 2962])).
% 1.44/1.60 tff(2965,plain,
% 1.44/1.60 (~b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2964, 128, 297, 922, 591, 1010])).
% 1.44/1.60 tff(2966,plain,
% 1.44/1.60 (r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1176, 21, 1123, 2965])).
% 1.44/1.60 tff(2967,plain,
% 1.44/1.60 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1485, 128, 297, 922, 1010])).
% 1.44/1.60 tff(2968,plain,
% 1.44/1.60 (r(s(z), s(s(s(s(s(s(z)))))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1041, 21, 1038, 2967])).
% 1.44/1.60 tff(2969,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(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(2970,plain,
% 1.44/1.60 (((~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(2971,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(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[2970])).
% 1.44/1.60 tff(2972,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(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.44/1.60 inference(transitivity,[status(thm)],[2971, 2969])).
% 1.44/1.60 tff(2973,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(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(z))))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(2974,plain,
% 1.44/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[2973, 2972])).
% 1.44/1.60 tff(2975,plain,
% 1.44/1.60 ($false),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2974, 45, 35, 2968, 2966])).
% 1.44/1.60 tff(2976,plain,((~b(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.60 tff(2977,plain,
% 1.44/1.60 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2976, 591, 297, 922, 35])).
% 1.44/1.60 tff(2978,plain,
% 1.44/1.60 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1055, 2977, 2956])).
% 1.44/1.60 tff(2979,plain,
% 1.44/1.60 (~b(s(s(s(s(z)))), elem!1)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2819, 591, 922, 297])).
% 1.44/1.60 tff(2980,plain,
% 1.44/1.60 (r(s(s(s(s(z)))), elem!1)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[632, 2979, 2953])).
% 1.44/1.60 tff(2981,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(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(2982,plain,
% 1.44/1.60 (((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(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(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(2983,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(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[2982])).
% 1.44/1.60 tff(2984,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(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.44/1.60 inference(transitivity,[status(thm)],[2983, 2981])).
% 1.44/1.60 tff(2985,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(s(s(z)))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(2986,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(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[2985, 2984])).
% 1.44/1.60 tff(2987,plain,
% 1.44/1.60 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2986, 45, 2980, 2978])).
% 1.44/1.60 tff(2988,plain,
% 1.44/1.60 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1215, 21, 1212, 2987])).
% 1.44/1.60 tff(2989,plain,
% 1.44/1.60 (~r(s(s(s(s(s(s(z)))))), z)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1423, 45, 1416, 2978])).
% 1.44/1.60 tff(2990,plain,
% 1.44/1.60 (b(s(s(s(s(s(s(z)))))), z)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1022, 21, 1019, 2989])).
% 1.44/1.60 tff(2991,plain,
% 1.44/1.60 (~r(s(s(s(s(z)))), z)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1459, 45, 1416, 2980])).
% 1.44/1.60 tff(2992,plain,
% 1.44/1.60 (b(s(s(s(s(z)))), z)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[589, 21, 586, 2991])).
% 1.44/1.60 tff(2993,assumption,(b(s(s(z)), z)), introduced(assumption)).
% 1.44/1.60 tff(2994,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(2995,plain,
% 1.44/1.60 (((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(2996,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[2995])).
% 1.44/1.60 tff(2997,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.44/1.60 inference(transitivity,[status(thm)],[2996, 2994])).
% 1.44/1.60 tff(2998,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(2999,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[2998, 2997])).
% 1.44/1.60 tff(3000,plain,
% 1.44/1.60 ($false),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2999, 128, 495, 2993, 2992, 2990, 2988])).
% 1.44/1.60 tff(3001,plain,((~b(s(s(z)), elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~r(z, elem!1)) | (s(s(s(s(s(s(z)))))) = elem!1) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.60 tff(3002,plain,
% 1.44/1.60 (~b(s(s(z)), elem!1)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[3001, 2958, 2956, 2955, 1609, 297, 922, 35, 2953])).
% 1.44/1.60 tff(3003,plain,
% 1.44/1.60 (r(s(s(z)), elem!1)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[370, 3002, 484])).
% 1.44/1.60 tff(3004,plain,
% 1.44/1.60 (~r(s(s(s(s(z)))), elem!1)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1469, 3003, 1609])).
% 1.44/1.60 tff(3005,plain,
% 1.44/1.60 (b(s(s(s(s(z)))), elem!1)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[632, 3004, 2953])).
% 1.44/1.60 tff(3006,plain,
% 1.44/1.60 ($false),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2802, 128, 297, 922, 3005, 2952])).
% 1.44/1.60 tff(3007,plain,(b(z, elem!1) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (s(s(s(s(z)))) = elem!1) | (s(s(z)) = elem!1) | (s(s(s(s(s(s(z)))))) = elem!1) | (~r(s(s(z)), s(z))) | b(s(z), z) | (s(z) = elem!1) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.60 tff(3008,plain,
% 1.44/1.60 (b(z, elem!1)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[3007, 1607, 1559, 243, 240, 246, 1501, 164, 257, 251])).
% 1.44/1.60 tff(3009,plain,
% 1.44/1.60 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 1.44/1.60 inference(commutativity,[status(thm)],[])).
% 1.44/1.60 tff(3010,plain,
% 1.44/1.60 ((s(s(s(s(z)))) = elem!1) <=> (elem!1 = s(s(s(s(z)))))),
% 1.44/1.60 inference(symmetry,[status(thm)],[3009])).
% 1.44/1.60 tff(3011,plain,
% 1.44/1.60 ((~(s(s(s(s(z)))) = elem!1)) <=> (~(elem!1 = s(s(s(s(z))))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[3010])).
% 1.44/1.60 tff(3012,plain,
% 1.44/1.60 (~(elem!1 = s(s(s(s(z)))))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[243, 3011])).
% 1.44/1.60 tff(3013,plain,
% 1.44/1.60 (~b(s(s(s(s(z)))), elem!1)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[950, 3008, 1559, 1607, 171])).
% 1.44/1.60 tff(3014,plain,
% 1.44/1.60 (r(s(s(s(s(z)))), elem!1)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[632, 3013, 243])).
% 1.44/1.60 tff(3015,plain,
% 1.44/1.60 (~b(z, s(z))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1156, 128, 3008, 1607, 1559])).
% 1.44/1.60 tff(3016,plain,
% 1.44/1.60 (r(z, s(z))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[415, 3015])).
% 1.44/1.60 tff(3017,plain,
% 1.44/1.60 (~r(z, s(s(z)))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2946, 3016, 1501])).
% 1.44/1.60 tff(3018,plain,
% 1.44/1.60 (b(z, s(s(z)))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[516, 3017])).
% 1.44/1.60 tff(3019,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z, s(s(z)))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z, s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(3020,plain,
% 1.44/1.60 (((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(z))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(3021,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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, 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(X0, 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(z, s(s(z)))) | (~b(s(s(z)), elem!1))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[3020])).
% 1.44/1.60 tff(3022,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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, 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(X0, 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(z, s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 1.44/1.60 inference(transitivity,[status(thm)],[3021, 3019])).
% 1.44/1.60 tff(3023,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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, s(z))) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(z)))))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(3024,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[3023, 3022])).
% 1.44/1.60 tff(3025,plain,
% 1.44/1.60 ($false),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[3024, 128, 498, 297, 922, 591, 495])).
% 1.44/1.60 tff(3026,plain,((~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.60 tff(3027,plain,
% 1.44/1.60 (~b(s(s(z)), elem!1)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[3026, 3008, 1607, 1559, 3018])).
% 1.44/1.60 tff(3028,plain,
% 1.44/1.60 (r(s(s(z)), elem!1)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[370, 3027, 240])).
% 1.44/1.60 tff(3029,plain,
% 1.44/1.60 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[967, 45, 3028, 3014])).
% 1.44/1.60 tff(3030,plain,
% 1.44/1.60 ((s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z)))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[971, 21, 3029])).
% 1.44/1.60 tff(3031,plain,
% 1.44/1.60 (b(s(s(s(s(z)))), s(s(z)))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[3030, 921])).
% 1.44/1.60 tff(3032,plain,
% 1.44/1.60 (~r(s(s(z)), z)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1509, 1501, 171])).
% 1.44/1.60 tff(3033,plain,
% 1.44/1.60 (b(s(s(z)), z)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[25, 3032])).
% 1.44/1.60 tff(3034,plain,
% 1.44/1.60 (((~b(z, s(s(z)))) | (~b(s(s(s(s(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)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(3035,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), 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(X0, 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)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[3034])).
% 1.44/1.60 tff(3036,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), 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(X0, 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)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 1.44/1.60 inference(transitivity,[status(thm)],[3035, 2875])).
% 1.44/1.60 tff(3037,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(3038,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[3037, 3036])).
% 1.44/1.60 tff(3039,plain,
% 1.44/1.60 (~b(s(s(s(s(z)))), z)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[3038, 128, 3018, 3033, 3031])).
% 1.44/1.60 tff(3040,plain,
% 1.44/1.60 (r(s(s(s(s(z)))), z)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[589, 21, 586, 3039])).
% 1.44/1.60 tff(3041,plain,
% 1.44/1.60 (~r(s(z), s(s(s(s(z)))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[948, 3040, 171])).
% 1.44/1.60 tff(3042,plain,
% 1.44/1.60 (b(s(z), s(s(s(s(z)))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[684, 21, 681, 3041])).
% 1.44/1.60 tff(3043,plain,
% 1.44/1.60 (~r(s(s(s(s(z)))), s(z))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1281, 45, 171, 3040])).
% 1.44/1.60 tff(3044,plain,
% 1.44/1.60 (b(s(s(s(s(z)))), s(z))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[784, 3043])).
% 1.44/1.60 tff(3045,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(3046,plain,
% 1.44/1.60 (((~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(3047,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[3046])).
% 1.44/1.61 tff(3048,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[3047, 3045])).
% 1.44/1.61 tff(3049,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(3050,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[3049, 3048])).
% 1.44/1.61 tff(3051,plain,
% 1.44/1.61 (~b(elem!1, s(s(s(s(z)))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[3050, 128, 1607, 3044, 3042])).
% 1.44/1.61 tff(3052,plain,
% 1.44/1.61 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(3053,plain,
% 1.44/1.61 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z))))))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(3054,plain,
% 1.44/1.61 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z)))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[3053, 3052])).
% 1.44/1.61 tff(3055,plain,
% 1.44/1.61 ((elem!1 = s(s(s(s(z))))) | r(elem!1, s(s(s(s(z)))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[3054, 21, 3051])).
% 1.44/1.61 tff(3056,plain,
% 1.44/1.61 (r(elem!1, s(s(s(s(z)))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[3055, 3012])).
% 1.44/1.61 tff(3057,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z)))) | (~b(s(s(z)), 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(X0, 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(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(3058,plain,
% 1.44/1.61 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~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, elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(3059,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~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(X0, 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(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z))))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[3058])).
% 1.44/1.61 tff(3060,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~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(X0, 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(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[3059, 3057])).
% 1.44/1.61 tff(3061,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~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)))))))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(3062,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[3061, 3060])).
% 1.44/1.61 tff(3063,plain,
% 1.44/1.61 (~b(z, s(s(s(s(z)))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[3062, 128, 3008, 3018, 3033, 3031])).
% 1.44/1.61 tff(3064,plain,
% 1.44/1.61 ((z = s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2905, 21, 3063])).
% 1.44/1.61 tff(3065,plain,
% 1.44/1.61 (r(z, s(s(s(s(z)))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[3064, 2895])).
% 1.44/1.61 tff(3066,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(z))) | (~r(elem!1, z)) | (~r(z, 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(z, s(z))) | (~r(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(3067,plain,
% 1.44/1.61 (((~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(elem!1, z))) <=> ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(3068,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(elem!1, s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[3067])).
% 1.44/1.61 tff(3069,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(elem!1, s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[3068, 3066])).
% 1.44/1.61 tff(3070,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(elem!1, s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(elem!1, z)))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(3071,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(z))) | (~r(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[3070, 3069])).
% 1.44/1.61 tff(3072,plain,
% 1.44/1.61 (~r(elem!1, z)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[3071, 45, 3016, 3065, 3056])).
% 1.44/1.61 tff(3073,plain,
% 1.44/1.61 (b(elem!1, z)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[574, 3072, 462])).
% 1.44/1.61 tff(3074,plain,
% 1.44/1.61 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1050, 3073, 1559, 171, 3008])).
% 1.44/1.61 tff(3075,plain,
% 1.44/1.61 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1055, 3074, 246])).
% 1.44/1.61 tff(3076,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)],[2986, 45, 3014, 3075])).
% 1.44/1.61 tff(3077,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)],[1215, 21, 1212, 3076])).
% 1.44/1.61 tff(3078,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)],[1172, 45, 3028, 3075])).
% 1.44/1.61 tff(3079,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)],[1176, 21, 1123, 3078])).
% 1.44/1.61 tff(3080,plain,
% 1.44/1.61 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[979, 45, 3028, 3014])).
% 1.44/1.61 tff(3081,plain,
% 1.44/1.61 (b(s(s(z)), s(s(s(s(z)))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[610, 21, 607, 3080])).
% 1.44/1.61 tff(3082,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(3083,plain,
% 1.44/1.61 (((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(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(s(s(z)))), 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(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(3084,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(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(X0, 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(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[3083])).
% 1.44/1.61 tff(3085,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(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(X0, 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(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[3084, 3082])).
% 1.44/1.61 tff(3086,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(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(3087,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[3086, 3085])).
% 1.44/1.61 tff(3088,plain,
% 1.44/1.61 ($false),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[3087, 128, 3031, 3081, 3079, 3077])).
% 1.44/1.61 tff(3089,plain,((~(s(s(elem!1)) = elem!1)) | b(s(z), z) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.61 tff(3090,plain,
% 1.44/1.61 (~(s(s(elem!1)) = elem!1)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[3089, 198, 164, 172])).
% 1.44/1.61 tff(3091,plain,
% 1.44/1.61 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1673])).
% 1.44/1.61 tff(3092,plain,
% 1.44/1.61 (r(s(z), z) <=> r(s(z), elem!1)),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1647])).
% 1.44/1.61 tff(3093,plain,
% 1.44/1.61 (r(s(z), elem!1)),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[272, 3092])).
% 1.44/1.61 tff(3094,plain,
% 1.44/1.61 (r(s(elem!1), elem!1)),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[3093, 1701])).
% 1.44/1.61 tff(3095,plain,
% 1.44/1.61 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1709, 45, 1703, 3094])).
% 1.44/1.61 tff(3096,plain,
% 1.44/1.61 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1727, 21, 1724, 3095])).
% 1.44/1.61 tff(3097,plain,
% 1.44/1.61 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1671])).
% 1.44/1.61 tff(3098,plain,
% 1.44/1.61 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[3097])).
% 1.44/1.61 tff(3099,plain,
% 1.44/1.61 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[239, 3098])).
% 1.44/1.61 tff(3100,plain,
% 1.44/1.61 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1065, 3099])).
% 1.44/1.61 tff(3101,plain,
% 1.44/1.61 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[693, 3100])).
% 1.44/1.61 tff(3102,plain,
% 1.44/1.61 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[700, 3101])).
% 1.44/1.61 tff(3103,plain,
% 1.44/1.61 (r(z, s(z)) <=> r(elem!1, s(z))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1647])).
% 1.44/1.61 tff(3104,plain,
% 1.44/1.61 (r(elem!1, s(z))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[27, 3103])).
% 1.44/1.61 tff(3105,plain,
% 1.44/1.61 (~r(s(s(z)), elem!1)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1356, 1245, 272, 3093])).
% 1.44/1.61 tff(3106,plain,
% 1.44/1.61 (b(s(s(z)), elem!1)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[370, 3105, 2399])).
% 1.44/1.61 tff(3107,plain,
% 1.44/1.61 (b(s(s(elem!1)), elem!1)),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[3106, 2395])).
% 1.44/1.61 tff(3108,plain,
% 1.44/1.61 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1)))))))),
% 1.44/1.61 inference(commutativity,[status(thm)],[])).
% 1.44/1.61 tff(3109,plain,
% 1.44/1.61 ((s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1)))))),
% 1.44/1.61 inference(symmetry,[status(thm)],[3108])).
% 1.44/1.61 tff(3110,plain,
% 1.44/1.61 ((~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1)))))))) <=> (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[3109])).
% 1.44/1.61 tff(3111,plain,
% 1.44/1.61 (s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1673])).
% 1.44/1.61 tff(3112,plain,
% 1.44/1.61 (s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(elem!1))))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[3111])).
% 1.44/1.61 tff(3113,plain,
% 1.44/1.61 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z))))))),
% 1.44/1.61 inference(symmetry,[status(thm)],[3112])).
% 1.44/1.61 tff(3114,assumption,(s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.44/1.61 tff(3115,plain,
% 1.44/1.61 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1)))))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(3116,plain,
% 1.44/1.61 (inj_0(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[3115, 62])).
% 1.44/1.61 tff(3117,plain,
% 1.44/1.61 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(elem!1))))))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(3118,plain,
% 1.44/1.61 (inj_0(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(elem!1)))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[3117, 62])).
% 1.44/1.61 tff(3119,plain,
% 1.44/1.61 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[3114])).
% 1.44/1.61 tff(3120,plain,
% 1.44/1.61 (s(s(s(elem!1))) = s(s(s(s(s(elem!1)))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[1720, 3119, 3118])).
% 1.44/1.61 tff(3121,plain,
% 1.44/1.61 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[3120])).
% 1.44/1.61 tff(3122,plain,
% 1.44/1.61 (s(s(z)) = s(s(s(s(s(s(z))))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[1671, 187, 3121, 3116, 3114, 3113])).
% 1.44/1.61 tff(3123,plain,
% 1.44/1.61 ($false),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1123, 3122])).
% 1.44/1.61 tff(3124,plain,((~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1)))))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.61 tff(3125,plain,
% 1.44/1.61 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1)))))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[3124, 1647])).
% 1.44/1.61 tff(3126,plain,
% 1.44/1.61 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1)))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[3125, 3110])).
% 1.44/1.61 tff(3127,plain,
% 1.44/1.61 (r(s(s(s(s(s(s(elem!1)))))), elem!1) <=> r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.44/1.61 inference(monotonicity,[status(thm)],[3113])).
% 1.44/1.61 tff(3128,plain,
% 1.44/1.61 (r(s(s(s(s(s(s(z)))))), elem!1) <=> r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.44/1.61 inference(symmetry,[status(thm)],[3127])).
% 1.44/1.61 tff(3129,plain,
% 1.44/1.61 ((s(s(s(s(s(s(z)))))) = z) <=> (s(s(s(s(s(s(z)))))) = elem!1)),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1647])).
% 1.44/1.61 tff(3130,plain,
% 1.44/1.61 ((~(s(s(s(s(s(s(z)))))) = z)) <=> (~(s(s(s(s(s(s(z)))))) = elem!1))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[3129])).
% 1.44/1.61 tff(3131,plain,
% 1.44/1.61 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[1019, 3130])).
% 1.44/1.61 tff(3132,plain,
% 1.44/1.61 (r(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[385, 2657])).
% 1.44/1.61 tff(3133,plain,
% 1.44/1.61 (r(elem!1, s(elem!1)) <=> r(elem!1, s(z))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1649])).
% 1.44/1.61 tff(3134,plain,
% 1.44/1.61 (r(elem!1, s(z)) <=> r(elem!1, s(elem!1))),
% 1.44/1.61 inference(symmetry,[status(thm)],[3133])).
% 1.44/1.61 tff(3135,plain,
% 1.44/1.61 (r(elem!1, s(elem!1))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[313, 3134])).
% 1.44/1.61 tff(3136,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(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(3137,plain,
% 1.44/1.61 (((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(3138,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(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[3137])).
% 1.44/1.61 tff(3139,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(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.44/1.61 inference(transitivity,[status(thm)],[3138, 3136])).
% 1.44/1.61 tff(3140,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(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(3141,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(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[3140, 3139])).
% 1.44/1.61 tff(3142,plain,
% 1.44/1.61 ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[3141, 45])).
% 1.44/1.61 tff(3143,plain,
% 1.44/1.61 (~r(s(s(s(elem!1))), elem!1)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[3142, 3135, 3132])).
% 1.44/1.61 tff(3144,plain,
% 1.44/1.61 (b(s(s(s(elem!1))), elem!1)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[742, 3143, 2446])).
% 1.44/1.61 tff(3145,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(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(3146,plain,
% 1.44/1.61 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(3147,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(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1)))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[3146])).
% 1.44/1.61 tff(3148,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(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[3147, 3145])).
% 1.44/1.61 tff(3149,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(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(3150,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(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[3149, 3148])).
% 1.44/1.61 tff(3151,plain,
% 1.44/1.61 ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[3150, 45])).
% 1.44/1.61 tff(3152,plain,
% 1.44/1.61 (~r(elem!1, s(s(s(elem!1))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[3151, 3135, 3132])).
% 1.44/1.61 tff(3153,plain,
% 1.44/1.61 (b(elem!1, s(s(s(elem!1))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2466, 3152, 2457])).
% 1.44/1.61 tff(3154,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(3155,plain,
% 1.44/1.61 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(3156,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[3155])).
% 1.44/1.61 tff(3157,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[3156, 3154])).
% 1.44/1.61 tff(3158,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(3159,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[3158, 3157])).
% 1.44/1.61 tff(3160,plain,
% 1.44/1.61 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[3159, 128, 1681, 3153, 3144])).
% 1.44/1.61 tff(3161,plain,
% 1.44/1.61 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[321, 3160, 3100])).
% 1.44/1.61 tff(3162,plain,
% 1.44/1.61 (~r(s(s(elem!1)), s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[393, 3161, 385])).
% 1.44/1.61 tff(3163,plain,
% 1.44/1.61 (b(s(s(elem!1)), s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[292, 3162])).
% 1.44/1.61 tff(3164,plain,
% 1.44/1.61 (b(s(s(elem!1)), s(elem!1))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[3163, 1944])).
% 1.44/1.61 tff(3165,plain,
% 1.44/1.61 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[803, 3100])).
% 1.44/1.61 tff(3166,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(3167,plain,
% 1.44/1.62 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(3168,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[3167])).
% 1.44/1.62 tff(3169,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.44/1.62 inference(transitivity,[status(thm)],[3168, 3166])).
% 1.44/1.62 tff(3170,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(3171,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[3170, 3169])).
% 1.44/1.62 tff(3172,plain,
% 1.44/1.62 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[3171, 128, 1681, 3153, 3144])).
% 1.44/1.62 tff(3173,plain,
% 1.44/1.62 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[889, 3172, 3165])).
% 1.44/1.62 tff(3174,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2122, 45, 272, 89, 1794, 385])).
% 1.44/1.62 tff(3175,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.62 tff(3176,plain,
% 1.44/1.62 (~r(s(z), s(s(elem!1)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[3175, 3173, 385, 272])).
% 1.44/1.62 tff(3177,plain,
% 1.44/1.62 (b(s(z), s(s(elem!1)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[117, 3176])).
% 1.44/1.62 tff(3178,plain,
% 1.44/1.62 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2608, 3177, 1841, 3163])).
% 1.44/1.62 tff(3179,plain,
% 1.44/1.62 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1897, 3178, 3099])).
% 1.44/1.62 tff(3180,plain,
% 1.44/1.62 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2103, 3179, 3161])).
% 1.44/1.62 tff(3181,plain,
% 1.44/1.62 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1820, 3180, 3102])).
% 1.44/1.62 tff(3182,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(3183,plain,
% 1.44/1.62 (((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1))))))) <=> ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(3184,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[3183])).
% 1.44/1.62 tff(3185,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.44/1.62 inference(transitivity,[status(thm)],[3184, 3182])).
% 1.44/1.62 tff(3186,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(3187,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[3186, 3185])).
% 1.44/1.62 tff(3188,plain,
% 1.44/1.62 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[3187, 128, 3153, 3144, 3181])).
% 1.44/1.62 tff(3189,plain,
% 1.44/1.62 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1766, 3188, 1699])).
% 1.44/1.62 tff(3190,plain,
% 1.44/1.62 (r(z, s(s(s(s(elem!1)))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[3189, 1693])).
% 1.44/1.62 tff(3191,assumption,(r(s(s(s(s(elem!1)))), elem!1)), introduced(assumption)).
% 1.44/1.62 tff(3192,plain,
% 1.44/1.62 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1709, 45, 3191, 3094])).
% 1.44/1.62 tff(3193,plain,
% 1.44/1.62 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1727, 21, 1724, 3192])).
% 1.44/1.62 tff(3194,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(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(3195,plain,
% 1.44/1.62 (((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(3196,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), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[3195])).
% 1.44/1.62 tff(3197,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), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.44/1.62 inference(transitivity,[status(thm)],[3196, 3194])).
% 1.44/1.62 tff(3198,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), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(3199,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(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[3198, 3197])).
% 1.44/1.62 tff(3200,plain,
% 1.44/1.62 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[3199, 45, 3191, 3094])).
% 1.44/1.62 tff(3201,plain,
% 1.44/1.62 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1920, 3200, 1751])).
% 1.44/1.62 tff(3202,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(3203,plain,
% 1.44/1.62 (((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(3204,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(elem!1)))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[3203])).
% 1.44/1.62 tff(3205,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.44/1.62 inference(transitivity,[status(thm)],[3204, 3202])).
% 1.44/1.62 tff(3206,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(3207,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[3206, 3205])).
% 1.44/1.62 tff(3208,plain,
% 1.44/1.62 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[3207, 128, 3201, 3164, 3193])).
% 1.44/1.62 tff(3209,plain,
% 1.44/1.62 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.44/1.62 inference(symmetry,[status(thm)],[1067])).
% 1.44/1.62 tff(3210,plain,
% 1.44/1.62 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.44/1.62 inference(transitivity,[status(thm)],[3097, 3209])).
% 1.44/1.62 tff(3211,plain,
% 1.44/1.62 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[3210])).
% 1.44/1.62 tff(3212,plain,
% 1.44/1.62 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[239, 3211])).
% 1.44/1.62 tff(3213,plain,
% 1.44/1.62 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2212, 21, 3212, 3208])).
% 1.44/1.62 tff(3214,assumption,(r(s(s(elem!1)), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.44/1.62 tff(3215,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(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(3216,plain,
% 1.44/1.62 (((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(3217,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)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1))))))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[3216])).
% 1.44/1.62 tff(3218,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)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.44/1.62 inference(transitivity,[status(thm)],[3217, 3215])).
% 1.44/1.62 tff(3219,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)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(elem!1)))))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(3220,plain,
% 1.44/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1))))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[3219, 3218])).
% 1.44/1.62 tff(3221,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[3220, 45, 88, 3214, 1782])).
% 1.44/1.62 tff(3222,plain,((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.62 tff(3223,plain,
% 1.44/1.62 (~r(z, s(s(elem!1)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[3222, 3213, 3190])).
% 1.44/1.62 tff(3224,plain,
% 1.44/1.62 (b(z, s(s(elem!1)))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[160, 3223])).
% 1.44/1.62 tff(3225,plain,
% 1.44/1.62 (b(elem!1, s(s(elem!1)))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[3224, 1652])).
% 1.44/1.62 tff(3226,plain,
% 1.44/1.62 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1)))))))),
% 1.44/1.62 inference(commutativity,[status(thm)],[])).
% 1.44/1.62 tff(3227,plain,
% 1.44/1.62 ((s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))),
% 1.44/1.62 inference(symmetry,[status(thm)],[3226])).
% 1.44/1.62 tff(3228,plain,
% 1.44/1.62 ((~(s(s(s(elem!1))) = s(s(s(s(s(s(elem!1)))))))) <=> (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[3227])).
% 1.44/1.62 tff(3229,assumption,(s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.44/1.62 tff(3230,plain,
% 1.44/1.62 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[3229])).
% 1.44/1.62 tff(3231,plain,
% 1.44/1.62 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 1.44/1.62 inference(transitivity,[status(thm)],[187, 3230, 3118])).
% 1.44/1.62 tff(3232,plain,
% 1.44/1.62 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[3231])).
% 1.44/1.62 tff(3233,plain,
% 1.44/1.62 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.44/1.62 inference(transitivity,[status(thm)],[106, 3232, 3116])).
% 1.44/1.62 tff(3234,assumption,(~(s(elem!1) = s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.44/1.62 tff(3235,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[3234, 3233])).
% 1.44/1.62 tff(3236,plain,((~(s(s(s(elem!1))) = s(s(s(s(s(s(elem!1)))))))) | (s(elem!1) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.62 tff(3237,plain,
% 1.44/1.62 (~(s(s(s(elem!1))) = s(s(s(s(s(s(elem!1)))))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[3236, 1724])).
% 1.44/1.62 tff(3238,plain,
% 1.44/1.62 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[3237, 3228])).
% 1.44/1.62 tff(3239,assumption,(b(s(s(s(s(s(s(elem!1)))))), elem!1)), introduced(assumption)).
% 1.44/1.62 tff(3240,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(3241,plain,
% 1.44/1.62 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(3242,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[3241])).
% 1.44/1.62 tff(3243,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.44/1.62 inference(transitivity,[status(thm)],[3242, 3240])).
% 1.44/1.62 tff(3244,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(3245,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[3244, 3243])).
% 1.44/1.62 tff(3246,plain,
% 1.44/1.62 ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[3245, 128, 1681, 1663, 2659])).
% 1.44/1.62 tff(3247,plain,
% 1.44/1.62 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[3246, 3239])).
% 1.44/1.62 tff(3248,plain,
% 1.44/1.62 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(3249,plain,
% 1.44/1.62 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(3250,plain,
% 1.44/1.62 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[3249, 3248])).
% 1.44/1.62 tff(3251,plain,
% 1.44/1.62 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[3250, 21, 3247])).
% 1.44/1.63 tff(3252,plain,
% 1.44/1.63 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[3251, 3238])).
% 1.44/1.63 tff(3253,plain,
% 1.44/1.63 (s(s(elem!1)) = s(s(z))),
% 1.44/1.63 inference(symmetry,[status(thm)],[1671])).
% 1.44/1.63 tff(3254,plain,
% 1.44/1.63 ((s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) <=> (s(s(s(s(s(s(z)))))) = s(s(z)))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[3113, 3253])).
% 1.44/1.63 tff(3255,plain,
% 1.44/1.63 ((s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) <=> (s(s(z)) = s(s(s(s(s(s(z)))))))),
% 1.44/1.63 inference(transitivity,[status(thm)],[3254, 1113])).
% 1.44/1.63 tff(3256,plain,
% 1.44/1.63 ((s(s(z)) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 1.44/1.63 inference(symmetry,[status(thm)],[3255])).
% 1.44/1.63 tff(3257,plain,
% 1.44/1.63 ((~(s(s(z)) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[3256])).
% 1.44/1.63 tff(3258,plain,
% 1.44/1.63 (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[1123, 3257])).
% 1.44/1.63 tff(3259,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(3260,plain,
% 1.44/1.63 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(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(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(3261,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[3260])).
% 1.44/1.63 tff(3262,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 1.44/1.63 inference(transitivity,[status(thm)],[3261, 3259])).
% 1.44/1.63 tff(3263,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(3264,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[3263, 3262])).
% 1.44/1.63 tff(3265,plain,
% 1.44/1.63 ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[3264, 128, 1681, 1663])).
% 1.44/1.63 tff(3266,plain,
% 1.44/1.63 (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[3265, 3239])).
% 1.44/1.63 tff(3267,plain,
% 1.44/1.63 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))) | r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))) | r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(3268,plain,
% 1.44/1.63 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))) | r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(3269,plain,
% 1.44/1.63 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))) | r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[3268, 3267])).
% 1.44/1.63 tff(3270,plain,
% 1.44/1.63 ((s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[3269, 21, 3266])).
% 1.44/1.63 tff(3271,plain,
% 1.44/1.63 (r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[3270, 3258])).
% 1.44/1.63 tff(3272,plain,
% 1.44/1.63 ((s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(z)) = s(s(s(s(s(s(z)))))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[3253, 3113])).
% 1.44/1.63 tff(3273,plain,
% 1.44/1.63 ((s(s(z)) = s(s(s(s(s(s(z))))))) <=> (s(s(elem!1)) = s(s(s(s(s(s(elem!1)))))))),
% 1.44/1.63 inference(symmetry,[status(thm)],[3272])).
% 1.44/1.63 tff(3274,plain,
% 1.44/1.63 ((~(s(s(z)) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[3273])).
% 1.44/1.63 tff(3275,plain,
% 1.44/1.63 (~(s(s(elem!1)) = s(s(s(s(s(s(elem!1)))))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[1123, 3274])).
% 1.44/1.63 tff(3276,assumption,(b(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 1.44/1.63 tff(3277,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(3278,plain,
% 1.44/1.63 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(3279,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[3278])).
% 1.44/1.63 tff(3280,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 1.44/1.63 inference(transitivity,[status(thm)],[3279, 3277])).
% 1.44/1.63 tff(3281,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(3282,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[3281, 3280])).
% 1.44/1.63 tff(3283,plain,
% 1.44/1.63 ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[3282, 128, 1681, 1663, 3276])).
% 1.44/1.63 tff(3284,plain,
% 1.44/1.63 (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[3283, 3239])).
% 1.44/1.63 tff(3285,plain,
% 1.44/1.63 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) | b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))) | r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) | b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))) | r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(3286,plain,
% 1.44/1.63 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) | b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))) | r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(3287,plain,
% 1.44/1.63 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) | b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))) | r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[3286, 3285])).
% 1.44/1.63 tff(3288,plain,
% 1.44/1.63 ((s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) | r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[3287, 21, 3284])).
% 1.44/1.63 tff(3289,plain,
% 1.44/1.63 (r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[3288, 3275])).
% 1.44/1.63 tff(3290,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(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(3291,plain,
% 1.44/1.63 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(3292,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(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[3291])).
% 1.44/1.63 tff(3293,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(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.44/1.63 inference(transitivity,[status(thm)],[3292, 3290])).
% 1.44/1.63 tff(3294,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(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(3295,plain,
% 1.44/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[3294, 3293])).
% 1.44/1.63 tff(3296,plain,
% 1.44/1.63 ($false),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[3295, 45, 324, 3289, 3271, 3252])).
% 1.44/1.63 tff(3297,plain,((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~(z = elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.63 tff(3298,plain,
% 1.44/1.63 (~b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[3297, 3225, 1647, 1681, 3164, 3144, 3161])).
% 1.44/1.63 tff(3299,plain,
% 1.44/1.63 (b(s(s(s(s(s(s(elem!1)))))), elem!1) <=> b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.44/1.63 inference(monotonicity,[status(thm)],[3113])).
% 1.44/1.63 tff(3300,plain,
% 1.44/1.63 (b(s(s(s(s(s(s(z)))))), elem!1) <=> b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.44/1.63 inference(symmetry,[status(thm)],[3299])).
% 1.44/1.63 tff(3301,plain,
% 1.44/1.63 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[1010, 3300])).
% 1.44/1.63 tff(3302,assumption,(~b(s(s(s(s(s(s(elem!1)))))), elem!1)), introduced(assumption)).
% 1.44/1.63 tff(3303,plain,
% 1.44/1.63 ($false),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[3302, 3301])).
% 1.44/1.63 tff(3304,plain,((~b(s(s(s(s(s(s(z)))))), elem!1)) | b(s(s(s(s(s(s(elem!1)))))), elem!1) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.63 tff(3305,plain,
% 1.44/1.63 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[3304, 3298, 1647])).
% 1.44/1.63 tff(3306,plain,
% 1.44/1.63 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1055, 3305, 3131])).
% 1.44/1.63 tff(3307,plain,
% 1.44/1.63 (r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[3306, 3128])).
% 1.44/1.63 tff(3308,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(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(3309,plain,
% 1.44/1.63 (((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(3310,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(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[3309])).
% 1.44/1.63 tff(3311,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(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.44/1.63 inference(transitivity,[status(thm)],[3310, 3308])).
% 1.44/1.63 tff(3312,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(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(3313,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(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[3312, 3311])).
% 1.44/1.63 tff(3314,plain,
% 1.44/1.63 ((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[3313, 45, 3191])).
% 1.44/1.63 tff(3315,plain,
% 1.44/1.63 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[3314, 3307])).
% 1.44/1.63 tff(3316,plain,
% 1.44/1.63 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(3317,plain,
% 1.44/1.63 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(3318,plain,
% 1.44/1.63 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[3317, 3316])).
% 1.44/1.63 tff(3319,plain,
% 1.44/1.63 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[3318, 21, 3315])).
% 1.44/1.63 tff(3320,plain,
% 1.44/1.63 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[3319, 3126])).
% 1.44/1.63 tff(3321,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(s(elem!1)))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(3322,plain,
% 1.44/1.63 (((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(3323,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(s(s(elem!1)))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(elem!1))))))))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[3322])).
% 1.44/1.63 tff(3324,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(s(s(elem!1)))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))))),
% 1.44/1.63 inference(transitivity,[status(thm)],[3323, 3321])).
% 1.44/1.63 tff(3325,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(s(s(elem!1)))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(3326,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(s(elem!1)))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(elem!1))))))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[3325, 3324])).
% 1.44/1.63 tff(3327,plain,
% 1.44/1.63 ((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(elem!1))))))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[3326, 45, 3094])).
% 1.44/1.63 tff(3328,plain,
% 1.44/1.63 (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[3327, 3307])).
% 1.44/1.63 tff(3329,assumption,(s(elem!1) = s(s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.44/1.63 tff(3330,plain,
% 1.44/1.63 (inj_0(s(elem!1)) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[3329])).
% 1.44/1.63 tff(3331,plain,
% 1.44/1.63 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(elem!1))),
% 1.44/1.63 inference(symmetry,[status(thm)],[3330])).
% 1.44/1.63 tff(3332,plain,
% 1.44/1.63 (s(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 1.44/1.63 inference(symmetry,[status(thm)],[3118])).
% 1.44/1.63 tff(3333,plain,
% 1.44/1.63 (s(s(s(s(s(elem!1))))) = z),
% 1.44/1.63 inference(transitivity,[status(thm)],[3332, 3331, 201, 1668])).
% 1.44/1.63 tff(3334,plain,
% 1.44/1.63 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(elem!1))))) = z))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(3335,plain,
% 1.44/1.63 (~(s(s(s(s(s(elem!1))))) = z)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[3334, 9])).
% 1.44/1.63 tff(3336,plain,
% 1.44/1.63 ($false),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[3335, 3333])).
% 1.44/1.63 tff(3337,plain,((~(s(elem!1) = s(s(s(s(s(s(elem!1)))))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.63 tff(3338,plain,
% 1.44/1.63 (~(s(elem!1) = s(s(s(s(s(s(elem!1)))))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[3337, 1647])).
% 1.44/1.63 tff(3339,plain,
% 1.44/1.63 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(s(s(elem!1))))))) | b(s(elem!1), s(s(s(s(s(s(elem!1))))))) | r(s(elem!1), s(s(s(s(s(s(elem!1))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(s(s(elem!1))))))) | b(s(elem!1), s(s(s(s(s(s(elem!1))))))) | r(s(elem!1), s(s(s(s(s(s(elem!1))))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(3340,plain,
% 1.44/1.63 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(s(s(elem!1))))))) | b(s(elem!1), s(s(s(s(s(s(elem!1))))))) | r(s(elem!1), s(s(s(s(s(s(elem!1))))))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(3341,plain,
% 1.44/1.63 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(s(s(elem!1))))))) | b(s(elem!1), s(s(s(s(s(s(elem!1))))))) | r(s(elem!1), s(s(s(s(s(s(elem!1)))))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[3340, 3339])).
% 1.44/1.63 tff(3342,plain,
% 1.44/1.63 (b(s(elem!1), s(s(s(s(s(s(elem!1)))))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[3341, 21, 3338, 3328])).
% 1.44/1.63 tff(3343,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(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(3344,plain,
% 1.44/1.63 (((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(3345,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(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[3344])).
% 1.44/1.63 tff(3346,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(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.44/1.63 inference(transitivity,[status(thm)],[3345, 3343])).
% 1.44/1.63 tff(3347,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(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(3348,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(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[3347, 3346])).
% 1.44/1.63 tff(3349,plain,
% 1.44/1.63 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[3348, 45, 3179, 3173])).
% 1.44/1.63 tff(3350,plain,
% 1.44/1.63 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1856, 3349, 3101])).
% 1.44/1.63 tff(3351,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(3352,plain,
% 1.44/1.64 (((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(3353,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[3352])).
% 1.44/1.64 tff(3354,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.44/1.64 inference(transitivity,[status(thm)],[3353, 3351])).
% 1.44/1.64 tff(3355,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(3356,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[3355, 3354])).
% 1.44/1.64 tff(3357,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3356, 128, 3350, 3181, 3193, 3342, 3320])).
% 1.44/1.64 tff(3358,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~(z = elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), z)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(3359,plain,
% 1.44/1.64 (~r(s(s(s(elem!1))), s(z))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3358, 1703, 1647, 3107, 1829, 272, 3104])).
% 1.44/1.64 tff(3360,plain,
% 1.44/1.64 (b(s(s(s(elem!1))), s(z))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[196, 3359])).
% 1.44/1.64 tff(3361,plain,
% 1.44/1.64 (b(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[3360, 2550])).
% 1.44/1.64 tff(3362,plain,
% 1.44/1.64 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3199, 45, 1703, 3094])).
% 1.44/1.64 tff(3363,plain,
% 1.44/1.64 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1920, 3362, 1751])).
% 1.44/1.64 tff(3364,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(3365,plain,
% 1.44/1.64 (((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(3366,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[3365])).
% 1.44/1.64 tff(3367,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.44/1.64 inference(transitivity,[status(thm)],[3366, 3364])).
% 1.44/1.64 tff(3368,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(3369,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[3368, 3367])).
% 1.44/1.64 tff(3370,plain,
% 1.44/1.64 ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3369, 128, 3363, 3096])).
% 1.44/1.64 tff(3371,plain,
% 1.44/1.64 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3370, 3361])).
% 1.44/1.64 tff(3372,plain,
% 1.44/1.64 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1820, 3371, 3102])).
% 1.44/1.64 tff(3373,plain,
% 1.44/1.64 (~r(s(s(s(elem!1))), z)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1780, 3372, 1690])).
% 1.44/1.64 tff(3374,plain,
% 1.44/1.64 (~r(s(s(s(elem!1))), elem!1)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2453, 3373, 1647])).
% 1.44/1.64 tff(3375,plain,
% 1.44/1.64 (b(s(s(s(elem!1))), elem!1)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[742, 3374, 2446])).
% 1.44/1.64 tff(3376,plain,
% 1.44/1.64 ((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) <=> (~r(s(s(s(s(s(s(z)))))), elem!1))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[3127])).
% 1.44/1.64 tff(3377,plain,
% 1.44/1.64 (~r(z, s(s(elem!1)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1383, 89, 272])).
% 1.44/1.64 tff(3378,plain,
% 1.44/1.64 (b(z, s(s(elem!1)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[160, 3377])).
% 1.44/1.64 tff(3379,plain,
% 1.44/1.64 (b(elem!1, s(s(elem!1)))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[3378, 1652])).
% 1.44/1.64 tff(3380,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(3381,plain,
% 1.44/1.64 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(3382,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[3381])).
% 1.44/1.64 tff(3383,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.44/1.64 inference(transitivity,[status(thm)],[3382, 3380])).
% 1.44/1.64 tff(3384,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(3385,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[3384, 3383])).
% 1.44/1.64 tff(3386,plain,
% 1.44/1.64 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3385, 128, 1681, 3379, 2659])).
% 1.44/1.64 tff(3387,plain,
% 1.44/1.64 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[889, 3386, 3165])).
% 1.44/1.64 tff(3388,plain,
% 1.44/1.64 (~r(s(z), s(s(s(elem!1))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1802, 3387, 89])).
% 1.44/1.64 tff(3389,plain,
% 1.44/1.64 (b(s(z), s(s(s(elem!1))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[339, 3388])).
% 1.44/1.64 tff(3390,plain,
% 1.44/1.64 (b(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[3389, 2572])).
% 1.44/1.64 tff(3391,assumption,(~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 1.44/1.64 tff(3392,plain,
% 1.44/1.64 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1)))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[3391, 3110])).
% 1.44/1.64 tff(3393,assumption,(r(s(s(s(s(s(s(elem!1)))))), elem!1)), introduced(assumption)).
% 1.44/1.64 tff(3394,plain,
% 1.44/1.64 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3314, 3393])).
% 1.44/1.64 tff(3395,plain,
% 1.44/1.64 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3318, 21, 3394])).
% 1.44/1.64 tff(3396,plain,
% 1.44/1.64 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3395, 3392])).
% 1.44/1.64 tff(3397,assumption,(r(s(elem!1), elem!1)), introduced(assumption)).
% 1.44/1.64 tff(3398,plain,
% 1.44/1.64 ((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(elem!1))))))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3326, 45, 3397])).
% 1.44/1.64 tff(3399,plain,
% 1.44/1.64 (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3398, 3393])).
% 1.44/1.64 tff(3400,assumption,(~(s(elem!1) = s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 1.44/1.64 tff(3401,plain,
% 1.44/1.64 (b(s(elem!1), s(s(s(s(s(s(elem!1)))))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3341, 21, 3400, 3399])).
% 1.44/1.64 tff(3402,assumption,(b(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 1.44/1.64 tff(3403,assumption,(b(s(elem!1), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.44/1.64 tff(3404,assumption,(b(s(s(s(s(elem!1)))), s(elem!1))), introduced(assumption)).
% 1.44/1.64 tff(3405,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(3406,plain,
% 1.44/1.64 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(3407,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[3406])).
% 1.44/1.64 tff(3408,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.44/1.64 inference(transitivity,[status(thm)],[3407, 3405])).
% 1.44/1.64 tff(3409,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(3410,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[3409, 3408])).
% 1.44/1.64 tff(3411,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3410, 128, 3404, 3403, 3402, 3401, 3396])).
% 1.44/1.64 tff(3412,plain,((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1))))))) | (s(elem!1) = s(s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(3413,plain,
% 1.44/1.64 (~r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3412, 3390, 3193, 3201, 3125, 3338, 3191, 3094])).
% 1.44/1.64 tff(3414,plain,
% 1.44/1.64 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[3413, 3376])).
% 1.44/1.64 tff(3415,plain,
% 1.44/1.64 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1055, 3414, 3131])).
% 1.44/1.64 tff(3416,plain,
% 1.44/1.64 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3304, 3415, 1647])).
% 1.44/1.64 tff(3417,plain,
% 1.44/1.64 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3245, 128, 1681, 3379, 2659, 3416])).
% 1.44/1.64 tff(3418,plain,
% 1.44/1.64 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3250, 21, 3417])).
% 1.44/1.64 tff(3419,plain,
% 1.44/1.64 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3418, 3238])).
% 1.44/1.64 tff(3420,plain,
% 1.44/1.64 (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3264, 128, 1681, 3379, 3416])).
% 1.44/1.64 tff(3421,plain,
% 1.44/1.64 ((s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3269, 21, 3420])).
% 1.44/1.64 tff(3422,plain,
% 1.44/1.64 (r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3421, 3258])).
% 1.44/1.64 tff(3423,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(3424,plain,
% 1.44/1.64 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(3425,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[3424])).
% 1.44/1.64 tff(3426,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 1.44/1.64 inference(transitivity,[status(thm)],[3425, 3423])).
% 1.44/1.64 tff(3427,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(3428,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[3427, 3426])).
% 1.44/1.64 tff(3429,plain,
% 1.44/1.64 (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3428, 128, 1681, 3379, 3416])).
% 1.44/1.64 tff(3430,plain,
% 1.44/1.64 ((s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) | r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3287, 21, 3429])).
% 1.44/1.64 tff(3431,plain,
% 1.44/1.64 (r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3430, 3275])).
% 1.44/1.64 tff(3432,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(3433,plain,
% 1.44/1.64 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(3434,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[3433])).
% 1.44/1.64 tff(3435,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.44/1.64 inference(transitivity,[status(thm)],[3434, 3432])).
% 1.44/1.64 tff(3436,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(3437,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[3436, 3435])).
% 1.44/1.64 tff(3438,plain,
% 1.44/1.64 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3437, 128, 1681, 3379, 2659])).
% 1.44/1.64 tff(3439,plain,
% 1.44/1.64 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[321, 3438, 3100])).
% 1.44/1.64 tff(3440,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3295, 45, 3439, 3431, 3422, 3419])).
% 1.44/1.64 tff(3441,plain,((~r(s(z), s(s(elem!1)))) | (~(z = elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(3442,plain,
% 1.44/1.64 (~r(s(z), s(s(elem!1)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[3441, 3107, 1647, 3375, 1703, 272])).
% 1.44/1.64 tff(3443,plain,
% 1.44/1.64 (b(s(z), s(s(elem!1)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[117, 3442])).
% 1.44/1.64 tff(3444,plain,
% 1.44/1.64 (b(s(elem!1), s(s(elem!1)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2709, 3443, 1647])).
% 1.44/1.64 tff(3445,plain,
% 1.44/1.64 (b(s(s(s(elem!1))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 1.44/1.64 inference(monotonicity,[status(thm)],[1647])).
% 1.44/1.64 tff(3446,plain,
% 1.44/1.64 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), z)),
% 1.44/1.64 inference(symmetry,[status(thm)],[3445])).
% 1.44/1.64 tff(3447,plain,
% 1.44/1.64 (b(s(s(s(elem!1))), z)),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[2659, 3446])).
% 1.44/1.64 tff(3448,plain,
% 1.44/1.64 (~b(s(s(elem!1)), s(z))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2726, 2106, 2718, 876])).
% 1.44/1.64 tff(3449,plain,
% 1.44/1.64 (r(s(s(elem!1)), s(z))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[292, 3448])).
% 1.44/1.64 tff(3450,plain,
% 1.44/1.64 (~r(z, s(s(elem!1)))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[405, 3449, 27])).
% 1.44/1.65 tff(3451,plain,
% 1.44/1.65 (b(z, s(s(elem!1)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[160, 3450])).
% 1.44/1.65 tff(3452,assumption,(b(s(s(s(elem!1))), z)), introduced(assumption)).
% 1.44/1.65 tff(3453,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(3454,plain,
% 1.44/1.65 (((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(3455,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[3454])).
% 1.44/1.65 tff(3456,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 1.44/1.65 inference(transitivity,[status(thm)],[3455, 3453])).
% 1.44/1.65 tff(3457,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(3458,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[3457, 3456])).
% 1.44/1.65 tff(3459,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[3458, 128, 453, 2106, 874, 3452])).
% 1.44/1.65 tff(3460,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(3461,plain,
% 1.44/1.65 (~b(z, s(s(s(elem!1))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[3460, 3451, 3447, 2106])).
% 1.44/1.65 tff(3462,plain,
% 1.44/1.65 (r(z, s(s(s(elem!1))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[858, 3461])).
% 1.44/1.65 tff(3463,plain,
% 1.44/1.65 (~r(s(z), s(s(s(elem!1))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[854, 3462, 272])).
% 1.44/1.65 tff(3464,plain,
% 1.44/1.65 (b(s(z), s(s(s(elem!1))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[339, 3463])).
% 1.44/1.65 tff(3465,plain,
% 1.44/1.65 (b(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[3464, 2572])).
% 1.44/1.65 tff(3466,plain,
% 1.44/1.65 (b(s(elem!1), s(s(elem!1)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2709, 876, 1647])).
% 1.44/1.65 tff(3467,plain,
% 1.44/1.65 (b(elem!1, s(s(elem!1)))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[3451, 1652])).
% 1.44/1.65 tff(3468,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(3469,plain,
% 1.44/1.65 (((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(3470,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[3469])).
% 1.44/1.65 tff(3471,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.44/1.65 inference(transitivity,[status(thm)],[3470, 3468])).
% 1.44/1.65 tff(3472,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(3473,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[3472, 3471])).
% 1.44/1.65 tff(3474,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[3473, 128, 3467, 2106, 2659, 3466, 3465])).
% 1.44/1.65 tff(3475,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~(z = elem!1)) | (~r(s(z), z)) | (~r(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(3476,plain,
% 1.44/1.65 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[3475, 3375, 1647, 272, 27, 3360, 3443])).
% 1.44/1.65 tff(3477,plain,
% 1.44/1.65 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[321, 3476, 3100])).
% 1.44/1.65 tff(3478,plain,
% 1.44/1.65 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2103, 3477, 3372])).
% 1.44/1.65 tff(3479,plain,
% 1.44/1.65 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1897, 3478, 3099])).
% 1.44/1.65 tff(3480,plain,
% 1.44/1.65 (~b(s(s(elem!1)), s(z))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2608, 3479, 1829, 3443])).
% 1.44/1.65 tff(3481,plain,
% 1.44/1.65 (r(s(s(elem!1)), s(z))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[292, 3480])).
% 1.44/1.65 tff(3482,plain,
% 1.44/1.65 (~r(z, s(s(elem!1)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[405, 3481, 27])).
% 1.44/1.65 tff(3483,plain,
% 1.44/1.65 (b(z, s(s(elem!1)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[160, 3482])).
% 1.44/1.65 tff(3484,plain,
% 1.44/1.65 (b(elem!1, s(s(elem!1)))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[3483, 1652])).
% 1.44/1.65 tff(3485,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(3486,plain,
% 1.44/1.65 (((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(3487,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[3486])).
% 1.44/1.65 tff(3488,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.44/1.65 inference(transitivity,[status(thm)],[3487, 3485])).
% 1.44/1.65 tff(3489,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(3490,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[3489, 3488])).
% 1.44/1.65 tff(3491,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[3490, 128, 3107, 3484, 3479, 3444, 3096])).
% 1.44/1.65 tff(3492,plain,((~r(s(s(s(s(z)))), elem!1)) | (~(z = elem!1)) | (~r(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(3493,plain,
% 1.44/1.65 (~r(s(s(s(s(z)))), elem!1)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[3492, 1647, 27, 272])).
% 1.44/1.65 tff(3494,plain,
% 1.44/1.65 (b(s(s(s(s(z)))), elem!1)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[632, 3493, 1677])).
% 1.44/1.65 tff(3495,plain,
% 1.44/1.65 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[3494, 3091])).
% 1.44/1.65 tff(3496,plain,
% 1.44/1.65 (~r(s(s(elem!1)), s(z))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[405, 88, 27])).
% 1.44/1.65 tff(3497,plain,
% 1.44/1.65 (b(s(s(elem!1)), s(z))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[292, 3496])).
% 1.44/1.65 tff(3498,plain,
% 1.44/1.65 (b(s(s(s(s(elem!1)))), z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2402, 3494, 1647])).
% 1.44/1.65 tff(3499,plain,
% 1.44/1.65 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2565, 45, 2450, 3094])).
% 1.44/1.65 tff(3500,plain,
% 1.44/1.65 (~r(s(s(s(elem!1))), s(z))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[3499, 2552])).
% 1.44/1.65 tff(3501,plain,
% 1.44/1.65 (b(s(s(s(elem!1))), s(z))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[196, 3500])).
% 1.44/1.65 tff(3502,plain,
% 1.44/1.65 (b(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[3501, 2550])).
% 1.44/1.65 tff(3503,plain,
% 1.44/1.65 (r(s(s(s(elem!1))), z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2453, 2450, 1647])).
% 1.44/1.65 tff(3504,plain,
% 1.44/1.65 (~r(s(z), s(s(s(elem!1))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1307, 3503, 272])).
% 1.44/1.65 tff(3505,plain,
% 1.44/1.65 (b(s(z), s(s(s(elem!1))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[339, 3504])).
% 1.44/1.65 tff(3506,plain,
% 1.44/1.65 (b(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[3505, 2572])).
% 1.44/1.65 tff(3507,plain,
% 1.44/1.65 (b(s(s(elem!1)), s(elem!1))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[3497, 1944])).
% 1.44/1.65 tff(3508,plain,
% 1.44/1.65 (b(s(elem!1), s(s(elem!1)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2709, 2409, 1647])).
% 1.44/1.65 tff(3509,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(3510,plain,
% 1.44/1.65 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(3511,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1)))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[3510])).
% 1.44/1.65 tff(3512,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.44/1.65 inference(transitivity,[status(thm)],[3511, 3509])).
% 1.44/1.65 tff(3513,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(3514,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[3513, 3512])).
% 1.44/1.65 tff(3515,plain,
% 1.44/1.65 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[3514, 128, 3508, 3507, 3502])).
% 1.44/1.65 tff(3516,plain,
% 1.44/1.65 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[889, 3515, 3165])).
% 1.44/1.65 tff(3517,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(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(3518,plain,
% 1.44/1.65 (((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(3519,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(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[3518])).
% 1.44/1.65 tff(3520,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(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.44/1.65 inference(transitivity,[status(thm)],[3519, 3517])).
% 1.44/1.65 tff(3521,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(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(3522,plain,
% 1.44/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[3521, 3520])).
% 1.44/1.65 tff(3523,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[3522, 45, 2612, 3516, 2450])).
% 1.44/1.65 tff(3524,plain,((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~(z = elem!1)) | (~r(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(3525,plain,
% 1.44/1.65 (~r(z, s(s(elem!1)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[3524, 2450, 1647, 27, 272])).
% 1.44/1.65 tff(3526,plain,
% 1.44/1.65 (b(z, s(s(elem!1)))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[160, 3525])).
% 1.44/1.65 tff(3527,assumption,(b(s(z), z)), introduced(assumption)).
% 1.44/1.65 tff(3528,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(3529,plain,
% 1.44/1.65 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(3530,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~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(X0, 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)))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[3529])).
% 1.44/1.65 tff(3531,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~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(X0, 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))))),
% 1.44/1.65 inference(transitivity,[status(thm)],[3530, 3528])).
% 1.44/1.65 tff(3532,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(3533,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[3532, 3531])).
% 1.44/1.65 tff(3534,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[3533, 128, 30, 550, 453, 3527])).
% 1.44/1.65 tff(3535,plain,((~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(3536,plain,
% 1.44/1.65 (~b(z, s(z))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[3535, 3527, 30, 453])).
% 1.44/1.65 tff(3537,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(z))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(3538,plain,
% 1.44/1.65 (((~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)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(3539,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, 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)), s(z)))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[3538])).
% 1.44/1.66 tff(3540,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, 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)), s(z))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[3539, 3537])).
% 1.44/1.66 tff(3541,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(3542,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z)))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[3541, 3540])).
% 1.44/1.66 tff(3543,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3542, 128, 30, 453, 3527, 2006])).
% 1.44/1.66 tff(3544,plain,((~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(3545,plain,
% 1.44/1.66 (~b(s(s(elem!1)), z)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3544, 453, 3527, 30])).
% 1.44/1.66 tff(3546,plain,
% 1.44/1.66 (r(s(s(elem!1)), z)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2018, 21, 154, 3545])).
% 1.44/1.66 tff(3547,plain,
% 1.44/1.66 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1895, 21, 1892, 1063])).
% 1.44/1.66 tff(3548,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(3549,plain,
% 1.44/1.66 (((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(3550,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[3549])).
% 1.44/1.66 tff(3551,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[3550, 3548])).
% 1.44/1.66 tff(3552,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(3553,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[3552, 3551])).
% 1.44/1.66 tff(3554,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3553, 128, 30, 453, 3527, 1841, 3547])).
% 1.44/1.66 tff(3555,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | r(s(s(s(s(elem!1)))), s(s(elem!1))) | (s(s(s(s(elem!1)))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(3556,plain,
% 1.44/1.66 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3555, 1892, 453, 3527, 30, 1063])).
% 1.44/1.66 tff(3557,plain,
% 1.44/1.66 (r(s(s(s(s(elem!1)))), s(z))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1826, 21, 1723, 3556])).
% 1.44/1.66 tff(3558,plain,
% 1.44/1.66 (~r(s(s(s(s(elem!1)))), z)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2160, 45, 27, 3557])).
% 1.44/1.66 tff(3559,plain,
% 1.44/1.66 (b(s(s(s(s(elem!1)))), z)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2079, 21, 176, 3558])).
% 1.44/1.66 tff(3560,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(3561,plain,
% 1.44/1.66 (((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(3562,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[3561])).
% 1.44/1.66 tff(3563,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.44/1.66 inference(transitivity,[status(thm)],[3562, 3560])).
% 1.44/1.66 tff(3564,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(3565,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[3564, 3563])).
% 1.44/1.66 tff(3566,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3565, 128, 30, 453, 3527, 3547, 3559])).
% 1.44/1.66 tff(3567,plain,(r(s(s(s(s(elem!1)))), s(s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~r(z, s(z))) | (s(s(s(s(elem!1)))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(3568,plain,
% 1.44/1.66 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3567, 453, 30, 3527, 27, 1063])).
% 1.44/1.66 tff(3569,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(3570,plain,
% 1.44/1.66 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(3571,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z)))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[3570])).
% 1.44/1.66 tff(3572,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[3571, 3569])).
% 1.44/1.66 tff(3573,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(3574,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z)))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[3573, 3572])).
% 1.44/1.66 tff(3575,plain,
% 1.44/1.66 (~b(s(z), s(s(elem!1)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3574, 128, 30, 453, 3527])).
% 1.44/1.66 tff(3576,plain,
% 1.44/1.66 (r(s(z), s(s(elem!1)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[117, 3575])).
% 1.44/1.66 tff(3577,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(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(3578,plain,
% 1.44/1.66 (((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z)))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(3579,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(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[3578])).
% 1.44/1.66 tff(3580,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(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[3579, 3577])).
% 1.44/1.66 tff(3581,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(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(3582,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(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[3581, 3580])).
% 1.44/1.66 tff(3583,plain,
% 1.44/1.66 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3582, 45, 3576, 3568])).
% 1.44/1.66 tff(3584,plain,
% 1.44/1.66 (b(s(s(s(s(elem!1)))), s(z))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1826, 21, 3583, 1723])).
% 1.44/1.66 tff(3585,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(3586,plain,
% 1.44/1.66 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z)))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(3587,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[3586])).
% 1.44/1.66 tff(3588,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[3587, 3585])).
% 1.44/1.66 tff(3589,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(3590,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[3589, 3588])).
% 1.44/1.66 tff(3591,plain,
% 1.44/1.66 (~b(s(s(s(s(elem!1)))), z)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3590, 128, 30, 453, 3527, 3584])).
% 1.44/1.66 tff(3592,plain,
% 1.44/1.66 (r(s(s(s(s(elem!1)))), z)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2079, 21, 176, 3591])).
% 1.44/1.66 tff(3593,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(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(3594,plain,
% 1.44/1.66 (((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(3595,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(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[3594])).
% 1.44/1.66 tff(3596,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(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[3595, 3593])).
% 1.44/1.66 tff(3597,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(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(3598,plain,
% 1.44/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[3597, 3596])).
% 1.44/1.66 tff(3599,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3598, 45, 3568, 3592, 3546])).
% 1.44/1.66 tff(3600,plain,((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~r(z, s(z))) | (s(s(s(s(elem!1)))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(3601,plain,
% 1.44/1.66 (~r(z, s(z))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3600, 3527, 453, 30, 1063])).
% 1.44/1.66 tff(3602,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[415, 3601, 3536])).
% 1.44/1.66 tff(3603,plain,((~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (s(s(s(s(elem!1)))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(3604,plain,
% 1.44/1.66 (~b(s(z), z)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3603, 453, 30, 1063])).
% 1.44/1.66 tff(3605,plain,
% 1.44/1.66 (r(s(z), z)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[170, 3604])).
% 1.44/1.66 tff(3606,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(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(3607,plain,
% 1.44/1.66 (((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(3608,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(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[3607])).
% 1.44/1.66 tff(3609,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(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[3608, 3606])).
% 1.44/1.66 tff(3610,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(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(3611,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(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[3610, 3609])).
% 1.44/1.66 tff(3612,plain,
% 1.44/1.66 (~r(z, s(s(s(elem!1))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3611, 45, 27, 385])).
% 1.44/1.66 tff(3613,plain,
% 1.44/1.66 (b(z, s(s(s(elem!1))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[436, 21, 3612, 384])).
% 1.44/1.66 tff(3614,plain,
% 1.44/1.66 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3175, 385, 89, 272])).
% 1.44/1.66 tff(3615,plain,
% 1.44/1.66 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[889, 3614, 1691])).
% 1.44/1.66 tff(3616,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(3617,plain,
% 1.44/1.67 (((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(3618,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1)))))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[3617])).
% 1.44/1.67 tff(3619,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[3618, 3616])).
% 1.44/1.67 tff(3620,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(3621,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1)))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[3620, 3619])).
% 1.44/1.67 tff(3622,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3621, 128, 30, 453, 549, 3615, 3613])).
% 1.44/1.67 tff(3623,plain,((~r(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(3624,plain,
% 1.44/1.67 (~r(s(s(s(elem!1))), s(z))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3623, 89, 453, 549, 1679, 30, 3605, 27])).
% 1.44/1.67 tff(3625,plain,
% 1.44/1.67 (b(s(s(s(elem!1))), s(z))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[195, 3624, 191])).
% 1.44/1.67 tff(3626,plain,
% 1.44/1.67 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2132, 89, 549, 3605, 30, 1679])).
% 1.44/1.67 tff(3627,plain,
% 1.44/1.67 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[321, 3626, 1678])).
% 1.44/1.67 tff(3628,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(3629,plain,
% 1.44/1.67 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(3630,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[3629])).
% 1.44/1.67 tff(3631,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[3630, 3628])).
% 1.44/1.67 tff(3632,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(3633,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[3632, 3631])).
% 1.44/1.67 tff(3634,plain,
% 1.44/1.67 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3633, 128, 549, 2718, 1841])).
% 1.44/1.67 tff(3635,plain,
% 1.44/1.67 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1820, 3634, 712])).
% 1.44/1.67 tff(3636,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(3637,plain,
% 1.44/1.67 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(3638,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[3637])).
% 1.44/1.67 tff(3639,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[3638, 3636])).
% 1.44/1.67 tff(3640,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(3641,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[3640, 3639])).
% 1.44/1.67 tff(3642,plain,
% 1.44/1.67 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3641, 128, 30, 549, 2718, 1841])).
% 1.44/1.67 tff(3643,plain,
% 1.44/1.67 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2212, 21, 1069, 3642])).
% 1.44/1.67 tff(3644,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(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(3645,plain,
% 1.44/1.67 (((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(3646,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(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[3645])).
% 1.44/1.67 tff(3647,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(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[3646, 3644])).
% 1.44/1.67 tff(3648,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(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(3649,plain,
% 1.44/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[3648, 3647])).
% 1.44/1.67 tff(3650,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3649, 45, 3643, 324, 3635])).
% 1.44/1.67 tff(3651,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(3652,plain,
% 1.44/1.67 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3651, 3627, 2511, 2392, 549, 3625, 30])).
% 1.44/1.67 tff(3653,plain,
% 1.44/1.67 (r(s(s(s(s(elem!1)))), s(z))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1828, 3652])).
% 1.44/1.67 tff(3654,plain,
% 1.44/1.67 (~r(s(s(s(s(elem!1)))), z)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1745, 3653, 3605])).
% 1.44/1.67 tff(3655,plain,
% 1.44/1.67 (b(s(s(s(s(elem!1)))), z)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2079, 21, 176, 3654])).
% 1.44/1.67 tff(3656,plain,
% 1.44/1.67 (~r(s(s(elem!1)), z)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1527, 89, 3605])).
% 1.44/1.67 tff(3657,plain,
% 1.44/1.67 (b(s(s(elem!1)), z)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2018, 21, 154, 3656])).
% 1.44/1.67 tff(3658,plain,
% 1.44/1.67 (((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(3659,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[3658])).
% 1.44/1.67 tff(3660,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.44/1.67 inference(transitivity,[status(thm)],[3659, 2085])).
% 1.44/1.67 tff(3661,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(3662,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[3661, 3660])).
% 1.44/1.67 tff(3663,plain,
% 1.44/1.67 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3662, 128, 453, 3657, 3655])).
% 1.44/1.67 tff(3664,plain,
% 1.44/1.67 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1897, 3663, 1063])).
% 1.44/1.67 tff(3665,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(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(3666,plain,
% 1.44/1.67 (((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(3667,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(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[3666])).
% 1.44/1.67 tff(3668,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(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[3667, 3665])).
% 1.44/1.67 tff(3669,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(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(3670,plain,
% 1.44/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[3669, 3668])).
% 1.44/1.67 tff(3671,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3670, 45, 3605, 89, 3653, 3664])).
% 1.44/1.67 tff(3672,plain,((~r(s(z), s(s(elem!1)))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(3673,plain,
% 1.44/1.67 (~b(s(s(elem!1)), s(z))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3672, 89, 27, 3099, 3505, 3526])).
% 1.44/1.67 tff(3674,plain,
% 1.44/1.67 (r(s(s(elem!1)), s(z))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[292, 3673])).
% 1.44/1.67 tff(3675,plain,
% 1.44/1.67 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2176, 3674, 27, 3099])).
% 1.44/1.67 tff(3676,plain,
% 1.44/1.67 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[3675, 1735])).
% 1.44/1.67 tff(3677,plain,
% 1.44/1.67 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1754, 21, 1751, 3676])).
% 1.44/1.67 tff(3678,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(3679,plain,
% 1.44/1.67 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(3680,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[3679])).
% 1.44/1.67 tff(3681,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[3680, 3678])).
% 1.44/1.67 tff(3682,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(3683,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[3682, 3681])).
% 1.44/1.67 tff(3684,plain,
% 1.44/1.67 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3683, 128, 3677, 3506, 3502])).
% 1.44/1.67 tff(3685,plain,
% 1.44/1.67 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1856, 3684, 3101])).
% 1.44/1.67 tff(3686,plain,
% 1.44/1.67 (b(elem!1, s(s(elem!1)))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[3526, 1652])).
% 1.44/1.67 tff(3687,plain,
% 1.44/1.67 (b(s(s(z)), z) <=> b(s(s(z)), elem!1)),
% 1.44/1.67 inference(monotonicity,[status(thm)],[1647])).
% 1.44/1.67 tff(3688,plain,
% 1.44/1.67 (b(s(s(z)), z) <=> b(s(s(elem!1)), elem!1)),
% 1.44/1.67 inference(transitivity,[status(thm)],[3687, 2395])).
% 1.44/1.67 tff(3689,plain,
% 1.44/1.67 (r(s(z), s(s(z))) <=> r(s(z), s(s(elem!1)))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[1671])).
% 1.44/1.68 tff(3690,plain,
% 1.44/1.68 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(z)))),
% 1.44/1.68 inference(symmetry,[status(thm)],[3689])).
% 1.44/1.68 tff(3691,plain,
% 1.44/1.68 (r(s(z), s(s(z)))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[89, 3690])).
% 1.44/1.68 tff(3692,plain,
% 1.44/1.68 (~r(s(s(z)), z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1327, 3691, 272])).
% 1.44/1.68 tff(3693,plain,
% 1.44/1.68 (b(s(s(z)), z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[25, 3692])).
% 1.44/1.68 tff(3694,plain,
% 1.44/1.68 (b(s(s(elem!1)), elem!1)),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[3693, 3688])).
% 1.44/1.68 tff(3695,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(3696,plain,
% 1.44/1.68 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(3697,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[3696])).
% 1.44/1.68 tff(3698,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.44/1.68 inference(transitivity,[status(thm)],[3697, 3695])).
% 1.44/1.68 tff(3699,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(3700,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[3699, 3698])).
% 1.44/1.68 tff(3701,plain,
% 1.44/1.68 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3700, 128, 3694, 3686, 3495])).
% 1.44/1.68 tff(3702,plain,
% 1.44/1.68 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2212, 21, 3212, 3701])).
% 1.44/1.68 tff(3703,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(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(3704,plain,
% 1.44/1.68 (((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(3705,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(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[3704])).
% 1.44/1.68 tff(3706,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(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[3705, 3703])).
% 1.44/1.68 tff(3707,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(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(3708,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(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[3707, 3706])).
% 1.44/1.68 tff(3709,plain,
% 1.44/1.68 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3708, 45, 3702, 3685])).
% 1.44/1.68 tff(3710,plain,
% 1.44/1.68 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[889, 3709, 3165])).
% 1.44/1.68 tff(3711,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(3712,plain,
% 1.44/1.68 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(3713,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[3712])).
% 1.44/1.68 tff(3714,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[3713, 3711])).
% 1.44/1.68 tff(3715,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(3716,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[3715, 3714])).
% 1.44/1.68 tff(3717,plain,
% 1.44/1.68 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3716, 128, 3677, 3506, 3502])).
% 1.44/1.68 tff(3718,plain,
% 1.44/1.68 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1820, 3717, 3102])).
% 1.44/1.68 tff(3719,plain,
% 1.44/1.68 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1888, 128, 3694, 3686, 3495])).
% 1.44/1.68 tff(3720,plain,
% 1.44/1.68 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1897, 3719, 3099])).
% 1.44/1.68 tff(3721,plain,
% 1.44/1.68 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2103, 3720, 3718])).
% 1.44/1.68 tff(3722,plain,
% 1.44/1.68 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[321, 3721, 3100])).
% 1.44/1.68 tff(3723,assumption,(~(s(s(s(elem!1))) = s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 1.44/1.68 tff(3724,plain,
% 1.44/1.68 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[3723, 3228])).
% 1.44/1.68 tff(3725,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(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(3726,plain,
% 1.44/1.68 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(3727,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(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[3726])).
% 1.44/1.68 tff(3728,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(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[3727, 3725])).
% 1.44/1.68 tff(3729,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(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(3730,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(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[3729, 3728])).
% 1.44/1.68 tff(3731,plain,
% 1.44/1.68 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3730, 45, 2450, 3393])).
% 1.44/1.68 tff(3732,plain,
% 1.44/1.68 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3250, 21, 3731])).
% 1.44/1.68 tff(3733,plain,
% 1.44/1.68 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3732, 3724])).
% 1.44/1.68 tff(3734,plain,
% 1.44/1.68 (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3326, 45, 3397, 3393])).
% 1.44/1.68 tff(3735,plain,
% 1.44/1.68 (b(s(elem!1), s(s(s(s(s(s(elem!1)))))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3341, 21, 3400, 3734])).
% 1.44/1.68 tff(3736,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(3737,plain,
% 1.44/1.68 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(3738,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[3737])).
% 1.44/1.68 tff(3739,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[3738, 3736])).
% 1.44/1.68 tff(3740,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(3741,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[3740, 3739])).
% 1.44/1.68 tff(3742,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3741, 128, 2106, 875, 3402, 3735, 3733])).
% 1.44/1.68 tff(3743,plain,((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))) | (s(elem!1) = s(s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(3744,plain,
% 1.44/1.68 (~r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3743, 3722, 3710, 3506, 3237, 3338, 2450, 3094])).
% 1.44/1.68 tff(3745,plain,
% 1.44/1.68 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[3744, 3376])).
% 1.44/1.68 tff(3746,plain,
% 1.44/1.68 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1055, 3745, 3131])).
% 1.44/1.68 tff(3747,plain,
% 1.44/1.68 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3304, 3746, 1647])).
% 1.44/1.68 tff(3748,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(3749,plain,
% 1.44/1.68 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(3750,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[3749])).
% 1.44/1.68 tff(3751,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[3750, 3748])).
% 1.44/1.68 tff(3752,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(3753,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[3752, 3751])).
% 1.44/1.68 tff(3754,plain,
% 1.44/1.68 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3753, 128, 3694, 3686, 3495, 3747])).
% 1.44/1.68 tff(3755,plain,
% 1.44/1.68 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3318, 21, 3754])).
% 1.44/1.68 tff(3756,plain,
% 1.44/1.68 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3755, 3126])).
% 1.44/1.68 tff(3757,plain,
% 1.44/1.68 (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3264, 128, 3694, 3686, 3747])).
% 1.44/1.68 tff(3758,plain,
% 1.44/1.68 ((s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3269, 21, 3757])).
% 1.44/1.68 tff(3759,plain,
% 1.44/1.68 (r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3758, 3258])).
% 1.44/1.68 tff(3760,plain,
% 1.44/1.68 (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3428, 128, 3694, 3686, 3747])).
% 1.44/1.68 tff(3761,plain,
% 1.44/1.68 ((s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) | r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3287, 21, 3760])).
% 1.44/1.68 tff(3762,plain,
% 1.44/1.68 (r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3761, 3275])).
% 1.44/1.68 tff(3763,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(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(3764,plain,
% 1.44/1.68 (((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(3765,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(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[3764])).
% 1.44/1.68 tff(3766,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(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[3765, 3763])).
% 1.44/1.68 tff(3767,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(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(3768,plain,
% 1.44/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[3767, 3766])).
% 1.44/1.68 tff(3769,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3768, 45, 3702, 3762, 3759, 3756])).
% 1.44/1.68 tff(3770,plain,((~r(s(z), s(s(elem!1)))) | (~(z = elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(3771,plain,
% 1.44/1.68 (~r(s(z), s(s(elem!1)))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3770, 2450, 1647, 272, 27])).
% 1.44/1.68 tff(3772,plain,
% 1.44/1.68 (b(s(z), s(s(elem!1)))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[117, 3771])).
% 1.44/1.68 tff(3773,plain,
% 1.44/1.68 (b(s(elem!1), s(s(elem!1)))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2709, 3772, 1647])).
% 1.44/1.68 tff(3774,plain,
% 1.44/1.68 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2565, 45, 2450, 3397])).
% 1.44/1.68 tff(3775,plain,
% 1.44/1.68 (~r(s(s(s(elem!1))), s(z))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[3774, 2552])).
% 1.44/1.68 tff(3776,plain,
% 1.44/1.68 (b(s(s(s(elem!1))), s(z))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[196, 3775])).
% 1.44/1.68 tff(3777,plain,
% 1.44/1.68 (b(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[3776, 2550])).
% 1.44/1.68 tff(3778,plain,
% 1.44/1.68 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 1.44/1.68 inference(monotonicity,[status(thm)],[1647])).
% 1.44/1.68 tff(3779,plain,
% 1.44/1.68 ((~(s(s(elem!1)) = z)) <=> (~(s(s(elem!1)) = elem!1))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[3778])).
% 1.44/1.69 tff(3780,plain,
% 1.44/1.69 (~(s(s(elem!1)) = elem!1)),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[154, 3779])).
% 1.44/1.69 tff(3781,plain,
% 1.44/1.69 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(z))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[1649])).
% 1.44/1.69 tff(3782,plain,
% 1.44/1.69 (r(s(s(elem!1)), s(z)) <=> r(s(s(elem!1)), s(elem!1))),
% 1.44/1.69 inference(symmetry,[status(thm)],[3781])).
% 1.44/1.69 tff(3783,plain,
% 1.44/1.69 (r(s(s(elem!1)), s(elem!1))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[325, 3782])).
% 1.44/1.69 tff(3784,plain,
% 1.44/1.69 (r(elem!1, s(elem!1))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[3104, 3134])).
% 1.44/1.69 tff(3785,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(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(3786,plain,
% 1.44/1.69 (((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(3787,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(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[3786])).
% 1.44/1.69 tff(3788,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(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.44/1.69 inference(transitivity,[status(thm)],[3787, 3785])).
% 1.44/1.69 tff(3789,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(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)))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(3790,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(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[3789, 3788])).
% 1.44/1.69 tff(3791,plain,
% 1.44/1.69 ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3790, 45])).
% 1.44/1.69 tff(3792,plain,
% 1.44/1.69 (~r(s(s(elem!1)), elem!1)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3791, 3784, 3783])).
% 1.44/1.69 tff(3793,plain,
% 1.44/1.69 (b(s(s(elem!1)), elem!1)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1934, 3792, 3780])).
% 1.44/1.69 tff(3794,plain,
% 1.44/1.69 (b(s(s(elem!1)), z)),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[3793, 2394])).
% 1.44/1.69 tff(3795,assumption,(b(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 1.44/1.69 tff(3796,plain,
% 1.44/1.69 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2176, 325, 27, 3099])).
% 1.44/1.69 tff(3797,plain,
% 1.44/1.69 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[3796, 1735])).
% 1.44/1.69 tff(3798,plain,
% 1.44/1.69 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1754, 21, 1751, 3797])).
% 1.44/1.69 tff(3799,plain,
% 1.44/1.69 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3716, 128, 3798, 3402, 3795])).
% 1.44/1.69 tff(3800,plain,
% 1.44/1.69 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1820, 3799, 3102])).
% 1.44/1.69 tff(3801,plain,
% 1.44/1.69 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2103, 3800, 324])).
% 1.44/1.69 tff(3802,plain,
% 1.44/1.69 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1897, 3801, 3099])).
% 1.44/1.69 tff(3803,plain,
% 1.44/1.69 (~b(s(s(elem!1)), z)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2092, 3802, 2083, 453])).
% 1.44/1.69 tff(3804,plain,
% 1.44/1.69 ($false),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3803, 3794])).
% 1.44/1.69 tff(3805,plain,((~r(s(s(elem!1)), s(z))) | (~(z = elem!1)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.69 tff(3806,plain,
% 1.44/1.69 (~r(s(s(elem!1)), s(z))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3805, 324, 2083, 453, 1647, 2573, 3777, 27])).
% 1.44/1.69 tff(3807,plain,
% 1.44/1.69 (b(s(s(elem!1)), s(z))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[292, 3806])).
% 1.44/1.69 tff(3808,plain,
% 1.44/1.69 (b(s(s(elem!1)), s(elem!1))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[3807, 1944])).
% 1.44/1.69 tff(3809,plain,
% 1.44/1.69 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3514, 128, 3466, 3808, 3777])).
% 1.44/1.69 tff(3810,plain,
% 1.44/1.69 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[889, 3809, 3165])).
% 1.44/1.69 tff(3811,plain,
% 1.44/1.69 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3651, 3807, 3212, 3102, 549, 3776, 324])).
% 1.44/1.69 tff(3812,plain,
% 1.44/1.69 (r(s(s(s(s(elem!1)))), s(z))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1828, 3811])).
% 1.44/1.69 tff(3813,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(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(3814,plain,
% 1.44/1.69 (((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(3815,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(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[3814])).
% 1.44/1.69 tff(3816,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(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.44/1.69 inference(transitivity,[status(thm)],[3815, 3813])).
% 1.44/1.69 tff(3817,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(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(3818,plain,
% 1.44/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[3817, 3816])).
% 1.44/1.69 tff(3819,plain,
% 1.44/1.69 ($false),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3818, 45, 2349, 1794, 2450])).
% 1.44/1.69 tff(3820,plain,((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.69 tff(3821,plain,
% 1.44/1.69 (~r(s(s(elem!1)), elem!1)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3820, 3810, 2450])).
% 1.44/1.69 tff(3822,plain,
% 1.44/1.69 (b(s(s(elem!1)), elem!1)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1934, 3821, 3780])).
% 1.44/1.69 tff(3823,plain,
% 1.44/1.69 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1888, 128, 3822, 1653, 2656])).
% 1.44/1.69 tff(3824,plain,
% 1.44/1.69 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1897, 3823, 3099])).
% 1.44/1.69 tff(3825,plain,
% 1.44/1.69 (~r(s(s(elem!1)), s(z))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2141, 2095, 1737])).
% 1.44/1.69 tff(3826,plain,
% 1.44/1.69 (b(s(s(elem!1)), s(z))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[292, 3825])).
% 1.44/1.69 tff(3827,plain,
% 1.44/1.69 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2103, 2095, 1772])).
% 1.44/1.69 tff(3828,plain,
% 1.44/1.69 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[321, 3827, 691])).
% 1.44/1.69 tff(3829,plain,
% 1.44/1.69 ($false),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2726, 3828, 3826, 2718, 876])).
% 1.44/1.69 tff(3830,plain,((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.69 tff(3831,plain,
% 1.44/1.69 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3830, 3824, 876, 3100, 3776, 3812])).
% 1.44/1.69 tff(3832,plain,
% 1.44/1.69 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1820, 3831, 3102])).
% 1.44/1.69 tff(3833,plain,
% 1.44/1.69 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3348, 45, 3824, 3810])).
% 1.44/1.69 tff(3834,plain,
% 1.44/1.69 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1856, 3833, 3101])).
% 1.44/1.69 tff(3835,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(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(3836,plain,
% 1.44/1.69 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(3837,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(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[3836])).
% 1.44/1.69 tff(3838,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(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.44/1.69 inference(transitivity,[status(thm)],[3837, 3835])).
% 1.44/1.69 tff(3839,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(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(3840,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(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[3839, 3838])).
% 1.44/1.69 tff(3841,plain,
% 1.44/1.69 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3840, 45, 1794, 2450, 3393])).
% 1.44/1.69 tff(3842,plain,
% 1.44/1.69 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3250, 21, 3841])).
% 1.44/1.69 tff(3843,plain,
% 1.44/1.69 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3842, 3724])).
% 1.44/1.69 tff(3844,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(3845,plain,
% 1.44/1.69 (((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(3846,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[3845])).
% 1.44/1.69 tff(3847,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.44/1.69 inference(transitivity,[status(thm)],[3846, 3844])).
% 1.44/1.69 tff(3848,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(3849,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[3848, 3847])).
% 1.44/1.69 tff(3850,plain,
% 1.44/1.69 ($false),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3849, 128, 1843, 1842, 3402, 3735, 3843])).
% 1.44/1.69 tff(3851,plain,((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))) | (s(elem!1) = s(s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.69 tff(3852,plain,
% 1.44/1.69 (~r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3851, 3834, 3832, 2573, 3237, 3338, 3810, 2450, 3397])).
% 1.44/1.69 tff(3853,plain,
% 1.44/1.69 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[3852, 3376])).
% 1.44/1.69 tff(3854,plain,
% 1.44/1.69 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1055, 3853, 3131])).
% 1.44/1.69 tff(3855,plain,
% 1.44/1.69 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3304, 3854, 1647])).
% 1.44/1.69 tff(3856,plain,
% 1.44/1.69 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3753, 128, 3822, 1653, 2656, 3855])).
% 1.44/1.69 tff(3857,plain,
% 1.44/1.69 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3318, 21, 3856])).
% 1.44/1.69 tff(3858,plain,
% 1.44/1.69 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3857, 3126])).
% 1.44/1.69 tff(3859,plain,
% 1.44/1.69 (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3264, 128, 3822, 1653, 3855])).
% 1.44/1.69 tff(3860,plain,
% 1.44/1.69 ((s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3269, 21, 3859])).
% 1.44/1.69 tff(3861,plain,
% 1.44/1.69 (r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3860, 3258])).
% 1.44/1.69 tff(3862,plain,
% 1.44/1.69 (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3282, 128, 3822, 1653, 3855, 3808])).
% 1.44/1.69 tff(3863,plain,
% 1.44/1.69 ((s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) | r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3287, 21, 3862])).
% 1.44/1.69 tff(3864,plain,
% 1.44/1.69 (r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3863, 3275])).
% 1.44/1.69 tff(3865,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(s(s(s(elem!1)))))) | (~b(s(s(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(X0, 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)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(3866,plain,
% 1.44/1.69 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(3867,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[3866])).
% 1.44/1.69 tff(3868,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.44/1.69 inference(transitivity,[status(thm)],[3867, 3865])).
% 1.44/1.69 tff(3869,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(3870,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[3869, 3868])).
% 1.44/1.69 tff(3871,plain,
% 1.44/1.69 ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3870, 128, 1653, 2656, 3808])).
% 1.44/1.69 tff(3872,plain,
% 1.44/1.69 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3871, 3822])).
% 1.44/1.69 tff(3873,plain,
% 1.44/1.69 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2212, 21, 3212, 3872])).
% 1.44/1.69 tff(3874,plain,
% 1.44/1.69 ($false),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3768, 45, 3873, 3864, 3861, 3858])).
% 1.44/1.69 tff(3875,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~(z = elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(elem!1)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.69 tff(3876,plain,
% 1.44/1.69 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3875, 2450, 3495, 1647, 3094, 3772, 3505, 3498, 3526, 27])).
% 1.44/1.69 tff(3877,plain,
% 1.44/1.69 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[321, 3876, 3100])).
% 1.44/1.69 tff(3878,plain,
% 1.44/1.69 ($false),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2756, 128, 3877, 3773, 3506, 3502])).
% 1.44/1.69 tff(3879,plain,((~r(s(s(s(elem!1))), elem!1)) | (~(z = elem!1)) | (~r(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.69 tff(3880,plain,
% 1.44/1.69 (~r(s(s(s(elem!1))), elem!1)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3879, 1647, 27, 272])).
% 1.44/1.69 tff(3881,plain,
% 1.44/1.69 (b(s(s(s(elem!1))), elem!1)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[742, 3880, 2446])).
% 1.44/1.69 tff(3882,plain,
% 1.44/1.69 (~b(s(s(s(elem!1))), s(z))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2726, 2106, 30, 876])).
% 1.44/1.69 tff(3883,plain,
% 1.44/1.69 (r(s(s(s(elem!1))), s(z))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[196, 3882])).
% 1.44/1.69 tff(3884,plain,
% 1.44/1.69 (r(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[3883, 2657])).
% 1.44/1.69 tff(3885,plain,
% 1.44/1.69 (~r(elem!1, s(s(s(elem!1))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3151, 3784, 3884])).
% 1.44/1.69 tff(3886,plain,
% 1.44/1.69 (b(elem!1, s(s(s(elem!1))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2466, 3885, 2457])).
% 1.44/1.69 tff(3887,plain,
% 1.44/1.69 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(3888,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[3887])).
% 1.44/1.69 tff(3889,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.44/1.69 inference(transitivity,[status(thm)],[3888, 3154])).
% 1.44/1.69 tff(3890,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(3891,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[3890, 3889])).
% 1.44/1.69 tff(3892,plain,
% 1.44/1.69 (~b(s(s(elem!1)), elem!1)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3891, 128, 3886, 2106, 2659])).
% 1.44/1.69 tff(3893,plain,
% 1.44/1.69 (r(s(s(elem!1)), elem!1)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1934, 3892, 3780])).
% 1.44/1.69 tff(3894,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(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(3895,plain,
% 1.44/1.69 (((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 1.44/1.70 inference(rewrite,[status(thm)],[])).
% 1.44/1.70 tff(3896,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(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))))),
% 1.44/1.70 inference(monotonicity,[status(thm)],[3895])).
% 1.44/1.70 tff(3897,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(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 1.44/1.70 inference(transitivity,[status(thm)],[3896, 3894])).
% 1.44/1.70 tff(3898,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(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 1.44/1.70 inference(quant_inst,[status(thm)],[])).
% 1.44/1.70 tff(3899,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(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))),
% 1.44/1.70 inference(modus_ponens,[status(thm)],[3898, 3897])).
% 1.44/1.70 tff(3900,plain,
% 1.44/1.70 (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.44/1.70 inference(unit_resolution,[status(thm)],[3899, 45, 2349, 3393])).
% 1.44/1.70 tff(3901,plain,
% 1.44/1.70 ((s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.44/1.70 inference(unit_resolution,[status(thm)],[3269, 21, 3900])).
% 1.44/1.70 tff(3902,plain,
% 1.44/1.70 (b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.44/1.70 inference(unit_resolution,[status(thm)],[3901, 3258])).
% 1.44/1.70 tff(3903,plain,
% 1.44/1.70 (b(s(elem!1), s(s(s(s(s(s(elem!1)))))))),
% 1.44/1.70 inference(unit_resolution,[status(thm)],[3341, 21, 3338, 3734])).
% 1.44/1.70 tff(3904,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(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 1.44/1.70 inference(rewrite,[status(thm)],[])).
% 1.44/1.70 tff(3905,plain,
% 1.44/1.70 (((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 1.44/1.70 inference(rewrite,[status(thm)],[])).
% 1.44/1.70 tff(3906,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(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))))),
% 1.44/1.70 inference(monotonicity,[status(thm)],[3905])).
% 1.44/1.70 tff(3907,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(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 1.54/1.70 inference(transitivity,[status(thm)],[3906, 3904])).
% 1.54/1.70 tff(3908,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(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(3909,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(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[3908, 3907])).
% 1.54/1.70 tff(3910,plain,
% 1.54/1.70 (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3909, 45, 2349, 3393])).
% 1.54/1.70 tff(3911,plain,
% 1.54/1.70 ((s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) | b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3287, 21, 3910])).
% 1.54/1.70 tff(3912,plain,
% 1.54/1.70 (b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3911, 3275])).
% 1.54/1.70 tff(3913,assumption,(b(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 1.54/1.70 tff(3914,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(3915,plain,
% 1.54/1.70 (((~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(3916,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[3915])).
% 1.54/1.70 tff(3917,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 1.54/1.70 inference(transitivity,[status(thm)],[3916, 3914])).
% 1.54/1.70 tff(3918,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(3919,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[3918, 3917])).
% 1.54/1.70 tff(3920,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3919, 128, 3913, 3912, 3903, 3902])).
% 1.54/1.70 tff(3921,plain,((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~(z = elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(3922,plain,
% 1.54/1.70 (~r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3921, 3893, 1647, 3466, 3397])).
% 1.54/1.70 tff(3923,plain,
% 1.54/1.70 (r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[1094, 3128])).
% 1.54/1.70 tff(3924,assumption,(~r(s(s(s(s(s(s(elem!1)))))), elem!1)), introduced(assumption)).
% 1.54/1.70 tff(3925,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3924, 3923])).
% 1.54/1.70 tff(3926,plain,((~r(s(s(s(s(s(s(z)))))), elem!1)) | r(s(s(s(s(s(s(elem!1)))))), elem!1) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(3927,plain,
% 1.54/1.70 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3926, 3922, 1647])).
% 1.54/1.70 tff(3928,plain,
% 1.54/1.70 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[1055, 3927, 3131])).
% 1.54/1.70 tff(3929,plain,
% 1.54/1.70 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3304, 3928, 1647])).
% 1.54/1.70 tff(3930,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(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(3931,plain,
% 1.54/1.70 (((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(3932,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(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z)))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[3931])).
% 1.54/1.70 tff(3933,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(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 1.54/1.70 inference(transitivity,[status(thm)],[3932, 3930])).
% 1.54/1.70 tff(3934,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(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), z)))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(3935,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(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z)))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[3934, 3933])).
% 1.54/1.70 tff(3936,plain,
% 1.54/1.70 (~r(s(s(s(elem!1))), z)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3935, 45, 27, 385])).
% 1.54/1.70 tff(3937,plain,
% 1.54/1.70 (b(s(s(s(elem!1))), z)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[547, 21, 382, 3936])).
% 1.54/1.70 tff(3938,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(3939,plain,
% 1.54/1.70 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(3940,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[3939])).
% 1.54/1.70 tff(3941,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.54/1.70 inference(transitivity,[status(thm)],[3940, 3938])).
% 1.54/1.70 tff(3942,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(3943,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[3942, 3941])).
% 1.54/1.70 tff(3944,plain,
% 1.54/1.70 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3943, 128, 3613, 3937, 2083])).
% 1.54/1.70 tff(3945,plain,
% 1.54/1.70 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[1856, 3944, 698])).
% 1.54/1.70 tff(3946,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(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(3947,plain,
% 1.54/1.70 (((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(3948,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(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z)))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[3947])).
% 1.54/1.70 tff(3949,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(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.54/1.70 inference(transitivity,[status(thm)],[3948, 3946])).
% 1.54/1.70 tff(3950,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(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(3951,plain,
% 1.54/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z)))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[3950, 3949])).
% 1.54/1.70 tff(3952,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3951, 45, 1737, 3945, 385])).
% 1.54/1.70 tff(3953,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(3954,plain,
% 1.54/1.70 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3953, 3883, 27, 3101, 2083])).
% 1.54/1.70 tff(3955,plain,
% 1.54/1.70 (b(s(s(s(s(elem!1)))), s(z))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[1828, 3954])).
% 1.54/1.70 tff(3956,plain,
% 1.54/1.70 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2608, 3955, 30, 876])).
% 1.54/1.70 tff(3957,plain,
% 1.54/1.70 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[1897, 3956, 3099])).
% 1.54/1.70 tff(3958,plain,
% 1.54/1.70 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2618, 45, 2729, 3957])).
% 1.54/1.70 tff(3959,plain,
% 1.54/1.70 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[1766, 3958, 1699])).
% 1.54/1.70 tff(3960,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(3961,plain,
% 1.54/1.70 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(3962,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[3961])).
% 1.54/1.70 tff(3963,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))),
% 1.54/1.70 inference(transitivity,[status(thm)],[3962, 3960])).
% 1.54/1.70 tff(3964,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(3965,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[3964, 3963])).
% 1.54/1.70 tff(3966,plain,
% 1.54/1.70 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3965, 128, 3959, 2656, 3929])).
% 1.54/1.70 tff(3967,plain,
% 1.54/1.70 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(3968,plain,
% 1.54/1.70 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(3969,plain,
% 1.54/1.70 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[3968, 3967])).
% 1.54/1.70 tff(3970,plain,
% 1.54/1.70 (r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3969, 21, 3125, 3966])).
% 1.54/1.70 tff(3971,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(3972,plain,
% 1.54/1.71 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(3973,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1))))))))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3972])).
% 1.54/1.71 tff(3974,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[3973, 3971])).
% 1.54/1.71 tff(3975,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(3976,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1))))))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[3975, 3974])).
% 1.54/1.71 tff(3977,plain,
% 1.54/1.71 (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3976, 128, 3959, 2659, 2656, 3929])).
% 1.54/1.71 tff(3978,plain,
% 1.54/1.71 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1))))))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(3979,plain,
% 1.54/1.71 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1))))))))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(3980,plain,
% 1.54/1.71 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[3979, 3978])).
% 1.54/1.71 tff(3981,plain,
% 1.54/1.71 (r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3980, 21, 3237, 3977])).
% 1.54/1.71 tff(3982,plain,
% 1.54/1.71 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2473, 128, 3886, 2659, 2656])).
% 1.54/1.71 tff(3983,plain,
% 1.54/1.71 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1820, 3982, 3102])).
% 1.54/1.71 tff(3984,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(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(3985,plain,
% 1.54/1.71 (((~r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(3986,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(elem!1))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1))))))))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3985])).
% 1.54/1.71 tff(3987,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(elem!1))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[3986, 3984])).
% 1.54/1.71 tff(3988,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(elem!1))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(3989,plain,
% 1.54/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1))))))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[3988, 3987])).
% 1.54/1.71 tff(3990,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3989, 45, 3983, 3981, 3970])).
% 1.54/1.71 tff(3991,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~(z = elem!1)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~b(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(3992,plain,
% 1.54/1.71 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3991, 2729, 2659, 1647, 3397, 2656, 30, 876, 27, 2083])).
% 1.54/1.71 tff(3993,plain,
% 1.54/1.71 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[321, 3992, 3100])).
% 1.54/1.71 tff(3994,plain,
% 1.54/1.71 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2103, 1772, 3993])).
% 1.54/1.71 tff(3995,plain,
% 1.54/1.71 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1897, 3994, 3099])).
% 1.54/1.71 tff(3996,plain,
% 1.54/1.71 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2608, 3995, 30, 876])).
% 1.54/1.71 tff(3997,plain,
% 1.54/1.71 (r(s(s(s(s(elem!1)))), s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1828, 3996])).
% 1.54/1.71 tff(3998,plain,
% 1.54/1.71 (~r(s(s(s(elem!1))), s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3953, 3997, 27, 3101, 2083])).
% 1.54/1.71 tff(3999,plain,
% 1.54/1.71 (b(s(s(s(elem!1))), s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[196, 3998])).
% 1.54/1.71 tff(4000,plain,
% 1.54/1.71 (b(s(s(s(elem!1))), s(elem!1))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[3999, 2550])).
% 1.54/1.71 tff(4001,plain,
% 1.54/1.71 (b(s(s(elem!1)), s(elem!1))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[30, 1944])).
% 1.54/1.71 tff(4002,plain,
% 1.54/1.71 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3649, 45, 3993, 1772])).
% 1.54/1.71 tff(4003,plain,
% 1.54/1.71 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2212, 21, 4002, 3212])).
% 1.54/1.71 tff(4004,plain,
% 1.54/1.71 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3514, 128, 3466, 4001, 4000])).
% 1.54/1.71 tff(4005,plain,
% 1.54/1.71 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[889, 4004, 3165])).
% 1.54/1.71 tff(4006,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(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(4007,plain,
% 1.54/1.71 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(4008,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(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[4007])).
% 1.54/1.71 tff(4009,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(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[4008, 4006])).
% 1.54/1.71 tff(4010,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(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(4011,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(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[4010, 4009])).
% 1.54/1.71 tff(4012,plain,
% 1.54/1.71 (~r(elem!1, s(s(s(elem!1))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[4011, 45, 2729, 4005])).
% 1.54/1.71 tff(4013,plain,
% 1.54/1.71 (b(elem!1, s(s(s(elem!1))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2466, 4012, 2457])).
% 1.54/1.71 tff(4014,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(4015,plain,
% 1.54/1.71 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(4016,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1)))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[4015])).
% 1.54/1.71 tff(4017,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[4016, 4014])).
% 1.54/1.71 tff(4018,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(4019,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[4018, 4017])).
% 1.54/1.71 tff(4020,plain,
% 1.54/1.71 (~b(s(s(elem!1)), elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[4019, 128, 4013, 4003, 2656, 4001, 4000])).
% 1.54/1.71 tff(4021,plain,
% 1.54/1.71 (r(s(s(elem!1)), elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1934, 4020, 3780])).
% 1.54/1.71 tff(4022,plain,
% 1.54/1.71 (~r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3921, 4021, 1647, 3466, 3397])).
% 1.54/1.71 tff(4023,plain,
% 1.54/1.71 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3926, 4022, 1647])).
% 1.54/1.71 tff(4024,plain,
% 1.54/1.71 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1055, 4023, 3131])).
% 1.54/1.71 tff(4025,plain,
% 1.54/1.71 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3304, 4024, 1647])).
% 1.54/1.71 tff(4026,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(4027,plain,
% 1.54/1.71 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(4028,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[4027])).
% 1.54/1.71 tff(4029,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[4028, 4026])).
% 1.54/1.71 tff(4030,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(4031,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[4030, 4029])).
% 1.54/1.71 tff(4032,plain,
% 1.54/1.71 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[4031, 128, 4013, 2659, 2656, 4025])).
% 1.54/1.71 tff(4033,plain,
% 1.54/1.71 (r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3969, 21, 3125, 4032])).
% 1.54/1.71 tff(4034,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(4035,plain,
% 1.54/1.71 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(4036,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1))))))))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[4035])).
% 1.54/1.71 tff(4037,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[4036, 4034])).
% 1.54/1.71 tff(4038,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(4039,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1))))))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[4038, 4037])).
% 1.54/1.71 tff(4040,plain,
% 1.54/1.71 (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[4039, 128, 4013, 2659, 4025])).
% 1.54/1.71 tff(4041,plain,
% 1.54/1.71 (r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3980, 21, 3237, 4040])).
% 1.54/1.71 tff(4042,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3989, 45, 1772, 4041, 4033])).
% 1.54/1.71 tff(4043,plain,((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~(z = elem!1)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(4044,plain,
% 1.54/1.71 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[4043, 2612, 3495, 1647, 3094, 3881, 27, 3498, 3497, 2409])).
% 1.54/1.71 tff(4045,plain,
% 1.54/1.71 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1820, 4044, 3102])).
% 1.54/1.71 tff(4046,plain,
% 1.54/1.71 ((~b(s(elem!1), s(s(s(elem!1))))) <=> (~b(s(z), s(s(s(elem!1)))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[2571])).
% 1.54/1.71 tff(4047,plain,
% 1.54/1.71 (~r(s(s(s(elem!1))), elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3522, 45, 2729, 1794])).
% 1.54/1.71 tff(4048,plain,
% 1.54/1.71 (b(s(s(s(elem!1))), elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[742, 4047, 817])).
% 1.54/1.71 tff(4049,assumption,(~(elem!1 = s(s(s(elem!1))))), introduced(assumption)).
% 1.54/1.71 tff(4050,plain,
% 1.54/1.71 (~r(elem!1, s(s(s(elem!1))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[4011, 45, 2729, 1794])).
% 1.54/1.71 tff(4051,plain,
% 1.54/1.71 (b(elem!1, s(s(s(elem!1))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2466, 4050, 4049])).
% 1.54/1.71 tff(4052,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2596, 128, 4051, 4048, 1842, 2656])).
% 1.54/1.71 tff(4053,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (s(s(s(elem!1))) = elem!1) | (elem!1 = s(s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(4054,plain,
% 1.54/1.71 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[4053, 4045, 3495, 2446, 2457, 2612])).
% 1.54/1.71 tff(4055,plain,
% 1.54/1.71 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[889, 4054, 3165])).
% 1.54/1.71 tff(4056,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(4057,plain,
% 1.54/1.71 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(4058,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1)))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[4057])).
% 1.54/1.71 tff(4059,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.54/1.72 inference(transitivity,[status(thm)],[4058, 4056])).
% 1.54/1.72 tff(4060,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(4061,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[4060, 4059])).
% 1.54/1.72 tff(4062,plain,
% 1.54/1.72 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[4061, 128, 4055, 3508, 3507])).
% 1.54/1.72 tff(4063,plain,
% 1.54/1.72 (~b(s(z), s(s(s(elem!1))))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[4062, 4046])).
% 1.54/1.72 tff(4064,plain,
% 1.54/1.72 (r(s(z), s(s(s(elem!1))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[339, 4063])).
% 1.54/1.72 tff(4065,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(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(4066,plain,
% 1.54/1.72 (((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(4067,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(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1)))))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[4066])).
% 1.54/1.72 tff(4068,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(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.54/1.72 inference(transitivity,[status(thm)],[4067, 4065])).
% 1.54/1.72 tff(4069,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(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(4070,plain,
% 1.54/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1)))))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[4069, 4068])).
% 1.54/1.72 tff(4071,plain,
% 1.54/1.72 ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[4070, 45, 2458])).
% 1.54/1.72 tff(4072,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[4071, 2391, 3135])).
% 1.54/1.72 tff(4073,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~(z = elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(4074,plain,
% 1.54/1.72 (~r(elem!1, s(s(s(elem!1))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[4073, 4064, 1647, 3104])).
% 1.54/1.72 tff(4075,plain,
% 1.54/1.72 (b(elem!1, s(s(s(elem!1))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2466, 4074, 2457])).
% 1.54/1.72 tff(4076,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2596, 128, 4075, 3881, 4045, 3495])).
% 1.54/1.72 tff(4077,plain,((~r(z, s(s(elem!1)))) | (~(z = elem!1)) | (~r(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(4078,plain,
% 1.54/1.72 (~r(z, s(s(elem!1)))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[4077, 1647, 27, 272])).
% 1.54/1.72 tff(4079,plain,
% 1.54/1.72 (b(z, s(s(elem!1)))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[160, 4078])).
% 1.54/1.72 tff(4080,plain,
% 1.54/1.72 (b(s(s(s(elem!1))), z)),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[3881, 3446])).
% 1.54/1.72 tff(4081,plain,
% 1.54/1.72 (b(elem!1, s(s(elem!1)))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[4079, 1652])).
% 1.54/1.72 tff(4082,plain,
% 1.54/1.72 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3437, 128, 1681, 1663, 2659])).
% 1.54/1.72 tff(4083,plain,
% 1.54/1.72 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[321, 4082, 1678])).
% 1.54/1.72 tff(4084,plain,
% 1.54/1.72 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1888, 128, 1681, 1663, 2656])).
% 1.54/1.72 tff(4085,plain,
% 1.54/1.72 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1897, 4084, 1063])).
% 1.54/1.72 tff(4086,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(4087,plain,
% 1.54/1.72 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(4088,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[4087])).
% 1.54/1.72 tff(4089,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.54/1.72 inference(transitivity,[status(thm)],[4088, 4086])).
% 1.54/1.72 tff(4090,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(4091,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[4090, 4089])).
% 1.54/1.72 tff(4092,plain,
% 1.54/1.72 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[4091, 128, 1681, 1663, 2659, 2656])).
% 1.54/1.72 tff(4093,plain,
% 1.54/1.72 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1820, 4092, 2392])).
% 1.54/1.72 tff(4094,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2103, 4093, 4085, 4083])).
% 1.54/1.72 tff(4095,plain,((~b(s(s(elem!1)), elem!1)) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(4096,plain,
% 1.54/1.72 (~b(s(s(elem!1)), elem!1)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[4095, 3099, 4081, 3881, 3495])).
% 1.54/1.72 tff(4097,plain,
% 1.54/1.72 (r(s(s(elem!1)), elem!1)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1934, 4096, 3780])).
% 1.54/1.72 tff(4098,plain,
% 1.54/1.72 (r(s(s(elem!1)), z)),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[4097, 1662])).
% 1.54/1.72 tff(4099,plain,
% 1.54/1.72 (~r(s(z), s(s(elem!1)))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1527, 4098, 272])).
% 1.54/1.72 tff(4100,plain,
% 1.54/1.72 (b(s(z), s(s(elem!1)))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[117, 4099])).
% 1.54/1.72 tff(4101,plain,
% 1.54/1.72 (~r(s(s(elem!1)), s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1962, 4098, 272])).
% 1.54/1.72 tff(4102,plain,
% 1.54/1.72 (b(s(s(elem!1)), s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[292, 4101])).
% 1.54/1.72 tff(4103,plain,
% 1.54/1.72 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3953, 3883, 27, 698, 2083])).
% 1.54/1.72 tff(4104,plain,
% 1.54/1.72 (b(s(s(s(s(elem!1)))), s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1828, 4103])).
% 1.54/1.72 tff(4105,plain,
% 1.54/1.72 (~b(z, s(s(s(elem!1))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3460, 2106, 3452, 453])).
% 1.54/1.72 tff(4106,plain,
% 1.54/1.72 (r(z, s(s(s(elem!1))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[858, 4105])).
% 1.54/1.72 tff(4107,plain,
% 1.54/1.72 (~r(s(z), s(s(s(elem!1))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[854, 4106, 272])).
% 1.54/1.72 tff(4108,plain,
% 1.54/1.72 (b(s(z), s(s(s(elem!1))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[339, 4107])).
% 1.54/1.72 tff(4109,plain,
% 1.54/1.72 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1851, 549, 1841, 1842])).
% 1.54/1.72 tff(4110,plain,
% 1.54/1.72 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1856, 4109, 2037])).
% 1.54/1.72 tff(4111,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(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(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(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(4112,plain,
% 1.54/1.72 (((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(4113,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(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z)))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[4112])).
% 1.54/1.72 tff(4114,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(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.54/1.72 inference(transitivity,[status(thm)],[4113, 4111])).
% 1.54/1.72 tff(4115,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(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(elem!1))))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(4116,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(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z)))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[4115, 4114])).
% 1.54/1.72 tff(4117,plain,
% 1.54/1.72 (~r(z, s(s(s(elem!1))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[4116, 45, 27, 1866, 385])).
% 1.54/1.72 tff(4118,plain,
% 1.54/1.72 (b(z, s(s(s(elem!1))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[858, 4117])).
% 1.54/1.72 tff(4119,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(4120,plain,
% 1.54/1.72 (((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z)))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(4121,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[4120])).
% 1.54/1.72 tff(4122,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.54/1.72 inference(transitivity,[status(thm)],[4121, 4119])).
% 1.54/1.72 tff(4123,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(4124,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[4123, 4122])).
% 1.54/1.72 tff(4125,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[4124, 128, 549, 1842, 1841, 4118, 3937])).
% 1.54/1.72 tff(4126,plain,((~r(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(4127,plain,
% 1.54/1.72 (~r(z, s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[4126, 549, 1842, 1841, 4110, 385])).
% 1.54/1.72 tff(4128,plain,
% 1.54/1.72 (b(z, s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[415, 4127])).
% 1.54/1.72 tff(4129,plain,
% 1.54/1.72 (~b(z, s(s(elem!1)))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3535, 3527, 30, 550])).
% 1.54/1.72 tff(4130,plain,
% 1.54/1.72 (r(z, s(s(elem!1)))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[160, 4129])).
% 1.54/1.72 tff(4131,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(4132,plain,
% 1.54/1.72 (((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(4133,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[4132])).
% 1.54/1.72 tff(4134,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.54/1.72 inference(transitivity,[status(thm)],[4133, 4131])).
% 1.54/1.72 tff(4135,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(4136,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[4135, 4134])).
% 1.54/1.72 tff(4137,plain,
% 1.54/1.72 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[4136, 128, 30, 550, 3527, 1841])).
% 1.54/1.72 tff(4138,plain,
% 1.54/1.72 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2212, 21, 1069, 4137])).
% 1.54/1.72 tff(4139,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(4140,plain,
% 1.54/1.72 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1))))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(4141,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[4140])).
% 1.54/1.72 tff(4142,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.54/1.72 inference(transitivity,[status(thm)],[4141, 4139])).
% 1.54/1.72 tff(4143,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(4144,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[4143, 4142])).
% 1.54/1.72 tff(4145,plain,
% 1.54/1.72 (~b(z, s(s(s(s(elem!1)))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[4144, 128, 550, 3527, 1841])).
% 1.54/1.72 tff(4146,plain,
% 1.54/1.72 (r(z, s(s(s(s(elem!1)))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2047, 21, 4145, 178])).
% 1.54/1.72 tff(4147,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3222, 4146, 4138, 4130])).
% 1.54/1.72 tff(4148,plain,((~b(s(z), z)) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(4149,plain,
% 1.54/1.73 (~b(s(z), z)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[4148, 4128, 1069, 1841, 30])).
% 1.54/1.73 tff(4150,plain,
% 1.54/1.73 (r(s(z), z)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[170, 4149])).
% 1.54/1.73 tff(4151,plain,
% 1.54/1.73 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3175, 89, 385, 272])).
% 1.54/1.73 tff(4152,plain,
% 1.54/1.73 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[889, 4151, 1691])).
% 1.54/1.73 tff(4153,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(4154,plain,
% 1.54/1.73 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(4155,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[4154])).
% 1.54/1.73 tff(4156,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.54/1.73 inference(transitivity,[status(thm)],[4155, 4153])).
% 1.54/1.73 tff(4157,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(4158,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[4157, 4156])).
% 1.54/1.73 tff(4159,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[4158, 128, 30, 550, 3378, 549, 4152])).
% 1.54/1.73 tff(4160,plain,((~r(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(4161,plain,
% 1.54/1.73 (~r(s(z), s(s(elem!1)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[4160, 4150, 4128, 549, 2025, 385, 30])).
% 1.54/1.73 tff(4162,plain,
% 1.54/1.73 (b(s(z), s(s(elem!1)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[117, 4161])).
% 1.54/1.73 tff(4163,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(4164,plain,
% 1.54/1.73 (((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(4165,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[4164])).
% 1.54/1.73 tff(4166,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 1.54/1.73 inference(transitivity,[status(thm)],[4165, 4163])).
% 1.54/1.73 tff(4167,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(4168,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[4167, 4166])).
% 1.54/1.73 tff(4169,plain,
% 1.54/1.73 (~b(z, s(s(elem!1)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[4168, 128, 30, 4128, 4162])).
% 1.54/1.73 tff(4170,plain,
% 1.54/1.73 (r(z, s(s(elem!1)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[160, 4169])).
% 1.54/1.73 tff(4171,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(4172,plain,
% 1.54/1.73 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(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(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(4173,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[4172])).
% 1.54/1.73 tff(4174,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.54/1.73 inference(transitivity,[status(thm)],[4173, 4171])).
% 1.54/1.73 tff(4175,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(4176,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[4175, 4174])).
% 1.54/1.73 tff(4177,plain,
% 1.54/1.73 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[4176, 128, 30, 4162, 1841])).
% 1.54/1.73 tff(4178,plain,
% 1.54/1.73 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2212, 21, 1069, 4177])).
% 1.54/1.73 tff(4179,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(4180,plain,
% 1.54/1.73 (((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1))))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(4181,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[4180])).
% 1.54/1.73 tff(4182,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.54/1.73 inference(transitivity,[status(thm)],[4181, 4179])).
% 1.54/1.73 tff(4183,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(4184,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[4183, 4182])).
% 1.54/1.73 tff(4185,plain,
% 1.54/1.73 (~b(z, s(s(s(s(elem!1)))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[4184, 128, 30, 4128, 4162, 1841])).
% 1.54/1.73 tff(4186,plain,
% 1.54/1.73 (r(z, s(s(s(s(elem!1)))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2047, 21, 4185, 178])).
% 1.54/1.73 tff(4187,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3222, 4186, 4178, 4170])).
% 1.54/1.73 tff(4188,plain,((~b(s(z), s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(4189,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[4188, 4108, 4104, 1069, 1842, 3883, 30])).
% 1.54/1.73 tff(4190,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (~r(z, s(z))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(4191,plain,
% 1.54/1.73 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[4190, 1842, 1069, 30, 272, 27, 808, 2083, 3452, 453, 876])).
% 1.54/1.73 tff(4192,plain,
% 1.54/1.73 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[321, 4191, 691])).
% 1.54/1.73 tff(4193,assumption,(b(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 1.54/1.73 tff(4194,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2596, 128, 4193, 2659, 1842, 2656])).
% 1.54/1.73 tff(4195,plain,((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(4196,plain,
% 1.54/1.73 (~b(elem!1, s(s(s(elem!1))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[4195, 1842, 2659, 2656])).
% 1.54/1.73 tff(4197,plain,
% 1.54/1.73 (r(elem!1, s(s(s(elem!1))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2466, 4196, 4049])).
% 1.54/1.73 tff(4198,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(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(4199,plain,
% 1.54/1.73 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(4200,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(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[4199])).
% 1.54/1.73 tff(4201,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(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.54/1.73 inference(transitivity,[status(thm)],[4200, 4198])).
% 1.54/1.73 tff(4202,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(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(4203,plain,
% 1.54/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[4202, 4201])).
% 1.54/1.73 tff(4204,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[4203, 45, 2349, 4197, 4192])).
% 1.54/1.73 tff(4205,plain,((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (elem!1 = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (~r(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(4206,plain,
% 1.54/1.73 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[4205, 4097, 2457, 3881, 3495, 3100, 3212, 4102, 272, 27, 3498, 4080, 4079, 4100])).
% 1.54/1.73 tff(4207,plain,
% 1.54/1.73 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1820, 4206, 3102])).
% 1.54/1.73 tff(4208,plain,
% 1.54/1.73 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3649, 45, 324, 1772])).
% 1.54/1.73 tff(4209,plain,
% 1.54/1.73 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2212, 21, 4208, 1069])).
% 1.54/1.73 tff(4210,plain,
% 1.54/1.73 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2103, 324, 1772])).
% 1.54/1.73 tff(4211,plain,
% 1.54/1.73 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1897, 4210, 1063])).
% 1.54/1.73 tff(4212,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(4213,plain,
% 1.54/1.73 (((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(4214,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[4213])).
% 1.54/1.73 tff(4215,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.54/1.73 inference(transitivity,[status(thm)],[4214, 4212])).
% 1.54/1.73 tff(4216,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(4217,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[4216, 4215])).
% 1.54/1.73 tff(4218,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[4217, 128, 1663, 4211, 4209, 2656])).
% 1.54/1.73 tff(4219,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(4220,plain,
% 1.54/1.73 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[4219, 4081, 3495, 3212, 4207, 3099])).
% 1.54/1.73 tff(4221,plain,
% 1.54/1.73 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[321, 4220, 3100])).
% 1.54/1.73 tff(4222,plain,
% 1.54/1.73 (~b(z, s(s(s(elem!1))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3460, 4221, 4080, 4079])).
% 1.54/1.73 tff(4223,plain,
% 1.54/1.73 (r(z, s(s(s(elem!1))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[858, 4222])).
% 1.54/1.73 tff(4224,plain,
% 1.54/1.73 (~r(s(z), s(s(s(elem!1))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[854, 4223, 272])).
% 1.54/1.73 tff(4225,plain,
% 1.54/1.73 (b(s(z), s(s(s(elem!1))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[339, 4224])).
% 1.54/1.73 tff(4226,plain,
% 1.54/1.73 (b(s(elem!1), s(s(s(elem!1))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[4225, 2572])).
% 1.54/1.73 tff(4227,plain,
% 1.54/1.73 (b(s(elem!1), s(s(elem!1)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2709, 4100, 1647])).
% 1.54/1.73 tff(4228,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3473, 128, 4081, 4221, 3881, 4227, 4226])).
% 1.54/1.73 tff(4229,plain,((~(z = elem!1)) | (~r(s(z), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(4230,plain,
% 1.54/1.73 (~r(z, s(z))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[4229, 1647, 171])).
% 1.54/1.73 tff(4231,plain,
% 1.54/1.73 (b(z, s(z))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[415, 4230])).
% 1.54/1.73 tff(4232,plain,
% 1.54/1.73 (b(z, elem!1) <=> b(elem!1, elem!1)),
% 1.54/1.73 inference(monotonicity,[status(thm)],[1647])).
% 1.54/1.73 tff(4233,plain,
% 1.54/1.73 (b(elem!1, elem!1) <=> b(z, elem!1)),
% 1.54/1.73 inference(symmetry,[status(thm)],[4232])).
% 1.54/1.73 tff(4234,plain,
% 1.54/1.73 ((~b(elem!1, elem!1)) <=> (~b(z, elem!1))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[4233])).
% 1.54/1.73 tff(4235,plain,
% 1.54/1.73 (^[X: $i] : refl((~b(X, X)) <=> (~b(X, X)))),
% 1.54/1.73 inference(bind,[status(th)],[])).
% 1.54/1.73 tff(4236,plain,
% 1.54/1.73 (![X: $i] : (~b(X, X)) <=> ![X: $i] : (~b(X, X))),
% 1.54/1.73 inference(quant_intro,[status(thm)],[4235])).
% 1.54/1.73 tff(4237,plain,
% 1.54/1.73 (![X: $i] : (~b(X, X)) <=> ![X: $i] : (~b(X, X))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(4238,axiom,(![X: $i] : (~b(X, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bi')).
% 1.54/1.73 tff(4239,plain,
% 1.54/1.73 (![X: $i] : (~b(X, X))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[4238, 4237])).
% 1.54/1.73 tff(4240,plain,(
% 1.54/1.73 ![X: $i] : (~b(X, X))),
% 1.54/1.73 inference(skolemize,[status(sab)],[4239])).
% 1.54/1.73 tff(4241,plain,
% 1.54/1.73 (![X: $i] : (~b(X, X))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[4240, 4236])).
% 1.54/1.73 tff(4242,plain,
% 1.54/1.73 ((~![X: $i] : (~b(X, X))) | (~b(elem!1, elem!1))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(4243,plain,
% 1.54/1.73 (~b(elem!1, elem!1)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[4242, 4241])).
% 1.54/1.73 tff(4244,plain,
% 1.54/1.73 (~b(z, elem!1)),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[4243, 4234])).
% 1.54/1.73 tff(4245,plain,
% 1.54/1.73 (b(elem!1, z) <=> b(elem!1, elem!1)),
% 1.54/1.73 inference(monotonicity,[status(thm)],[1647])).
% 1.54/1.73 tff(4246,plain,
% 1.54/1.73 (b(elem!1, elem!1) <=> b(elem!1, z)),
% 1.54/1.73 inference(symmetry,[status(thm)],[4245])).
% 1.54/1.73 tff(4247,plain,
% 1.54/1.73 ((~b(elem!1, elem!1)) <=> (~b(elem!1, z))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[4246])).
% 1.54/1.73 tff(4248,plain,
% 1.54/1.73 (~b(elem!1, z)),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[4243, 4247])).
% 1.54/1.73 tff(4249,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2758, 4248, 4244, 164, 1086, 4231])).
% 1.54/1.73 tff(4250,plain,((~(z = elem!1)) | b(s(z), z) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(4251,plain,
% 1.54/1.73 (~(z = elem!1)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[4250, 1086, 164])).
% 1.54/1.73 tff(4252,assumption,(s(s(elem!1)) = s(s(z))), introduced(assumption)).
% 1.54/1.73 tff(4253,plain,
% 1.54/1.73 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[4252])).
% 1.54/1.73 tff(4254,plain,
% 1.54/1.73 (s(elem!1) = s(z)),
% 1.54/1.73 inference(transitivity,[status(thm)],[106, 4253, 69])).
% 1.54/1.73 tff(4255,plain,
% 1.54/1.73 (inj_0(s(elem!1)) = inj_0(s(z))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[4254])).
% 1.54/1.73 tff(4256,plain,
% 1.54/1.73 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.54/1.73 inference(symmetry,[status(thm)],[4255])).
% 1.54/1.73 tff(4257,plain,
% 1.54/1.73 (z = inj_0(s(z))),
% 1.54/1.73 inference(symmetry,[status(thm)],[64])).
% 1.54/1.73 tff(4258,plain,
% 1.54/1.73 (z = elem!1),
% 1.54/1.73 inference(transitivity,[status(thm)],[4257, 4256, 201])).
% 1.54/1.73 tff(4259,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1608, 4258])).
% 1.54/1.73 tff(4260,plain,((~(s(s(elem!1)) = s(s(z)))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(4261,plain,
% 1.54/1.73 (~(s(s(elem!1)) = s(s(z)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[4260, 4251])).
% 1.54/1.73 tff(4262,plain,
% 1.54/1.73 (~(s(s(z)) = s(s(elem!1)))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[4261, 33])).
% 1.54/1.73 tff(4263,plain,
% 1.54/1.73 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[321, 2648, 198])).
% 1.54/1.73 tff(4264,assumption,(~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))), introduced(assumption)).
% 1.54/1.73 tff(4265,plain,
% 1.54/1.73 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1820, 2650, 4264])).
% 1.54/1.73 tff(4266,plain,
% 1.54/1.73 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2103, 1772, 324])).
% 1.54/1.73 tff(4267,plain,
% 1.54/1.73 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1897, 4266, 2023])).
% 1.54/1.73 tff(4268,plain,
% 1.54/1.73 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 1.54/1.73 inference(commutativity,[status(thm)],[])).
% 1.54/1.73 tff(4269,plain,
% 1.54/1.73 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(z)) = s(s(s(elem!1))))),
% 1.54/1.73 inference(symmetry,[status(thm)],[4268])).
% 1.54/1.73 tff(4270,plain,
% 1.54/1.73 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(elem!1)))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[4269])).
% 1.54/1.73 tff(4271,plain,
% 1.54/1.73 (~(s(s(z)) = s(s(s(elem!1))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[283, 4270])).
% 1.54/1.73 tff(4272,plain,
% 1.54/1.73 (~r(s(z), s(s(s(elem!1))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[333, 325, 324])).
% 1.54/1.73 tff(4273,plain,
% 1.54/1.73 (b(s(z), s(s(s(elem!1))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[339, 4272])).
% 1.54/1.74 tff(4274,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(4275,plain,
% 1.54/1.74 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(4276,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(z)))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[4275])).
% 1.54/1.74 tff(4277,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))))),
% 1.54/1.74 inference(transitivity,[status(thm)],[4276, 4274])).
% 1.54/1.74 tff(4278,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(4279,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(z)))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[4278, 4277])).
% 1.54/1.74 tff(4280,plain,
% 1.54/1.74 (~b(s(s(z)), s(s(s(elem!1))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4279, 128, 4273, 2718, 273])).
% 1.54/1.74 tff(4281,plain,
% 1.54/1.74 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(elem!1)))) | b(s(s(z)), s(s(s(elem!1)))) | r(s(s(z)), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(elem!1)))) | b(s(s(z)), s(s(s(elem!1)))) | r(s(s(z)), s(s(s(elem!1)))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(4282,plain,
% 1.54/1.74 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(elem!1)))) | b(s(s(z)), s(s(s(elem!1)))) | r(s(s(z)), s(s(s(elem!1)))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(4283,plain,
% 1.54/1.74 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(elem!1)))) | b(s(s(z)), s(s(s(elem!1)))) | r(s(s(z)), s(s(s(elem!1))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[4282, 4281])).
% 1.54/1.74 tff(4284,plain,
% 1.54/1.74 ((s(s(z)) = s(s(s(elem!1)))) | r(s(s(z)), s(s(s(elem!1))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4283, 21, 4280])).
% 1.54/1.74 tff(4285,plain,
% 1.54/1.74 (r(s(s(z)), s(s(s(elem!1))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4284, 4271])).
% 1.54/1.74 tff(4286,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(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(4287,plain,
% 1.54/1.74 (((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))) <=> ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(4288,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(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[4287])).
% 1.54/1.74 tff(4289,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(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.54/1.74 inference(transitivity,[status(thm)],[4288, 4286])).
% 1.54/1.74 tff(4290,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(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(4291,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(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[4290, 4289])).
% 1.54/1.74 tff(4292,plain,
% 1.54/1.74 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4291, 45, 1772, 4285])).
% 1.54/1.74 tff(4293,assumption,(b(s(s(elem!1)), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.54/1.74 tff(4294,plain,
% 1.54/1.74 (~r(z, s(s(elem!1)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[438, 325, 324])).
% 1.54/1.74 tff(4295,plain,
% 1.54/1.74 (b(z, s(s(elem!1)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[160, 4294])).
% 1.54/1.74 tff(4296,plain,
% 1.54/1.74 (~b(s(s(s(s(elem!1)))), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2336, 128, 4295, 2084, 4293])).
% 1.54/1.74 tff(4297,plain,
% 1.54/1.74 (r(s(s(s(s(elem!1)))), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2081, 4296])).
% 1.54/1.74 tff(4298,plain,
% 1.54/1.74 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[1745, 4297, 272])).
% 1.54/1.74 tff(4299,plain,
% 1.54/1.74 (b(s(s(s(s(elem!1)))), s(z))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[1828, 4298])).
% 1.54/1.74 tff(4300,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(4301,plain,
% 1.54/1.74 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(4302,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z))))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[4301])).
% 1.54/1.74 tff(4303,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.54/1.74 inference(transitivity,[status(thm)],[4302, 4300])).
% 1.54/1.74 tff(4304,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(4305,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[4304, 4303])).
% 1.54/1.74 tff(4306,plain,
% 1.54/1.74 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4305, 128, 4273, 2718, 4299, 273])).
% 1.54/1.74 tff(4307,plain,
% 1.54/1.74 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(z))) | b(s(s(s(s(elem!1)))), s(s(z))) | r(s(s(s(s(elem!1)))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(z))) | b(s(s(s(s(elem!1)))), s(s(z))) | r(s(s(s(s(elem!1)))), s(s(z))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(4308,plain,
% 1.54/1.74 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(z))) | b(s(s(s(s(elem!1)))), s(s(z))) | r(s(s(s(s(elem!1)))), s(s(z))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(4309,plain,
% 1.54/1.74 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(z))) | b(s(s(s(s(elem!1)))), s(s(z))) | r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[4308, 4307])).
% 1.54/1.74 tff(4310,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4309, 21, 239, 4306, 4292])).
% 1.54/1.74 tff(4311,plain,((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~r(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(4312,plain,
% 1.54/1.74 (~r(s(s(elem!1)), s(z))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4311, 273, 2718, 1772, 272, 4267, 4209, 324])).
% 1.54/1.74 tff(4313,plain,
% 1.54/1.74 (b(s(s(elem!1)), s(z))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[292, 4312])).
% 1.54/1.74 tff(4314,plain,
% 1.54/1.74 (~b(s(z), s(s(s(elem!1))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3651, 1841, 2718, 1069, 2073, 30, 324])).
% 1.54/1.74 tff(4315,plain,
% 1.54/1.74 (r(s(z), s(s(s(elem!1))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[339, 4314])).
% 1.54/1.74 tff(4316,plain,
% 1.54/1.74 (~b(s(z), s(s(elem!1)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2608, 1841, 2084, 30])).
% 1.54/1.74 tff(4317,plain,
% 1.54/1.74 (r(s(z), s(s(elem!1)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[117, 4316])).
% 1.54/1.74 tff(4318,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(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(4319,plain,
% 1.54/1.74 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(4320,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)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[4319])).
% 1.54/1.74 tff(4321,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)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.54/1.74 inference(transitivity,[status(thm)],[4320, 4318])).
% 1.54/1.74 tff(4322,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)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(4323,plain,
% 1.54/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[4322, 4321])).
% 1.54/1.74 tff(4324,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4323, 45, 4317, 324, 4315])).
% 1.54/1.74 tff(4325,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (s(s(elem!1)) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(4326,plain,
% 1.54/1.74 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4325, 4313, 4267, 324, 2718, 1069])).
% 1.54/1.74 tff(4327,plain,
% 1.54/1.74 (r(s(s(s(s(elem!1)))), s(z))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[1828, 4326])).
% 1.54/1.74 tff(4328,plain,
% 1.54/1.74 (~r(s(z), s(s(s(elem!1))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2519, 4327, 272, 1772])).
% 1.54/1.74 tff(4329,plain,
% 1.54/1.74 (b(s(z), s(s(s(elem!1))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[339, 4328])).
% 1.54/1.74 tff(4330,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(4331,plain,
% 1.54/1.74 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(4332,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z))))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[4331])).
% 1.54/1.74 tff(4333,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.54/1.74 inference(transitivity,[status(thm)],[4332, 4330])).
% 1.54/1.74 tff(4334,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(4335,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[4334, 4333])).
% 1.54/1.74 tff(4336,plain,
% 1.54/1.74 (~b(s(s(elem!1)), s(s(z)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4335, 128, 4313, 4329, 2718, 273])).
% 1.54/1.74 tff(4337,plain,
% 1.54/1.74 (((~![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))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(4338,plain,
% 1.54/1.74 ((~![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))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(4339,plain,
% 1.54/1.74 ((~![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)))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[4338, 4337])).
% 1.54/1.74 tff(4340,plain,
% 1.54/1.74 (r(s(s(elem!1)), s(s(z)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4339, 21, 1, 4336])).
% 1.54/1.74 tff(4341,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(4342,plain,
% 1.54/1.74 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(4343,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[4342])).
% 1.54/1.74 tff(4344,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.54/1.74 inference(transitivity,[status(thm)],[4343, 4341])).
% 1.54/1.74 tff(4345,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(4346,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[4345, 4344])).
% 1.54/1.74 tff(4347,plain,
% 1.54/1.74 (~b(s(s(s(elem!1))), s(s(z)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4346, 128, 4329, 2718, 273])).
% 1.54/1.74 tff(4348,plain,
% 1.54/1.74 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z))) | r(s(s(s(elem!1))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z))) | r(s(s(s(elem!1))), s(s(z))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(4349,plain,
% 1.54/1.74 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z))) | r(s(s(s(elem!1))), s(s(z))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(4350,plain,
% 1.54/1.74 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z))) | r(s(s(s(elem!1))), s(s(z)))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[4349, 4348])).
% 1.54/1.74 tff(4351,plain,
% 1.54/1.74 (r(s(s(s(elem!1))), s(s(z)))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4350, 21, 4347, 283])).
% 1.54/1.74 tff(4352,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(4353,plain,
% 1.54/1.75 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(4354,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[4353])).
% 1.54/1.75 tff(4355,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[4354, 4352])).
% 1.54/1.75 tff(4356,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(4357,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[4356, 4355])).
% 1.54/1.75 tff(4358,plain,
% 1.54/1.75 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4357, 128, 4313, 4329, 2718])).
% 1.54/1.75 tff(4359,plain,
% 1.54/1.75 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[889, 4358, 2025])).
% 1.54/1.75 tff(4360,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(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(4361,plain,
% 1.54/1.75 (((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(4362,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)), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z))))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[4361])).
% 1.54/1.75 tff(4363,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)), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[4362, 4360])).
% 1.54/1.75 tff(4364,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)), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(4365,plain,
% 1.54/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[4364, 4363])).
% 1.54/1.75 tff(4366,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4365, 45, 4359, 4351, 4340])).
% 1.54/1.75 tff(4367,plain,((~b(s(s(z)), s(z))) | (s(s(elem!1)) = s(s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(4368,plain,
% 1.54/1.75 (~b(s(s(z)), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4367, 4261, 2718, 171, 4265, 4263, 1646])).
% 1.54/1.75 tff(4369,plain,
% 1.54/1.75 (r(s(s(z)), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[86, 4368])).
% 1.54/1.75 tff(4370,plain,
% 1.54/1.75 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4325, 30, 4267, 324, 2718, 1069])).
% 1.54/1.75 tff(4371,plain,
% 1.54/1.75 (r(s(s(s(s(elem!1)))), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1828, 4370])).
% 1.54/1.75 tff(4372,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(elem!1)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(4373,plain,
% 1.54/1.75 (((~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z))))) <=> ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(4374,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(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z))))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[4373])).
% 1.54/1.75 tff(4375,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(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[4374, 4372])).
% 1.54/1.75 tff(4376,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(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(4377,plain,
% 1.54/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[4376, 4375])).
% 1.54/1.75 tff(4378,plain,
% 1.54/1.75 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4377, 45, 4371, 35])).
% 1.54/1.75 tff(4379,plain,
% 1.54/1.75 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4309, 21, 239, 4378])).
% 1.54/1.75 tff(4380,plain,
% 1.54/1.75 (~r(s(z), s(s(s(elem!1))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2519, 4371, 272, 1772])).
% 1.54/1.75 tff(4381,plain,
% 1.54/1.75 (b(s(z), s(s(s(elem!1))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[339, 4380])).
% 1.54/1.75 tff(4382,plain,
% 1.54/1.75 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4357, 128, 30, 4381, 2718])).
% 1.54/1.75 tff(4383,plain,
% 1.54/1.75 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[889, 4382, 2025])).
% 1.54/1.75 tff(4384,plain,
% 1.54/1.75 (~r(s(s(s(s(elem!1)))), z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1745, 4371, 272])).
% 1.54/1.75 tff(4385,plain,
% 1.54/1.75 (b(s(s(s(s(elem!1)))), z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2081, 4384])).
% 1.54/1.75 tff(4386,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2336, 128, 453, 2084, 2083, 4293])).
% 1.54/1.75 tff(4387,plain,((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(4388,plain,
% 1.54/1.75 (~b(z, s(s(elem!1)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4387, 4385, 4267, 4209])).
% 1.54/1.75 tff(4389,plain,
% 1.54/1.75 (r(z, s(s(elem!1)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[160, 4388])).
% 1.54/1.75 tff(4390,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(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(4391,plain,
% 1.54/1.75 (((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(4392,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(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1))))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[4391])).
% 1.54/1.75 tff(4393,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(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[4392, 4390])).
% 1.54/1.75 tff(4394,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(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(4395,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(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[4394, 4393])).
% 1.54/1.75 tff(4396,plain,
% 1.54/1.75 (~r(s(s(s(elem!1))), z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4395, 45, 4389, 4383])).
% 1.54/1.75 tff(4397,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(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(4398,plain,
% 1.54/1.75 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(4399,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(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[4398])).
% 1.54/1.75 tff(4400,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(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[4399, 4397])).
% 1.54/1.75 tff(4401,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(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(4402,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(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[4401, 4400])).
% 1.54/1.75 tff(4403,plain,
% 1.54/1.75 (~r(z, s(s(s(elem!1))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4402, 45, 4389, 4383])).
% 1.54/1.75 tff(4404,plain,
% 1.54/1.75 (~b(z, s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[561, 4403, 4381, 4396])).
% 1.54/1.75 tff(4405,plain,
% 1.54/1.75 (r(z, s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[415, 4404])).
% 1.54/1.75 tff(4406,plain,
% 1.54/1.75 (~r(s(s(z)), z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[51, 45, 4405, 35])).
% 1.54/1.75 tff(4407,plain,
% 1.54/1.75 (b(s(s(z)), z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[25, 4406])).
% 1.54/1.75 tff(4408,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(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(4409,plain,
% 1.54/1.75 (((~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1))))))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(4410,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(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1))))))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[4409])).
% 1.54/1.75 tff(4411,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(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[4410, 4408])).
% 1.54/1.75 tff(4412,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(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(4413,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(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1))))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[4412, 4411])).
% 1.54/1.75 tff(4414,plain,
% 1.54/1.75 (~r(z, s(s(s(s(elem!1)))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4413, 45, 4405, 4371])).
% 1.54/1.75 tff(4415,plain,
% 1.54/1.75 (b(z, s(s(s(s(elem!1)))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2047, 21, 4414, 178])).
% 1.54/1.75 tff(4416,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(4417,plain,
% 1.54/1.75 (((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(4418,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z))))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[4417])).
% 1.54/1.75 tff(4419,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[4418, 4416])).
% 1.54/1.75 tff(4420,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(4421,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[4420, 4419])).
% 1.54/1.75 tff(4422,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4421, 128, 4267, 4385, 4415, 4407, 4379])).
% 1.54/1.75 tff(4423,plain,((~b(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(4424,plain,
% 1.54/1.75 (~b(s(s(elem!1)), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4423, 4369, 2718, 171, 4265, 4263, 1646])).
% 1.54/1.75 tff(4425,plain,
% 1.54/1.75 (r(s(s(elem!1)), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[292, 4424])).
% 1.54/1.75 tff(4426,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)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(4427,plain,
% 1.54/1.75 (((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(4428,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)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1))))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[4427])).
% 1.54/1.75 tff(4429,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)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[4428, 4426])).
% 1.54/1.75 tff(4430,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)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(4431,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)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[4430, 4429])).
% 1.54/1.75 tff(4432,plain,
% 1.54/1.75 (~r(s(s(z)), s(s(elem!1)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4431, 45, 4425, 4369])).
% 1.54/1.75 tff(4433,plain,
% 1.54/1.75 ((s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[138, 21, 4432])).
% 1.54/1.75 tff(4434,plain,
% 1.54/1.75 (b(s(s(z)), s(s(elem!1)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4433, 4262])).
% 1.54/1.75 tff(4435,plain,
% 1.54/1.75 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3649, 45, 4263, 4265])).
% 1.54/1.75 tff(4436,plain,
% 1.54/1.75 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2212, 21, 4435, 1646])).
% 1.54/1.75 tff(4437,plain,
% 1.54/1.75 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2103, 4265, 4263])).
% 1.54/1.75 tff(4438,plain,
% 1.54/1.75 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1897, 4437, 1664])).
% 1.54/1.75 tff(4439,plain,
% 1.54/1.75 (~r(z, s(s(elem!1)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[438, 4425, 4263])).
% 1.54/1.75 tff(4440,plain,
% 1.54/1.75 (b(z, s(s(elem!1)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[160, 4439])).
% 1.54/1.76 tff(4441,plain,
% 1.54/1.76 (~b(s(s(s(s(elem!1)))), z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4387, 4440, 4438, 4436])).
% 1.54/1.76 tff(4442,plain,
% 1.54/1.76 (r(s(s(s(s(elem!1)))), z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2081, 4441])).
% 1.54/1.76 tff(4443,plain,
% 1.54/1.76 (~r(s(s(s(elem!1))), z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1780, 4442, 4265])).
% 1.54/1.76 tff(4444,plain,
% 1.54/1.76 (~r(s(z), s(s(s(elem!1))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[333, 4425, 4263])).
% 1.54/1.76 tff(4445,plain,
% 1.54/1.76 (b(s(z), s(s(s(elem!1))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[339, 4444])).
% 1.54/1.76 tff(4446,assumption,(b(z, s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.54/1.76 tff(4447,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(4448,plain,
% 1.54/1.76 (((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(4449,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1))))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[4448])).
% 1.54/1.76 tff(4450,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[4449, 4447])).
% 1.54/1.76 tff(4451,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(4452,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1))))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[4451, 4450])).
% 1.54/1.76 tff(4453,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4452, 128, 453, 2084, 4293, 4446])).
% 1.54/1.76 tff(4454,plain,((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(4455,plain,
% 1.54/1.76 (~b(z, s(s(s(s(elem!1)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4454, 4440, 4436, 4438])).
% 1.54/1.76 tff(4456,plain,
% 1.54/1.76 (r(z, s(s(s(s(elem!1)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2047, 21, 4455, 178])).
% 1.54/1.76 tff(4457,plain,
% 1.54/1.76 (~r(z, s(s(s(elem!1))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1790, 4456, 4265])).
% 1.54/1.76 tff(4458,plain,
% 1.54/1.76 (~b(z, s(z))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[561, 4457, 4445, 4443])).
% 1.54/1.76 tff(4459,plain,
% 1.54/1.76 (r(z, s(z))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[415, 4458])).
% 1.54/1.76 tff(4460,plain,
% 1.54/1.76 (~r(z, s(s(z)))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2946, 4459, 4369])).
% 1.54/1.76 tff(4461,plain,
% 1.54/1.76 (b(z, s(s(z)))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[516, 4460])).
% 1.54/1.76 tff(4462,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(4463,plain,
% 1.54/1.76 (((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(4464,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[4463])).
% 1.54/1.76 tff(4465,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[4464, 4462])).
% 1.54/1.76 tff(4466,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(4467,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[4466, 4465])).
% 1.54/1.76 tff(4468,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4467, 128, 4440, 4438, 4436, 4461, 4434])).
% 1.54/1.76 tff(4469,plain,((s(s(elem!1)) = elem!1) | (~b(s(s(s(elem!1))), s(z))) | b(s(z), z) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(4470,plain,
% 1.54/1.76 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4469, 3090, 164, 197, 198])).
% 1.54/1.76 tff(4471,plain,
% 1.54/1.76 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1089, 3090])).
% 1.54/1.76 tff(4472,plain,
% 1.54/1.76 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1073, 4471])).
% 1.54/1.76 tff(4473,plain,
% 1.54/1.76 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1065, 4472])).
% 1.54/1.76 tff(4474,plain,
% 1.54/1.76 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[321, 4473, 198])).
% 1.54/1.76 tff(4475,plain,
% 1.54/1.76 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z)))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(4476,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[4475])).
% 1.54/1.76 tff(4477,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[4476, 3628])).
% 1.54/1.76 tff(4478,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(4479,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[4478, 4477])).
% 1.54/1.76 tff(4480,plain,
% 1.54/1.76 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4479, 128, 4273, 1842, 2718])).
% 1.54/1.76 tff(4481,plain,
% 1.54/1.76 (r(s(s(s(s(elem!1)))), s(z))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1828, 4480])).
% 1.54/1.76 tff(4482,plain,
% 1.54/1.76 (~r(s(s(s(s(elem!1)))), z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1745, 4481, 272])).
% 1.54/1.76 tff(4483,plain,
% 1.54/1.76 (b(s(s(s(s(elem!1)))), z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2081, 4482])).
% 1.54/1.76 tff(4484,plain,
% 1.54/1.76 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2141, 4481, 325])).
% 1.54/1.76 tff(4485,plain,
% 1.54/1.76 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1897, 4484, 2023])).
% 1.54/1.76 tff(4486,plain,
% 1.54/1.76 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4387, 4485, 4295, 4483])).
% 1.54/1.76 tff(4487,plain,
% 1.54/1.76 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2208, 45, 325, 4481])).
% 1.54/1.76 tff(4488,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2212, 21, 4487, 1069, 4486])).
% 1.54/1.76 tff(4489,plain,((~r(s(s(elem!1)), s(z))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~r(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(4490,plain,
% 1.54/1.76 (~r(s(s(elem!1)), s(z))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4489, 1646, 171, 1842, 2718, 324])).
% 1.54/1.76 tff(4491,plain,
% 1.54/1.76 (b(s(s(elem!1)), s(z))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[292, 4490])).
% 1.54/1.76 tff(4492,plain,
% 1.54/1.76 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[803, 2648])).
% 1.54/1.76 tff(4493,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(4494,plain,
% 1.54/1.76 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(4495,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[4494])).
% 1.54/1.76 tff(4496,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[4495, 4493])).
% 1.54/1.76 tff(4497,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(4498,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[4497, 4496])).
% 1.54/1.76 tff(4499,plain,
% 1.54/1.76 (~b(s(s(s(elem!1))), z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4498, 128, 550, 549, 2718])).
% 1.54/1.76 tff(4500,plain,
% 1.54/1.76 (r(s(s(s(elem!1))), z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[547, 21, 382, 4499])).
% 1.54/1.76 tff(4501,plain,
% 1.54/1.76 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4357, 128, 30, 549, 2718])).
% 1.54/1.76 tff(4502,plain,
% 1.54/1.76 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[889, 4501, 1691])).
% 1.54/1.76 tff(4503,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(4504,plain,
% 1.54/1.76 (((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(4505,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[4504])).
% 1.54/1.76 tff(4506,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[4505, 4503])).
% 1.54/1.76 tff(4507,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(4508,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[4507, 4506])).
% 1.54/1.76 tff(4509,plain,
% 1.54/1.76 (~b(z, s(s(elem!1)))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4508, 128, 30, 550, 549, 2718])).
% 1.54/1.76 tff(4510,plain,
% 1.54/1.76 (r(z, s(s(elem!1)))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[160, 4509])).
% 1.54/1.76 tff(4511,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4395, 45, 4510, 4502, 4500])).
% 1.54/1.76 tff(4512,plain,((~b(s(z), s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(4513,plain,
% 1.54/1.76 (~b(s(z), s(s(s(elem!1))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4512, 30, 550, 2718, 1691])).
% 1.54/1.76 tff(4514,plain,
% 1.54/1.76 (r(s(z), s(s(s(elem!1))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[339, 4513])).
% 1.54/1.76 tff(4515,plain,
% 1.54/1.76 (~r(z, s(s(s(elem!1))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[854, 4514, 272])).
% 1.54/1.76 tff(4516,plain,
% 1.54/1.76 (b(z, s(s(s(elem!1))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[858, 4515])).
% 1.54/1.76 tff(4517,plain,
% 1.54/1.76 (~r(s(z), s(s(elem!1)))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4323, 45, 324, 4514])).
% 1.54/1.76 tff(4518,plain,
% 1.54/1.76 (b(s(z), s(s(elem!1)))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[117, 4517])).
% 1.54/1.76 tff(4519,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(4520,plain,
% 1.54/1.76 (((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(4521,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1)))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[4520])).
% 1.54/1.76 tff(4522,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[4521, 4519])).
% 1.54/1.76 tff(4523,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(4524,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1)))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[4523, 4522])).
% 1.54/1.76 tff(4525,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4524, 128, 30, 550, 4518, 2718, 4516])).
% 1.54/1.76 tff(4526,plain,((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), z)) | (s(s(s(elem!1))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(4527,plain,
% 1.54/1.76 (~b(z, s(z))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4526, 4491, 2718, 324, 171, 4492])).
% 1.54/1.76 tff(4528,plain,
% 1.54/1.76 (r(z, s(z))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[415, 4527])).
% 1.54/1.76 tff(4529,plain,
% 1.54/1.76 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3651, 549, 2718, 1646, 2650, 4491, 324])).
% 1.54/1.76 tff(4530,plain,
% 1.54/1.76 (r(s(s(s(s(elem!1)))), s(z))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1828, 4529])).
% 1.54/1.76 tff(4531,plain,
% 1.54/1.76 (~r(s(s(s(s(elem!1)))), z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1745, 4530, 171])).
% 1.54/1.76 tff(4532,plain,
% 1.54/1.76 (b(s(s(s(s(elem!1)))), z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2081, 4531])).
% 1.54/1.76 tff(4533,plain,
% 1.54/1.76 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4357, 128, 4491, 549, 2718])).
% 1.54/1.76 tff(4534,plain,
% 1.54/1.76 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[889, 4533, 4492])).
% 1.54/1.76 tff(4535,plain,
% 1.54/1.76 (~r(s(s(s(elem!1))), z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4395, 45, 88, 1794])).
% 1.54/1.76 tff(4536,plain,
% 1.54/1.76 (b(s(s(s(elem!1))), z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[547, 21, 382, 4535])).
% 1.54/1.76 tff(4537,plain,
% 1.54/1.76 (~r(z, s(s(s(elem!1))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4402, 45, 88, 1794])).
% 1.54/1.76 tff(4538,plain,
% 1.54/1.76 (b(z, s(s(s(elem!1))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[858, 4537])).
% 1.54/1.76 tff(4539,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(4540,plain,
% 1.54/1.76 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(4541,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[4540])).
% 1.54/1.76 tff(4542,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.54/1.76 inference(transitivity,[status(thm)],[4541, 4539])).
% 1.54/1.76 tff(4543,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(4544,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[4543, 4542])).
% 1.54/1.76 tff(4545,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4544, 128, 1842, 4538, 4536, 2083])).
% 1.54/1.76 tff(4546,plain,((~r(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(4547,plain,
% 1.54/1.77 (~r(z, s(s(elem!1)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4546, 4534, 1842, 4532])).
% 1.54/1.77 tff(4548,plain,
% 1.54/1.77 (b(z, s(s(elem!1)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[160, 4547])).
% 1.54/1.77 tff(4549,plain,
% 1.54/1.77 (~r(s(z), s(s(elem!1)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3672, 4548, 1664, 4528, 4491, 549])).
% 1.54/1.77 tff(4550,plain,
% 1.54/1.77 (b(s(z), s(s(elem!1)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[117, 4549])).
% 1.54/1.77 tff(4551,assumption,(elem!1 = z), introduced(assumption)).
% 1.54/1.77 tff(4552,plain,
% 1.54/1.77 (z = elem!1),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[4551, 247])).
% 1.54/1.77 tff(4553,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1608, 4552])).
% 1.54/1.77 tff(4554,plain,((~(elem!1 = z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(4555,plain,
% 1.54/1.77 (~(elem!1 = z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4554, 4251])).
% 1.54/1.77 tff(4556,plain,
% 1.54/1.77 (~r(z, s(s(s(s(elem!1)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4413, 45, 4528, 4530])).
% 1.54/1.77 tff(4557,plain,
% 1.54/1.77 (b(z, s(s(s(s(elem!1)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2047, 21, 4556, 178])).
% 1.54/1.77 tff(4558,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(4559,plain,
% 1.54/1.77 (((~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1))))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(4560,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1))))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[4559])).
% 1.54/1.77 tff(4561,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[4560, 4558])).
% 1.54/1.77 tff(4562,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(4563,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1))))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[4562, 4561])).
% 1.54/1.77 tff(4564,plain,
% 1.54/1.77 ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1))))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4563, 128, 4548, 4550, 1842, 2718])).
% 1.54/1.77 tff(4565,plain,
% 1.54/1.77 (~b(z, s(s(s(elem!1))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4564, 4557])).
% 1.54/1.77 tff(4566,plain,
% 1.54/1.77 (r(z, s(s(s(elem!1))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[858, 4565])).
% 1.54/1.77 tff(4567,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)), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(4568,plain,
% 1.54/1.77 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z))) <=> ((~r(s(s(elem!1)), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(4569,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(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[4568])).
% 1.54/1.77 tff(4570,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(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[4569, 4567])).
% 1.54/1.77 tff(4571,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(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(4572,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)), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[4571, 4570])).
% 1.54/1.77 tff(4573,plain,
% 1.54/1.77 (~r(s(s(elem!1)), z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4572, 45, 324, 4566])).
% 1.54/1.77 tff(4574,plain,
% 1.54/1.77 (b(s(s(elem!1)), z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2018, 21, 154, 4573])).
% 1.54/1.77 tff(4575,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(4576,plain,
% 1.54/1.77 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(4577,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[4576])).
% 1.54/1.77 tff(4578,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.54/1.77 inference(transitivity,[status(thm)],[4577, 4575])).
% 1.54/1.77 tff(4579,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(4580,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[4579, 4578])).
% 1.54/1.77 tff(4581,plain,
% 1.54/1.77 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4580, 128, 4491, 4548, 549, 1842, 4532])).
% 1.54/1.77 tff(4582,plain,
% 1.54/1.77 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1897, 4581, 1664])).
% 1.54/1.77 tff(4583,plain,
% 1.54/1.77 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3348, 45, 4582, 4534])).
% 1.54/1.77 tff(4584,plain,
% 1.54/1.77 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1856, 4583, 2649])).
% 1.54/1.77 tff(4585,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(4586,plain,
% 1.54/1.77 (((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(4587,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[4586])).
% 1.54/1.77 tff(4588,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[4587, 4585])).
% 1.54/1.77 tff(4589,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(4590,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[4589, 4588])).
% 1.54/1.77 tff(4591,plain,
% 1.54/1.77 (~b(s(s(s(elem!1))), z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4590, 128, 4584, 1842, 4557])).
% 1.54/1.77 tff(4592,plain,
% 1.54/1.77 (r(s(s(s(elem!1))), z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[547, 21, 382, 4591])).
% 1.54/1.77 tff(4593,plain,
% 1.54/1.77 (r(z, elem!1)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1549, 455, 4251])).
% 1.54/1.77 tff(4594,plain,
% 1.54/1.77 (~r(s(z), elem!1)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1544, 4593, 171])).
% 1.54/1.77 tff(4595,plain,
% 1.54/1.77 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.54/1.77 inference(commutativity,[status(thm)],[])).
% 1.54/1.77 tff(4596,plain,
% 1.54/1.77 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.54/1.77 inference(symmetry,[status(thm)],[4595])).
% 1.54/1.77 tff(4597,plain,
% 1.54/1.77 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[4596])).
% 1.54/1.77 tff(4598,assumption,(s(s(s(elem!1))) = s(elem!1)), introduced(assumption)).
% 1.54/1.77 tff(4599,plain,
% 1.54/1.77 (inj_0(s(s(s(elem!1)))) = inj_0(s(elem!1))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[4598])).
% 1.54/1.77 tff(4600,plain,
% 1.54/1.77 (s(s(elem!1)) = elem!1),
% 1.54/1.77 inference(transitivity,[status(thm)],[187, 4599, 201])).
% 1.54/1.77 tff(4601,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1086, 4600])).
% 1.54/1.77 tff(4602,plain,((~(s(s(s(elem!1))) = s(elem!1))) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(4603,plain,
% 1.54/1.77 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4602, 1086])).
% 1.54/1.77 tff(4604,plain,
% 1.54/1.77 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[4603, 4597])).
% 1.54/1.77 tff(4605,plain,
% 1.54/1.77 (s(s(z)) = s(elem!1)),
% 1.54/1.77 inference(monotonicity,[status(thm)],[1640])).
% 1.54/1.77 tff(4606,plain,
% 1.54/1.77 (b(s(s(z)), elem!1) <=> b(s(elem!1), elem!1)),
% 1.54/1.77 inference(monotonicity,[status(thm)],[4605])).
% 1.54/1.77 tff(4607,plain,
% 1.54/1.77 (elem!1 = s(z)),
% 1.54/1.77 inference(symmetry,[status(thm)],[1640])).
% 1.54/1.77 tff(4608,plain,
% 1.54/1.77 (s(elem!1) = s(s(z))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[4607])).
% 1.54/1.77 tff(4609,plain,
% 1.54/1.77 (s(s(z)) = s(elem!1)),
% 1.54/1.77 inference(symmetry,[status(thm)],[4608])).
% 1.54/1.77 tff(4610,assumption,(s(s(z)) = elem!1), introduced(assumption)).
% 1.54/1.77 tff(4611,plain,
% 1.54/1.77 (elem!1 = s(s(z))),
% 1.54/1.77 inference(symmetry,[status(thm)],[4610])).
% 1.54/1.77 tff(4612,plain,
% 1.54/1.77 (s(z) = s(elem!1)),
% 1.54/1.77 inference(transitivity,[status(thm)],[1640, 4611, 4609])).
% 1.54/1.77 tff(4613,plain,
% 1.54/1.77 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[4612])).
% 1.54/1.77 tff(4614,plain,
% 1.54/1.77 (z = elem!1),
% 1.54/1.77 inference(transitivity,[status(thm)],[4257, 4613, 201])).
% 1.54/1.77 tff(4615,plain,
% 1.54/1.77 ((s(z) = z) <=> (elem!1 = z)),
% 1.54/1.77 inference(monotonicity,[status(thm)],[1640])).
% 1.54/1.77 tff(4616,plain,
% 1.54/1.77 ((s(z) = z) <=> (z = elem!1)),
% 1.54/1.77 inference(transitivity,[status(thm)],[4615, 247])).
% 1.54/1.77 tff(4617,plain,
% 1.54/1.77 ((~(s(z) = z)) <=> (~(z = elem!1))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[4616])).
% 1.54/1.77 tff(4618,plain,
% 1.54/1.77 (~(z = elem!1)),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[166, 4617])).
% 1.54/1.77 tff(4619,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4618, 4614])).
% 1.54/1.77 tff(4620,plain,((~(s(s(z)) = elem!1)) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(4621,plain,
% 1.54/1.77 (~(s(s(z)) = elem!1)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4620, 1640])).
% 1.54/1.77 tff(4622,plain,
% 1.54/1.77 ((elem!1 = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = elem!1)),
% 1.54/1.77 inference(commutativity,[status(thm)],[])).
% 1.54/1.77 tff(4623,plain,
% 1.54/1.77 ((s(z) = s(s(s(s(s(s(z))))))) <=> (elem!1 = s(s(s(s(s(s(z)))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[1640])).
% 1.54/1.77 tff(4624,plain,
% 1.54/1.77 ((s(z) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = elem!1)),
% 1.54/1.77 inference(transitivity,[status(thm)],[4623, 4622])).
% 1.54/1.77 tff(4625,plain,
% 1.54/1.77 ((~(s(z) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(s(s(z)))))) = elem!1))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[4624])).
% 1.54/1.77 tff(4626,plain,
% 1.54/1.77 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[1038, 4625])).
% 1.54/1.77 tff(4627,plain,
% 1.54/1.77 (elem!1 = s(z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1644, 1640])).
% 1.54/1.77 tff(4628,plain,
% 1.54/1.77 (~b(z, s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1638, 4627, 455])).
% 1.54/1.77 tff(4629,plain,
% 1.54/1.77 (r(z, s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[415, 4628])).
% 1.54/1.77 tff(4630,plain,
% 1.54/1.77 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
% 1.54/1.77 inference(monotonicity,[status(thm)],[1640])).
% 1.54/1.77 tff(4631,plain,
% 1.54/1.77 (b(s(s(s(elem!1))), elem!1)),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[2718, 4630])).
% 1.54/1.77 tff(4632,plain,
% 1.54/1.77 (s(s(s(z))) = s(s(elem!1))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[4605])).
% 1.54/1.77 tff(4633,plain,
% 1.54/1.77 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[4632])).
% 1.54/1.77 tff(4634,plain,
% 1.54/1.77 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.54/1.77 inference(symmetry,[status(thm)],[4633])).
% 1.54/1.77 tff(4635,plain,
% 1.54/1.77 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[4633])).
% 1.54/1.77 tff(4636,plain,
% 1.54/1.77 (s(s(s(s(s(s(z)))))) = s(s(s(s(s(elem!1)))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[4635])).
% 1.54/1.77 tff(4637,plain,
% 1.54/1.77 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(s(z))))))),
% 1.54/1.77 inference(symmetry,[status(thm)],[4636])).
% 1.54/1.77 tff(4638,plain,
% 1.54/1.77 ((s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[4637, 4634])).
% 1.54/1.77 tff(4639,plain,
% 1.54/1.77 ((s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.54/1.77 inference(symmetry,[status(thm)],[4638])).
% 1.54/1.77 tff(4640,plain,
% 1.54/1.77 ((~(s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[4639])).
% 1.54/1.77 tff(4641,plain,
% 1.54/1.77 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[1212, 4640])).
% 1.54/1.77 tff(4642,plain,
% 1.54/1.77 (b(s(s(s(s(s(elem!1))))), elem!1) <=> b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.54/1.77 inference(monotonicity,[status(thm)],[4637])).
% 1.54/1.77 tff(4643,plain,
% 1.54/1.77 (b(s(s(s(s(s(s(z)))))), elem!1) <=> b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.54/1.77 inference(symmetry,[status(thm)],[4642])).
% 1.54/1.77 tff(4644,plain,
% 1.54/1.77 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[1010, 4643])).
% 1.54/1.77 tff(4645,plain,
% 1.54/1.77 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[1640])).
% 1.54/1.77 tff(4646,plain,
% 1.54/1.77 ((~(s(z) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[4645])).
% 1.54/1.77 tff(4647,plain,
% 1.54/1.77 (~(elem!1 = s(s(s(elem!1))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[190, 4646])).
% 1.54/1.77 tff(4648,plain,
% 1.54/1.77 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.54/1.77 inference(monotonicity,[status(thm)],[1640])).
% 1.54/1.77 tff(4649,plain,
% 1.54/1.77 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(elem!1)))), s(z))),
% 1.54/1.77 inference(symmetry,[status(thm)],[4648])).
% 1.54/1.77 tff(4650,plain,
% 1.54/1.77 ((~b(s(s(s(s(elem!1)))), elem!1)) <=> (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[4649])).
% 1.54/1.77 tff(4651,plain,
% 1.54/1.77 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2596, 128, 4193, 2659, 1842])).
% 1.54/1.77 tff(4652,plain,
% 1.54/1.77 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[4651, 4650])).
% 1.54/1.77 tff(4653,plain,
% 1.54/1.77 (r(s(s(s(s(elem!1)))), s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1828, 4652])).
% 1.54/1.77 tff(4654,plain,
% 1.54/1.77 (~r(s(s(elem!1)), s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2176, 4653, 1063, 27])).
% 1.54/1.77 tff(4655,plain,
% 1.54/1.77 (b(s(s(elem!1)), s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[292, 4654])).
% 1.54/1.77 tff(4656,plain,
% 1.54/1.77 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 1.54/1.77 inference(monotonicity,[status(thm)],[1640])).
% 1.54/1.77 tff(4657,plain,
% 1.54/1.77 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(z))),
% 1.54/1.77 inference(symmetry,[status(thm)],[4656])).
% 1.54/1.77 tff(4658,plain,
% 1.54/1.77 ((~b(s(s(elem!1)), elem!1)) <=> (~b(s(s(elem!1)), s(z)))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[4657])).
% 1.54/1.77 tff(4659,assumption,(~b(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.54/1.77 tff(4660,plain,
% 1.54/1.77 (~b(s(s(elem!1)), s(z))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[4659, 4658])).
% 1.54/1.77 tff(4661,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[30, 4660])).
% 1.54/1.77 tff(4662,plain,((~(s(z) = elem!1)) | (~b(s(s(elem!1)), s(z))) | b(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(4663,plain,
% 1.54/1.77 (b(s(s(elem!1)), elem!1)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4662, 4655, 1640])).
% 1.54/1.77 tff(4664,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(4665,plain,
% 1.54/1.77 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(4666,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[4665])).
% 1.54/1.77 tff(4667,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[4666, 4664])).
% 1.54/1.77 tff(4668,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(4669,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[4668, 4667])).
% 1.54/1.77 tff(4670,plain,
% 1.54/1.77 (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4669, 128, 4663, 4193, 2659, 4644])).
% 1.54/1.77 tff(4671,plain,
% 1.54/1.77 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[4605])).
% 1.54/1.77 tff(4672,plain,
% 1.54/1.77 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[4671, 1712])).
% 1.54/1.77 tff(4673,plain,
% 1.54/1.77 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(elem!1) = s(s(s(s(elem!1))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[4672])).
% 1.54/1.77 tff(4674,plain,
% 1.54/1.77 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[239, 4673])).
% 1.54/1.77 tff(4675,assumption,(s(s(elem!1)) = s(s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.54/1.77 tff(4676,plain,
% 1.54/1.77 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[4675])).
% 1.54/1.77 tff(4677,plain,
% 1.54/1.77 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[106, 4676, 3116])).
% 1.54/1.77 tff(4678,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3234, 4677])).
% 1.54/1.77 tff(4679,plain,((~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))) | (s(elem!1) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(4680,plain,
% 1.54/1.77 (~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4679, 4674])).
% 1.54/1.77 tff(4681,plain,
% 1.54/1.77 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | b(s(s(elem!1)), s(s(s(s(s(elem!1)))))) | r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | b(s(s(elem!1)), s(s(s(s(s(elem!1)))))) | r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(4682,plain,
% 1.54/1.77 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | b(s(s(elem!1)), s(s(s(s(s(elem!1)))))) | r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(4683,plain,
% 1.54/1.77 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | b(s(s(elem!1)), s(s(s(s(s(elem!1)))))) | r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[4682, 4681])).
% 1.54/1.78 tff(4684,plain,
% 1.54/1.78 (r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4683, 21, 4680, 4670])).
% 1.54/1.78 tff(4685,plain,
% 1.54/1.78 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 1.54/1.78 inference(commutativity,[status(thm)],[])).
% 1.54/1.78 tff(4686,plain,
% 1.54/1.78 ((s(s(s(elem!1))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[4634, 4637])).
% 1.54/1.78 tff(4687,plain,
% 1.54/1.78 ((s(s(s(elem!1))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[4686, 4685])).
% 1.54/1.78 tff(4688,plain,
% 1.54/1.78 ((s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(s(s(s(elem!1))))))),
% 1.54/1.78 inference(symmetry,[status(thm)],[4687])).
% 1.54/1.78 tff(4689,plain,
% 1.54/1.78 ((~(s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(s(elem!1)))))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[4688])).
% 1.54/1.78 tff(4690,plain,
% 1.54/1.78 (~(s(s(s(elem!1))) = s(s(s(s(s(elem!1))))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[1212, 4689])).
% 1.54/1.78 tff(4691,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(4692,plain,
% 1.54/1.78 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(4693,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[4692])).
% 1.54/1.78 tff(4694,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.54/1.78 inference(transitivity,[status(thm)],[4693, 4691])).
% 1.54/1.78 tff(4695,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(4696,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[4695, 4694])).
% 1.54/1.78 tff(4697,plain,
% 1.54/1.78 ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4696, 128, 4193, 2659])).
% 1.54/1.78 tff(4698,plain,
% 1.54/1.78 (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4697, 4644])).
% 1.54/1.78 tff(4699,plain,
% 1.54/1.78 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))) | r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))) | r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(4700,plain,
% 1.54/1.78 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))) | r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(4701,plain,
% 1.54/1.78 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))) | r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[4700, 4699])).
% 1.54/1.78 tff(4702,plain,
% 1.54/1.78 ((s(s(s(elem!1))) = s(s(s(s(s(elem!1)))))) | r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4701, 21, 4698])).
% 1.54/1.78 tff(4703,plain,
% 1.54/1.78 (r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4702, 4690])).
% 1.54/1.78 tff(4704,plain,
% 1.54/1.78 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3171, 128, 4663, 4193, 2659])).
% 1.54/1.78 tff(4705,plain,
% 1.54/1.78 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[889, 4704, 1679])).
% 1.54/1.78 tff(4706,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(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(4707,plain,
% 1.54/1.78 (((~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(4708,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(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[4707])).
% 1.54/1.78 tff(4709,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(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[4708, 4706])).
% 1.54/1.78 tff(4710,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(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(4711,plain,
% 1.54/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[4710, 4709])).
% 1.54/1.78 tff(4712,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4711, 45, 4705, 4703, 4684])).
% 1.54/1.78 tff(4713,plain,((~b(elem!1, s(s(s(elem!1))))) | (~(s(z) = elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~r(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(4714,plain,
% 1.54/1.78 (~b(elem!1, s(s(s(elem!1))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4713, 1010, 2659, 1664, 27, 1640, 1842])).
% 1.54/1.78 tff(4715,plain,
% 1.54/1.78 (r(elem!1, s(s(s(elem!1))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[2466, 4714, 4647])).
% 1.54/1.78 tff(4716,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(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(4717,plain,
% 1.54/1.78 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(4718,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(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[4717])).
% 1.54/1.78 tff(4719,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(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[4718, 4716])).
% 1.54/1.78 tff(4720,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(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(4721,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(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[4720, 4719])).
% 1.54/1.78 tff(4722,plain,
% 1.54/1.78 (~r(elem!1, s(s(elem!1)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4721, 45, 4715, 324])).
% 1.54/1.78 tff(4723,plain,
% 1.54/1.78 (b(elem!1, s(s(elem!1)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[2371, 4722, 2344])).
% 1.54/1.78 tff(4724,plain,
% 1.54/1.78 (~r(s(s(elem!1)), elem!1)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4203, 45, 4715, 324])).
% 1.54/1.78 tff(4725,plain,
% 1.54/1.78 (b(s(s(elem!1)), elem!1)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1934, 4724, 1086])).
% 1.54/1.78 tff(4726,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(4727,plain,
% 1.54/1.78 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(4728,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[4727])).
% 1.54/1.78 tff(4729,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.54/1.78 inference(transitivity,[status(thm)],[4728, 4726])).
% 1.54/1.78 tff(4730,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(4731,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[4730, 4729])).
% 1.54/1.78 tff(4732,plain,
% 1.54/1.78 ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4731, 128, 4725, 4723, 2659])).
% 1.54/1.78 tff(4733,plain,
% 1.54/1.78 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4732, 4644])).
% 1.54/1.78 tff(4734,plain,
% 1.54/1.78 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) | r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) | r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(4735,plain,
% 1.54/1.78 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) | r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(4736,plain,
% 1.54/1.78 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) | r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[4735, 4734])).
% 1.54/1.78 tff(4737,plain,
% 1.54/1.78 ((s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4736, 21, 4733])).
% 1.54/1.78 tff(4738,plain,
% 1.54/1.78 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4737, 4641])).
% 1.54/1.78 tff(4739,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(4740,plain,
% 1.54/1.78 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(4741,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[4740])).
% 1.54/1.78 tff(4742,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[4741, 4739])).
% 1.54/1.78 tff(4743,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(4744,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[4743, 4742])).
% 1.54/1.78 tff(4745,plain,
% 1.54/1.78 ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4744, 128, 4725, 4723])).
% 1.54/1.78 tff(4746,plain,
% 1.54/1.78 (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4745, 4644])).
% 1.54/1.78 tff(4747,plain,
% 1.54/1.78 (r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4683, 21, 4680, 4746])).
% 1.54/1.78 tff(4748,plain,
% 1.54/1.78 ((s(s(s(s(s(elem!1))))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 1.54/1.78 inference(commutativity,[status(thm)],[])).
% 1.54/1.78 tff(4749,plain,
% 1.54/1.78 ((s(s(elem!1)) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 1.54/1.78 inference(symmetry,[status(thm)],[4748])).
% 1.54/1.78 tff(4750,plain,
% 1.54/1.78 ((~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(elem!1))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[4749])).
% 1.54/1.78 tff(4751,plain,
% 1.54/1.78 (~(s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[4680, 4750])).
% 1.54/1.78 tff(4752,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(4753,plain,
% 1.54/1.78 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(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(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(4754,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[4753])).
% 1.54/1.78 tff(4755,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[4754, 4752])).
% 1.54/1.78 tff(4756,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(4757,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[4756, 4755])).
% 1.54/1.79 tff(4758,plain,
% 1.54/1.79 ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4757, 128, 4725, 4723])).
% 1.54/1.79 tff(4759,plain,
% 1.54/1.79 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4758, 4644])).
% 1.54/1.79 tff(4760,plain,
% 1.54/1.79 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(s(elem!1))) | b(s(s(s(s(s(elem!1))))), s(s(elem!1))) | r(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | b(s(s(s(s(s(elem!1))))), s(s(elem!1))) | r(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(4761,plain,
% 1.54/1.79 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(s(elem!1))) | b(s(s(s(s(s(elem!1))))), s(s(elem!1))) | r(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(4762,plain,
% 1.54/1.79 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | b(s(s(s(s(s(elem!1))))), s(s(elem!1))) | r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[4761, 4760])).
% 1.54/1.79 tff(4763,plain,
% 1.54/1.79 ((s(s(s(s(s(elem!1))))) = s(s(elem!1))) | r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4762, 21, 4759])).
% 1.54/1.79 tff(4764,plain,
% 1.54/1.79 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4763, 4751])).
% 1.54/1.79 tff(4765,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(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(4766,plain,
% 1.54/1.79 (((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(4767,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(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[4766])).
% 1.54/1.79 tff(4768,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(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[4767, 4765])).
% 1.54/1.79 tff(4769,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(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(4770,plain,
% 1.54/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[4769, 4768])).
% 1.54/1.79 tff(4771,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4770, 45, 324, 4764, 4747, 4738])).
% 1.54/1.79 tff(4772,plain,((~b(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~(s(z) = elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (s(s(elem!1)) = elem!1) | (~r(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(4773,plain,
% 1.54/1.79 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4772, 1640, 324, 4631, 1086, 4629, 1842])).
% 1.54/1.79 tff(4774,plain,
% 1.54/1.79 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1055, 4773, 4626])).
% 1.54/1.79 tff(4775,plain,
% 1.54/1.79 (~r(s(s(z)), elem!1)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1451, 4774, 1416])).
% 1.54/1.79 tff(4776,plain,
% 1.54/1.79 (b(s(s(z)), elem!1)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[370, 4775, 4621])).
% 1.54/1.79 tff(4777,plain,
% 1.54/1.79 (b(s(elem!1), elem!1)),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[4776, 4606])).
% 1.54/1.79 tff(4778,plain,
% 1.54/1.79 (b(s(z), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[1640])).
% 1.54/1.79 tff(4779,plain,
% 1.54/1.79 (b(elem!1, s(s(s(elem!1))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[4273, 4778])).
% 1.54/1.79 tff(4780,plain,
% 1.54/1.79 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[2596, 128, 4779, 2659, 1842])).
% 1.54/1.79 tff(4781,plain,
% 1.54/1.79 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[4780, 4650])).
% 1.54/1.79 tff(4782,plain,
% 1.54/1.79 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[2176, 325, 1063, 27])).
% 1.54/1.79 tff(4783,plain,
% 1.54/1.79 (b(s(s(s(s(elem!1)))), s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1828, 4782])).
% 1.54/1.79 tff(4784,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4783, 4781])).
% 1.54/1.79 tff(4785,plain,((~r(s(s(elem!1)), s(z))) | (~(s(z) = elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(4786,plain,
% 1.54/1.79 (~r(s(s(elem!1)), s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4785, 1640, 4631, 1842, 1664, 4629, 324])).
% 1.54/1.79 tff(4787,plain,
% 1.54/1.79 (b(s(s(elem!1)), s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[292, 4786])).
% 1.54/1.79 tff(4788,plain,
% 1.54/1.79 (b(s(s(elem!1)), elem!1)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4662, 4787, 1640])).
% 1.54/1.79 tff(4789,assumption,(~(s(s(s(elem!1))) = s(elem!1))), introduced(assumption)).
% 1.54/1.79 tff(4790,plain,
% 1.54/1.79 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[4789, 4597])).
% 1.54/1.79 tff(4791,assumption,(b(s(elem!1), elem!1)), introduced(assumption)).
% 1.54/1.79 tff(4792,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(4793,plain,
% 1.54/1.79 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(4794,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[4793])).
% 1.54/1.79 tff(4795,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[4794, 4792])).
% 1.54/1.79 tff(4796,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(4797,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[4796, 4795])).
% 1.54/1.79 tff(4798,plain,
% 1.54/1.79 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4797, 128, 4193, 2659, 4791])).
% 1.54/1.79 tff(4799,plain,
% 1.54/1.79 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1)))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(4800,plain,
% 1.54/1.79 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1)))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(4801,plain,
% 1.54/1.79 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[4800, 4799])).
% 1.54/1.79 tff(4802,plain,
% 1.54/1.79 ((s(elem!1) = s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4801, 21, 4798])).
% 1.54/1.79 tff(4803,plain,
% 1.54/1.79 (r(s(elem!1), s(s(s(elem!1))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4802, 4790])).
% 1.54/1.79 tff(4804,plain,
% 1.54/1.79 (s(elem!1) = s(s(z))),
% 1.54/1.79 inference(symmetry,[status(thm)],[4605])).
% 1.54/1.79 tff(4805,plain,
% 1.54/1.79 ((s(elem!1) = s(s(elem!1))) <=> (s(s(z)) = s(s(elem!1)))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[4804])).
% 1.54/1.79 tff(4806,plain,
% 1.54/1.79 ((s(elem!1) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(z)))),
% 1.54/1.79 inference(transitivity,[status(thm)],[4805, 31])).
% 1.54/1.79 tff(4807,plain,
% 1.54/1.79 ((s(s(elem!1)) = s(s(z))) <=> (s(elem!1) = s(s(elem!1)))),
% 1.54/1.79 inference(symmetry,[status(thm)],[4806])).
% 1.54/1.79 tff(4808,plain,
% 1.54/1.79 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[4807])).
% 1.54/1.79 tff(4809,plain,
% 1.54/1.79 (~(s(elem!1) = s(s(elem!1)))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[1, 4808])).
% 1.54/1.79 tff(4810,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(4811,plain,
% 1.54/1.79 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(4812,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[4811])).
% 1.54/1.79 tff(4813,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[4812, 4810])).
% 1.54/1.79 tff(4814,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(4815,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[4814, 4813])).
% 1.54/1.79 tff(4816,plain,
% 1.54/1.79 (~b(s(elem!1), s(s(elem!1)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4815, 128, 1681, 4193, 2659, 4791])).
% 1.54/1.79 tff(4817,plain,
% 1.54/1.79 (((~![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))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(4818,plain,
% 1.54/1.79 ((~![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))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(4819,plain,
% 1.54/1.79 ((~![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)))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[4818, 4817])).
% 1.54/1.79 tff(4820,plain,
% 1.54/1.79 ((s(elem!1) = s(s(elem!1))) | r(s(elem!1), s(s(elem!1)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4819, 21, 4816])).
% 1.54/1.79 tff(4821,plain,
% 1.54/1.79 (r(s(elem!1), s(s(elem!1)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4820, 4809])).
% 1.54/1.79 tff(4822,plain,
% 1.54/1.79 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(elem!1)) = s(s(z)))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[4804])).
% 1.54/1.79 tff(4823,plain,
% 1.54/1.79 ((s(s(elem!1)) = s(s(z))) <=> (s(s(elem!1)) = s(elem!1))),
% 1.54/1.79 inference(symmetry,[status(thm)],[4822])).
% 1.54/1.79 tff(4824,plain,
% 1.54/1.79 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[4823])).
% 1.54/1.79 tff(4825,plain,
% 1.54/1.79 (~(s(s(elem!1)) = s(elem!1))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[1, 4824])).
% 1.54/1.79 tff(4826,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(4827,plain,
% 1.54/1.79 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(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(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(4828,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1)))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[4827])).
% 1.54/1.79 tff(4829,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[4828, 4826])).
% 1.54/1.79 tff(4830,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(4831,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[4830, 4829])).
% 1.54/1.79 tff(4832,plain,
% 1.54/1.79 (~b(s(s(elem!1)), s(elem!1))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4831, 128, 1681, 4193, 2659, 4791])).
% 1.54/1.79 tff(4833,plain,
% 1.54/1.79 (((~![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)))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(4834,plain,
% 1.54/1.79 ((~![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)))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(4835,plain,
% 1.54/1.79 ((~![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))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[4834, 4833])).
% 1.54/1.79 tff(4836,plain,
% 1.54/1.79 ((s(s(elem!1)) = s(elem!1)) | r(s(s(elem!1)), s(elem!1))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4835, 21, 4832])).
% 1.54/1.79 tff(4837,plain,
% 1.54/1.79 (r(s(s(elem!1)), s(elem!1))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4836, 4825])).
% 1.54/1.79 tff(4838,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(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(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(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(4839,plain,
% 1.54/1.79 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(4840,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(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(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(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[4839])).
% 1.54/1.79 tff(4841,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(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(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(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[4840, 4838])).
% 1.54/1.79 tff(4842,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(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(4843,plain,
% 1.54/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[4842, 4841])).
% 1.54/1.79 tff(4844,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4843, 45, 324, 4837, 4821, 4803])).
% 1.54/1.79 tff(4845,plain,((~b(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1)) | (s(s(elem!1)) = s(s(z))) | (~(s(z) = elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(4846,plain,
% 1.54/1.79 (~b(elem!1, s(s(s(elem!1))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4845, 1640, 4603, 1, 324, 4631, 4777, 4788])).
% 1.54/1.79 tff(4847,plain,
% 1.54/1.79 (r(elem!1, s(s(s(elem!1))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[2466, 4846, 4647])).
% 1.54/1.79 tff(4848,plain,
% 1.54/1.79 (~r(elem!1, s(s(elem!1)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4721, 45, 4847, 324])).
% 1.54/1.79 tff(4849,plain,
% 1.54/1.79 (b(elem!1, s(s(elem!1)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[2371, 4848, 2344])).
% 1.54/1.79 tff(4850,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(4851,plain,
% 1.54/1.79 (((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(4852,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[4851])).
% 1.54/1.79 tff(4853,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[4852, 4850])).
% 1.54/1.79 tff(4854,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(4855,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[4854, 4853])).
% 1.54/1.79 tff(4856,plain,
% 1.54/1.79 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4855, 128, 4788, 4849, 4631, 4777])).
% 1.54/1.80 tff(4857,plain,
% 1.54/1.80 ((s(elem!1) = s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1))))),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[4801, 21, 4856])).
% 1.54/1.80 tff(4858,plain,
% 1.54/1.80 (r(s(elem!1), s(s(s(elem!1))))),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[4857, 4604])).
% 1.54/1.80 tff(4859,plain,
% 1.54/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.54/1.80 inference(rewrite,[status(thm)],[])).
% 1.54/1.80 tff(4860,plain,
% 1.54/1.80 (((~b(s(s(elem!1)), elem!1)) | (~b(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(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.54/1.80 inference(rewrite,[status(thm)],[])).
% 1.54/1.80 tff(4861,plain,
% 1.54/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1))))))),
% 1.54/1.80 inference(monotonicity,[status(thm)],[4860])).
% 1.54/1.80 tff(4862,plain,
% 1.54/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.54/1.80 inference(transitivity,[status(thm)],[4861, 4859])).
% 1.54/1.80 tff(4863,plain,
% 1.54/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.54/1.80 inference(quant_inst,[status(thm)],[])).
% 1.54/1.80 tff(4864,plain,
% 1.54/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1))))),
% 1.54/1.80 inference(modus_ponens,[status(thm)],[4863, 4862])).
% 1.54/1.80 tff(4865,plain,
% 1.54/1.80 (~b(s(elem!1), s(s(elem!1)))),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[4864, 128, 4788, 4849, 4777])).
% 1.54/1.80 tff(4866,plain,
% 1.54/1.80 ((s(elem!1) = s(s(elem!1))) | r(s(elem!1), s(s(elem!1)))),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[4819, 21, 4865])).
% 1.54/1.80 tff(4867,plain,
% 1.54/1.80 (r(s(elem!1), s(s(elem!1)))),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[4866, 4809])).
% 1.54/1.80 tff(4868,plain,
% 1.54/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(4869,plain,
% 1.64/1.80 (((~b(s(s(elem!1)), 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(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(4870,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[4869])).
% 1.64/1.80 tff(4871,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[4870, 4868])).
% 1.64/1.80 tff(4872,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(4873,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[4872, 4871])).
% 1.64/1.80 tff(4874,plain,
% 1.64/1.80 (~b(s(s(elem!1)), s(elem!1))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4873, 128, 4788, 4849, 4777])).
% 1.64/1.80 tff(4875,plain,
% 1.64/1.80 ((s(s(elem!1)) = s(elem!1)) | r(s(s(elem!1)), s(elem!1))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4835, 21, 4874])).
% 1.64/1.80 tff(4876,plain,
% 1.64/1.80 (r(s(s(elem!1)), s(elem!1))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4875, 4825])).
% 1.64/1.80 tff(4877,plain,
% 1.64/1.80 ($false),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4843, 45, 324, 4876, 4867, 4858])).
% 1.64/1.80 tff(4878,plain,((~(s(z) = elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, elem!1)) | (s(s(elem!1)) = elem!1) | (~b(s(s(s(elem!1))), s(z))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.80 tff(4879,plain,
% 1.64/1.80 (~(s(z) = elem!1)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4878, 4593, 4261, 1842, 324, 1086, 2718, 455])).
% 1.64/1.80 tff(4880,plain,
% 1.64/1.80 (b(s(z), elem!1)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[665, 4879, 4594])).
% 1.64/1.80 tff(4881,plain,
% 1.64/1.80 (~r(z, s(s(elem!1)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[2380, 4880, 164, 1086, 455])).
% 1.64/1.80 tff(4882,plain,
% 1.64/1.80 (b(z, s(s(elem!1)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[160, 4881])).
% 1.64/1.80 tff(4883,assumption,(~b(elem!1, s(z))), introduced(assumption)).
% 1.64/1.80 tff(4884,plain,
% 1.64/1.80 (s(z) = elem!1),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[1633, 253])).
% 1.64/1.80 tff(4885,plain,
% 1.64/1.80 ($false),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1610, 4884])).
% 1.64/1.80 tff(4886,plain,((~(elem!1 = s(z))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.80 tff(4887,plain,
% 1.64/1.80 (~(elem!1 = s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4886, 4879])).
% 1.64/1.80 tff(4888,plain,
% 1.64/1.80 (r(elem!1, s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[305, 4887, 4883])).
% 1.64/1.80 tff(4889,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, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(4890,plain,
% 1.64/1.80 (((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(4891,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(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(z, s(z))) | (~r(elem!1, s(z)))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[4890])).
% 1.64/1.80 tff(4892,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(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(z, s(z))) | (~r(elem!1, s(z))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[4891, 4889])).
% 1.64/1.80 tff(4893,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(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, elem!1)))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(4894,plain,
% 1.64/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z)))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[4893, 4892])).
% 1.64/1.80 tff(4895,plain,
% 1.64/1.80 ($false),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4894, 45, 1416, 313, 27])).
% 1.64/1.80 tff(4896,plain,((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.80 tff(4897,plain,
% 1.64/1.80 (~r(z, s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4896, 4888, 4593])).
% 1.64/1.80 tff(4898,plain,
% 1.64/1.80 (b(z, s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[415, 4897])).
% 1.64/1.80 tff(4899,plain,
% 1.64/1.80 (b(elem!1, z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[2915, 4898, 164, 455])).
% 1.64/1.80 tff(4900,plain,
% 1.64/1.80 ((~(elem!1 = s(s(elem!1)))) <=> (~(s(s(elem!1)) = elem!1))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[372])).
% 1.64/1.80 tff(4901,plain,
% 1.64/1.80 (~(elem!1 = s(s(elem!1)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[457, 453, 455])).
% 1.64/1.80 tff(4902,plain,
% 1.64/1.80 (~(s(s(elem!1)) = elem!1)),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[4901, 4900])).
% 1.64/1.80 tff(4903,plain,
% 1.64/1.80 ((~(elem!1 = s(z))) <=> (~(s(z) = elem!1))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[253])).
% 1.64/1.80 tff(4904,plain,
% 1.64/1.80 (~(s(z) = elem!1)),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[1639, 4903])).
% 1.64/1.80 tff(4905,plain,
% 1.64/1.80 (~b(s(z), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3535, 550, 30, 453])).
% 1.64/1.80 tff(4906,plain,
% 1.64/1.80 (r(s(z), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[170, 4905])).
% 1.64/1.80 tff(4907,plain,
% 1.64/1.80 (~r(s(z), elem!1)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1544, 4906, 1416])).
% 1.64/1.80 tff(4908,plain,
% 1.64/1.80 (b(s(z), elem!1)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[665, 4907, 4904])).
% 1.64/1.80 tff(4909,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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, z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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, z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(4910,plain,
% 1.64/1.80 (((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(4911,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (~b(s(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(X0, 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, z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[4910])).
% 1.64/1.80 tff(4912,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (~b(s(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(X0, 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, z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[4911, 4909])).
% 1.64/1.80 tff(4913,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(4914,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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, z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[4913, 4912])).
% 1.64/1.80 tff(4915,plain,
% 1.64/1.80 (~b(s(s(elem!1)), elem!1)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4914, 128, 577, 30, 550, 4908])).
% 1.64/1.80 tff(4916,plain,
% 1.64/1.80 (r(s(s(elem!1)), elem!1)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1934, 4915, 4902])).
% 1.64/1.80 tff(4917,plain,
% 1.64/1.80 (~r(s(s(elem!1)), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[2004, 45, 1416, 4916])).
% 1.64/1.80 tff(4918,plain,
% 1.64/1.80 (b(s(s(elem!1)), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[2018, 21, 154, 4917])).
% 1.64/1.80 tff(4919,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(4920,plain,
% 1.64/1.80 (((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(4921,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), elem!1)) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[4920])).
% 1.64/1.80 tff(4922,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), elem!1)) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[4921, 4919])).
% 1.64/1.80 tff(4923,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(4924,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[4923, 4922])).
% 1.64/1.80 tff(4925,plain,
% 1.64/1.80 ($false),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4924, 128, 577, 30, 550, 4908, 4918])).
% 1.64/1.80 tff(4926,plain,((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(z))) | (~r(z, elem!1)) | (~b(z, s(s(elem!1)))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.80 tff(4927,plain,
% 1.64/1.80 (~b(s(s(elem!1)), s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4926, 4899, 4593, 4898, 4882, 455])).
% 1.64/1.80 tff(4928,plain,
% 1.64/1.80 (r(s(s(elem!1)), s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[292, 4927])).
% 1.64/1.80 tff(4929,plain,
% 1.64/1.80 (~r(s(z), s(s(s(elem!1))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[333, 4928, 324])).
% 1.64/1.80 tff(4930,plain,
% 1.64/1.80 (b(s(z), s(s(s(elem!1))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[339, 4929])).
% 1.64/1.80 tff(4931,plain,
% 1.64/1.80 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4479, 128, 4930, 1842, 2718])).
% 1.64/1.80 tff(4932,plain,
% 1.64/1.80 (r(s(s(s(s(elem!1)))), s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1828, 4931])).
% 1.64/1.80 tff(4933,plain,
% 1.64/1.80 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[2141, 4932, 4928])).
% 1.64/1.80 tff(4934,plain,
% 1.64/1.80 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1897, 4933, 1664])).
% 1.64/1.80 tff(4935,assumption,(~(elem!1 = s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.64/1.80 tff(4936,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(elem!1, s(z))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(4937,plain,
% 1.64/1.80 (((~r(s(s(s(s(elem!1)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(elem!1, s(s(s(s(elem!1))))))) <=> ((~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(4938,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(s(s(s(s(elem!1)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z)))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[4937])).
% 1.64/1.80 tff(4939,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(s(s(s(s(elem!1)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[4938, 4936])).
% 1.64/1.80 tff(4940,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(s(s(s(s(elem!1)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(4941,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(elem!1, s(z))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[4940, 4939])).
% 1.64/1.80 tff(4942,plain,
% 1.64/1.80 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4941, 45, 313, 1737])).
% 1.64/1.80 tff(4943,plain,
% 1.64/1.80 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1766, 4942, 4935])).
% 1.64/1.80 tff(4944,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(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(4945,plain,
% 1.64/1.80 (((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(4946,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(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1))))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[4945])).
% 1.64/1.80 tff(4947,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(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[4946, 4944])).
% 1.64/1.80 tff(4948,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(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)))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(4949,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(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[4948, 4947])).
% 1.64/1.80 tff(4950,plain,
% 1.64/1.80 (~r(elem!1, s(s(elem!1)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4949, 45, 325, 313])).
% 1.64/1.80 tff(4951,plain,
% 1.64/1.80 (b(elem!1, s(s(elem!1)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[2371, 4950, 2344])).
% 1.64/1.80 tff(4952,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(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(4953,plain,
% 1.64/1.80 (((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(4954,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(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z)))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[4953])).
% 1.64/1.81 tff(4955,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(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[4954, 4952])).
% 1.64/1.81 tff(4956,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(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(4957,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(z))) | (~r(elem!1, s(z)))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[4956, 4955])).
% 1.64/1.81 tff(4958,plain,
% 1.64/1.81 (~r(s(s(elem!1)), elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4957, 45, 325, 313])).
% 1.64/1.81 tff(4959,plain,
% 1.64/1.81 (b(s(s(elem!1)), elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1934, 4958, 1086])).
% 1.64/1.81 tff(4960,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(4961,plain,
% 1.64/1.81 (((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1))))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(4962,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[4961])).
% 1.64/1.81 tff(4963,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[4962, 4960])).
% 1.64/1.81 tff(4964,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(4965,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[4964, 4963])).
% 1.64/1.81 tff(4966,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4965, 128, 4959, 4951, 4943, 2084])).
% 1.64/1.81 tff(4967,plain,((~r(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (elem!1 = s(s(s(s(elem!1))))) | (s(s(elem!1)) = elem!1) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(4968,plain,
% 1.64/1.81 (elem!1 = s(s(s(s(elem!1))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4967, 4934, 4888, 1086, 4928, 4932])).
% 1.64/1.81 tff(4969,plain,
% 1.64/1.81 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[4968])).
% 1.64/1.81 tff(4970,plain,
% 1.64/1.81 (b(s(s(elem!1)), s(s(s(s(elem!1))))) <=> b(s(s(elem!1)), elem!1)),
% 1.64/1.81 inference(symmetry,[status(thm)],[4969])).
% 1.64/1.81 tff(4971,plain,
% 1.64/1.81 ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) <=> (~b(s(s(elem!1)), elem!1))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[4970])).
% 1.64/1.81 tff(4972,plain,
% 1.64/1.81 (~r(s(s(s(s(elem!1)))), z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1745, 4932, 171])).
% 1.64/1.81 tff(4973,plain,
% 1.64/1.81 (b(s(s(s(s(elem!1)))), z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[2081, 4972])).
% 1.64/1.81 tff(4974,plain,
% 1.64/1.81 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4387, 4934, 4882, 4973])).
% 1.64/1.81 tff(4975,plain,
% 1.64/1.81 (~b(s(s(elem!1)), elem!1)),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[4974, 4971])).
% 1.64/1.81 tff(4976,plain,
% 1.64/1.81 (~r(s(s(elem!1)), elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4957, 45, 4928, 4888])).
% 1.64/1.81 tff(4977,plain,
% 1.64/1.81 (b(s(s(elem!1)), elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1934, 4976, 1086])).
% 1.64/1.81 tff(4978,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4977, 4975])).
% 1.64/1.81 tff(4979,plain,(b(z, elem!1) | (s(s(elem!1)) = elem!1) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | b(s(z), z) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(4980,plain,
% 1.64/1.81 (b(elem!1, s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4979, 455, 1842, 2718, 324, 164, 1086])).
% 1.64/1.81 tff(4981,plain,
% 1.64/1.81 (~b(s(s(elem!1)), elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[2736, 4980, 4491, 876])).
% 1.64/1.81 tff(4982,plain,
% 1.64/1.81 (r(s(s(elem!1)), elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1934, 4981, 1086])).
% 1.64/1.81 tff(4983,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(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(4984,plain,
% 1.64/1.81 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(4985,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(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[4984])).
% 1.64/1.81 tff(4986,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(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.64/1.81 inference(transitivity,[status(thm)],[4985, 4983])).
% 1.64/1.81 tff(4987,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(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(4988,plain,
% 1.64/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[4987, 4986])).
% 1.64/1.81 tff(4989,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4988, 45, 2349, 324, 2450])).
% 1.64/1.81 tff(4990,plain,((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(4991,plain,
% 1.64/1.81 (~r(s(s(s(elem!1))), elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4990, 4982, 324])).
% 1.64/1.81 tff(4992,plain,
% 1.64/1.81 (b(s(z), elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[665, 4594, 1610])).
% 1.64/1.81 tff(4993,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(4994,plain,
% 1.64/1.81 (((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(4995,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[4994])).
% 1.64/1.81 tff(4996,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[4995, 4993])).
% 1.64/1.81 tff(4997,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(4998,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z)))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[4997, 4996])).
% 1.64/1.81 tff(4999,plain,
% 1.64/1.81 (~b(s(s(s(elem!1))), elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4998, 128, 4980, 4992, 2718])).
% 1.64/1.81 tff(5000,plain,
% 1.64/1.81 (s(s(s(elem!1))) = elem!1),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[742, 4999, 4991])).
% 1.64/1.81 tff(5001,plain,
% 1.64/1.81 ((s(s(s(elem!1))) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[5000])).
% 1.64/1.81 tff(5002,plain,
% 1.64/1.81 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 1.64/1.81 inference(transitivity,[status(thm)],[5001, 225])).
% 1.64/1.81 tff(5003,plain,
% 1.64/1.81 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[5002])).
% 1.64/1.81 tff(5004,plain,
% 1.64/1.81 (~(s(s(z)) = elem!1)),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[283, 5003])).
% 1.64/1.81 tff(5005,plain,
% 1.64/1.81 (s(s(s(s(elem!1)))) = s(elem!1)),
% 1.64/1.81 inference(monotonicity,[status(thm)],[5000])).
% 1.64/1.81 tff(5006,plain,
% 1.64/1.81 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(elem!1), s(z))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[5005])).
% 1.64/1.81 tff(5007,plain,
% 1.64/1.81 (r(s(elem!1), s(z))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[1737, 5006])).
% 1.64/1.81 tff(5008,plain,
% 1.64/1.81 (~(elem!1 = s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4886, 1610])).
% 1.64/1.81 tff(5009,assumption,(s(elem!1) = s(s(z))), introduced(assumption)).
% 1.64/1.81 tff(5010,plain,
% 1.64/1.81 (s(s(z)) = s(elem!1)),
% 1.64/1.81 inference(symmetry,[status(thm)],[5009])).
% 1.64/1.81 tff(5011,plain,
% 1.64/1.81 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[5010])).
% 1.64/1.81 tff(5012,plain,
% 1.64/1.81 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 1.64/1.81 inference(symmetry,[status(thm)],[5011])).
% 1.64/1.81 tff(5013,plain,
% 1.64/1.81 (elem!1 = s(z)),
% 1.64/1.81 inference(transitivity,[status(thm)],[1079, 5012, 69])).
% 1.64/1.81 tff(5014,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1642, 5013])).
% 1.64/1.81 tff(5015,plain,((~(s(elem!1) = s(s(z)))) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(5016,plain,
% 1.64/1.81 (~(s(elem!1) = s(s(z)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[5015, 5008])).
% 1.64/1.81 tff(5017,plain,
% 1.64/1.81 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(elem!1), elem!1)),
% 1.64/1.81 inference(monotonicity,[status(thm)],[5005])).
% 1.64/1.81 tff(5018,plain,
% 1.64/1.81 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.64/1.81 inference(monotonicity,[status(thm)],[5000])).
% 1.64/1.81 tff(5019,plain,
% 1.64/1.81 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[1842, 5018])).
% 1.64/1.81 tff(5020,plain,
% 1.64/1.81 (b(s(elem!1), elem!1)),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[5019, 5017])).
% 1.64/1.81 tff(5021,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z)), elem!1)) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z)), elem!1)) | (~b(s(elem!1), s(s(z)))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(5022,plain,
% 1.64/1.81 (((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(5023,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z)), elem!1)) | (~b(s(elem!1), s(s(z))))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[5022])).
% 1.64/1.81 tff(5024,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z)), elem!1)) | (~b(s(elem!1), s(s(z)))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[5023, 5021])).
% 1.64/1.81 tff(5025,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(5026,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z)), elem!1)) | (~b(s(elem!1), s(s(z))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[5025, 5024])).
% 1.64/1.81 tff(5027,plain,
% 1.64/1.81 (~b(s(elem!1), s(s(z)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[5026, 128, 297, 922, 591, 4791])).
% 1.64/1.81 tff(5028,plain,
% 1.64/1.81 (r(s(elem!1), s(s(z)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[473, 21, 759, 5027])).
% 1.64/1.81 tff(5029,assumption,(r(s(elem!1), s(z))), introduced(assumption)).
% 1.64/1.81 tff(5030,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(z)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(z)))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(5031,plain,
% 1.64/1.81 (((~r(s(s(z)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(z)))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(5032,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(z)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(z))))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[5031])).
% 1.64/1.81 tff(5033,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(z)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(z)))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[5032, 5030])).
% 1.64/1.81 tff(5034,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(z)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(s(z)))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(5035,plain,
% 1.64/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(z))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[5034, 5033])).
% 1.64/1.81 tff(5036,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[5035, 45, 2811, 5029, 5028])).
% 1.64/1.81 tff(5037,plain,((~b(s(s(z)), elem!1)) | (~r(s(elem!1), s(z))) | (s(elem!1) = s(s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(5038,plain,
% 1.64/1.81 (~b(s(s(z)), elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[5037, 5020, 5016, 4980, 4992, 5007])).
% 1.64/1.81 tff(5039,plain,
% 1.64/1.81 (r(s(s(z)), elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[370, 5038, 5004])).
% 1.64/1.81 tff(5040,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(z)), elem!1)) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(5041,plain,
% 1.64/1.81 (((~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), s(s(z))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(5042,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(z)), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), s(s(z))))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[5041])).
% 1.64/1.81 tff(5043,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(z)), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[5042, 5040])).
% 1.64/1.81 tff(5044,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(z)), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(5045,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(z)), elem!1)) | (~r(s(s(elem!1)), s(s(z))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[5044, 5043])).
% 1.64/1.81 tff(5046,plain,
% 1.64/1.81 (~r(s(s(elem!1)), s(s(z)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[5045, 45, 4982, 5039])).
% 1.64/1.81 tff(5047,plain,
% 1.64/1.81 (b(s(s(elem!1)), s(s(z)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4339, 21, 4261, 5046])).
% 1.64/1.81 tff(5048,plain,
% 1.64/1.81 (~r(s(s(z)), z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1433, 45, 4593, 5039])).
% 1.64/1.81 tff(5049,plain,
% 1.64/1.81 (b(s(s(z)), z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[25, 5048])).
% 1.64/1.81 tff(5050,plain,
% 1.64/1.81 (~r(z, s(s(z)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1441, 45, 4593, 5039])).
% 1.64/1.81 tff(5051,plain,
% 1.64/1.81 (b(z, s(s(z)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[516, 5050])).
% 1.64/1.81 tff(5052,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(5053,plain,
% 1.64/1.81 (((~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z))))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(5054,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z))))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[5053])).
% 1.64/1.81 tff(5055,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[5054, 5052])).
% 1.64/1.81 tff(5056,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(5057,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[5056, 5055])).
% 1.64/1.81 tff(5058,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[5057, 128, 2006, 5051, 5049, 5047])).
% 1.64/1.81 tff(5059,plain,(b(z, elem!1) | (~b(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(elem!1)) = elem!1) | (s(z) = elem!1) | (~b(s(z), s(s(elem!1)))) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(5060,plain,
% 1.64/1.81 (b(z, elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[5059, 1610, 4530, 1842, 2718, 324, 1086, 4574, 4550, 164])).
% 1.64/1.81 tff(5061,plain,
% 1.64/1.81 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3651, 549, 2718, 1646, 2650, 30, 324])).
% 1.64/1.81 tff(5062,plain,
% 1.64/1.81 (r(s(s(s(s(elem!1)))), s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1828, 5061])).
% 1.64/1.81 tff(5063,plain,
% 1.64/1.81 (~r(s(s(s(s(elem!1)))), z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1745, 5062, 272])).
% 1.64/1.81 tff(5064,plain,
% 1.64/1.81 (b(s(s(s(s(elem!1)))), z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[2081, 5063])).
% 1.64/1.81 tff(5065,assumption,(~(elem!1 = z)), introduced(assumption)).
% 1.64/1.81 tff(5066,plain,
% 1.64/1.81 (~b(z, s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4526, 30, 2718, 324, 272, 4492])).
% 1.64/1.81 tff(5067,plain,
% 1.64/1.81 (r(z, s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[415, 5066])).
% 1.64/1.81 tff(5068,plain,
% 1.64/1.81 (r(elem!1, s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[305, 4883, 5008])).
% 1.64/1.81 tff(5069,plain,
% 1.64/1.81 (~r(elem!1, z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[569, 45, 5068, 5067])).
% 1.64/1.81 tff(5070,plain,
% 1.64/1.81 (b(elem!1, z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[574, 5069, 5065])).
% 1.64/1.81 tff(5071,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(5072,plain,
% 1.64/1.81 (((~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(5073,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[5072])).
% 1.64/1.82 tff(5074,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.64/1.82 inference(transitivity,[status(thm)],[5073, 5071])).
% 1.64/1.82 tff(5075,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(5076,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[5075, 5074])).
% 1.64/1.82 tff(5077,plain,
% 1.64/1.82 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[5076, 128, 498, 5070, 5064])).
% 1.64/1.82 tff(5078,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(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(5079,plain,
% 1.64/1.82 (((~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), elem!1))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(5080,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(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(z)))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[5079])).
% 1.64/1.82 tff(5081,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(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[5080, 5078])).
% 1.64/1.82 tff(5082,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(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(5083,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(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[5082, 5081])).
% 1.64/1.82 tff(5084,plain,
% 1.64/1.82 ((~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[5083, 45])).
% 1.64/1.82 tff(5085,plain,
% 1.64/1.82 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[5084, 5068, 5062])).
% 1.64/1.82 tff(5086,plain,
% 1.64/1.82 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(5087,plain,
% 1.64/1.82 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(5088,plain,
% 1.64/1.82 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1)),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[5087, 5086])).
% 1.64/1.82 tff(5089,plain,
% 1.64/1.82 ((s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[5088, 21, 5085])).
% 1.64/1.82 tff(5090,plain,
% 1.64/1.82 (s(s(s(s(elem!1)))) = elem!1),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[5089, 5077])).
% 1.64/1.82 tff(5091,plain,
% 1.64/1.82 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[5090])).
% 1.64/1.82 tff(5092,plain,
% 1.64/1.82 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 1.64/1.82 inference(transitivity,[status(thm)],[5091, 225])).
% 1.64/1.82 tff(5093,plain,
% 1.64/1.82 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[5092])).
% 1.64/1.82 tff(5094,plain,
% 1.64/1.82 (~(s(s(z)) = elem!1)),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[239, 5093])).
% 1.64/1.82 tff(5095,plain,
% 1.64/1.82 (b(s(s(s(elem!1))), s(z)) <=> b(elem!1, s(z))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[710])).
% 1.64/1.82 tff(5096,plain,
% 1.64/1.82 (b(elem!1, s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.64/1.82 inference(symmetry,[status(thm)],[5095])).
% 1.64/1.82 tff(5097,plain,
% 1.64/1.82 ((~b(elem!1, s(z))) <=> (~b(s(s(s(elem!1))), s(z)))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[5096])).
% 1.64/1.82 tff(5098,plain,
% 1.64/1.82 (~b(s(s(s(elem!1))), s(z))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[4883, 5097])).
% 1.64/1.82 tff(5099,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[2718, 5098])).
% 1.64/1.82 tff(5100,plain,((~(s(s(s(elem!1))) = elem!1)) | (~b(s(s(s(elem!1))), s(z))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(5101,plain,
% 1.64/1.82 (~(s(s(s(elem!1))) = elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[5100, 4883, 2718])).
% 1.64/1.82 tff(5102,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(5103,plain,
% 1.64/1.82 (((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(5104,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[5103])).
% 1.64/1.82 tff(5105,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)))),
% 1.64/1.82 inference(transitivity,[status(thm)],[5104, 5102])).
% 1.64/1.82 tff(5106,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(5107,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[5106, 5105])).
% 1.64/1.82 tff(5108,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[5107, 128, 498, 577, 1681, 2006])).
% 1.64/1.82 tff(5109,plain,((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(5110,plain,
% 1.64/1.82 (~b(s(s(elem!1)), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[5109, 5070, 498, 2006])).
% 1.64/1.82 tff(5111,plain,
% 1.64/1.82 (r(s(s(elem!1)), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1934, 5110, 1086])).
% 1.64/1.82 tff(5112,plain,
% 1.64/1.82 (~r(s(s(s(elem!1))), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4990, 5111, 324])).
% 1.64/1.82 tff(5113,plain,
% 1.64/1.82 (b(s(s(s(elem!1))), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[742, 5112, 5101])).
% 1.64/1.82 tff(5114,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(5115,plain,
% 1.64/1.82 (((~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(5116,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), elem!1))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[5115])).
% 1.64/1.82 tff(5117,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 1.64/1.82 inference(transitivity,[status(thm)],[5116, 5114])).
% 1.64/1.82 tff(5118,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(5119,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), elem!1))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[5118, 5117])).
% 1.64/1.82 tff(5120,plain,
% 1.64/1.82 (~b(s(s(s(elem!1))), s(s(z)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[5119, 128, 498, 577, 2659, 591])).
% 1.64/1.82 tff(5121,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(5122,plain,
% 1.64/1.82 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(z))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(5123,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[5122])).
% 1.64/1.82 tff(5124,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 1.64/1.82 inference(transitivity,[status(thm)],[5123, 5121])).
% 1.64/1.82 tff(5125,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(z)))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(5126,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[5125, 5124])).
% 1.64/1.82 tff(5127,plain,
% 1.64/1.82 (~b(z, s(s(z)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[5126, 128, 498, 577, 591])).
% 1.64/1.82 tff(5128,plain,
% 1.64/1.82 (r(z, s(s(z)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[516, 5127])).
% 1.64/1.82 tff(5129,plain,
% 1.64/1.82 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[528, 5128, 520])).
% 1.64/1.82 tff(5130,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4350, 21, 5129, 5120, 283])).
% 1.64/1.82 tff(5131,plain,((~b(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(5132,plain,
% 1.64/1.82 (~b(s(s(z)), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[5131, 5070, 498, 520, 5113])).
% 1.64/1.82 tff(5133,plain,
% 1.64/1.82 (r(s(s(z)), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[370, 5132, 5094])).
% 1.64/1.82 tff(5134,plain,
% 1.64/1.82 (~r(s(s(elem!1)), s(s(z)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[5045, 45, 5111, 5133])).
% 1.64/1.82 tff(5135,plain,
% 1.64/1.82 (~r(s(z), s(s(elem!1)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3672, 453, 1664, 5067, 30, 549])).
% 1.64/1.82 tff(5136,plain,
% 1.64/1.82 (b(s(z), s(s(elem!1)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[117, 5135])).
% 1.64/1.82 tff(5137,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(5138,plain,
% 1.64/1.82 (((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(5139,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[5138])).
% 1.64/1.82 tff(5140,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[5139, 5137])).
% 1.64/1.82 tff(5141,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(5142,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1)))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[5141, 5140])).
% 1.64/1.82 tff(5143,plain,
% 1.64/1.82 (~b(s(z), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[5142, 128, 5070, 453, 5136, 549, 5113])).
% 1.64/1.82 tff(5144,plain,
% 1.64/1.82 (r(s(z), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[665, 5143, 1610])).
% 1.64/1.82 tff(5145,plain,
% 1.64/1.82 (~r(s(s(z)), s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1513, 5133, 272, 5144])).
% 1.64/1.82 tff(5146,plain,
% 1.64/1.82 (b(s(s(z)), s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[86, 5145])).
% 1.64/1.82 tff(5147,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(5148,plain,
% 1.64/1.82 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(5149,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(s(elem!1)), s(s(z))))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[5148])).
% 1.64/1.82 tff(5150,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[5149, 5147])).
% 1.64/1.82 tff(5151,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(5152,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[5151, 5150])).
% 1.64/1.82 tff(5153,plain,
% 1.64/1.82 (~b(s(s(elem!1)), s(s(z)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[5152, 128, 30, 5136, 5146])).
% 1.64/1.82 tff(5154,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4339, 21, 1, 5153, 5134])).
% 1.64/1.82 tff(5155,plain,(b(elem!1, s(z)) | (s(s(elem!1)) = s(s(z))) | (~b(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (~b(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (s(z) = elem!1) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(elem!1)) = elem!1) | (~b(s(s(elem!1)), z)) | (elem!1 = z) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(5156,plain,
% 1.64/1.82 (b(elem!1, s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[5155, 5060, 4491, 171, 4261, 4592, 1610, 4548, 549, 324, 1086, 4574, 4555, 2718])).
% 1.64/1.82 tff(5157,plain,
% 1.64/1.82 (~b(s(s(elem!1)), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[2736, 5156, 4491, 4550])).
% 1.64/1.82 tff(5158,plain,
% 1.64/1.82 (r(s(s(elem!1)), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1934, 5157, 1086])).
% 1.64/1.83 tff(5159,plain,
% 1.64/1.83 (~r(s(s(s(elem!1))), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4990, 5158, 324])).
% 1.64/1.83 tff(5160,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(5161,plain,
% 1.64/1.83 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(5162,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[5161])).
% 1.64/1.83 tff(5163,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[5162, 5160])).
% 1.64/1.83 tff(5164,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(5165,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z)))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[5164, 5163])).
% 1.64/1.83 tff(5166,plain,
% 1.64/1.83 (~b(s(s(s(elem!1))), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[5165, 128, 4491, 5156, 4550, 2718])).
% 1.64/1.83 tff(5167,plain,
% 1.64/1.83 (s(s(s(elem!1))) = elem!1),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[742, 5166, 5159])).
% 1.64/1.83 tff(5168,plain,
% 1.64/1.83 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.64/1.83 inference(monotonicity,[status(thm)],[5167])).
% 1.64/1.83 tff(5169,plain,
% 1.64/1.83 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.64/1.83 inference(symmetry,[status(thm)],[5168])).
% 1.64/1.83 tff(5170,plain,
% 1.64/1.83 ((~b(s(s(s(s(elem!1)))), elem!1)) <=> (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[5169])).
% 1.64/1.83 tff(5171,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(5172,plain,
% 1.64/1.83 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(5173,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[5172])).
% 1.64/1.83 tff(5174,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.64/1.83 inference(transitivity,[status(thm)],[5173, 5171])).
% 1.64/1.83 tff(5175,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(5176,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[5175, 5174])).
% 1.64/1.83 tff(5177,plain,
% 1.64/1.83 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[5176, 128, 5060, 5156, 549, 1842, 4532])).
% 1.64/1.83 tff(5178,plain,
% 1.64/1.83 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[5177, 5170])).
% 1.64/1.83 tff(5179,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1842, 5178])).
% 1.64/1.83 tff(5180,plain,((s(z) = elem!1) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(elem!1)) = elem!1) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(5181,plain,
% 1.64/1.83 (s(z) = elem!1),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[5180, 549, 1842, 2718, 324, 1086, 164])).
% 1.64/1.83 tff(5182,plain,
% 1.64/1.83 (b(z, s(z)) <=> b(z, elem!1)),
% 1.64/1.83 inference(monotonicity,[status(thm)],[5181])).
% 1.64/1.83 tff(5183,plain,
% 1.64/1.83 (b(z, elem!1) <=> b(z, s(z))),
% 1.64/1.83 inference(symmetry,[status(thm)],[5182])).
% 1.64/1.83 tff(5184,plain,
% 1.64/1.83 (b(s(s(elem!1)), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4662, 5181, 4491])).
% 1.64/1.83 tff(5185,plain,
% 1.64/1.83 (~b(elem!1, s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[2736, 5184, 4491, 4550])).
% 1.64/1.83 tff(5186,plain,
% 1.64/1.83 (b(z, elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4979, 5185, 1842, 2718, 324, 164, 1086])).
% 1.64/1.83 tff(5187,plain,
% 1.64/1.83 (b(z, s(z))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[5186, 5183])).
% 1.64/1.83 tff(5188,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4527, 5187])).
% 1.64/1.83 tff(5189,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | b(s(z), z) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(5190,plain,
% 1.64/1.83 (~b(s(z), s(s(s(elem!1))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[5189, 4470, 197, 4474, 164, 3090])).
% 1.64/1.83 tff(5191,plain,
% 1.64/1.83 (r(s(z), s(s(s(elem!1))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[339, 5190])).
% 1.64/1.83 tff(5192,plain,
% 1.64/1.83 (~r(s(z), s(s(elem!1)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4323, 45, 4474, 5191])).
% 1.64/1.83 tff(5193,plain,
% 1.64/1.83 (b(s(z), s(s(elem!1)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[117, 5192])).
% 1.64/1.83 tff(5194,plain,
% 1.64/1.83 (~r(s(s(elem!1)), s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4489, 4471, 171, 4470, 197, 4474])).
% 1.64/1.83 tff(5195,plain,
% 1.64/1.83 (b(s(s(elem!1)), s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[292, 5194])).
% 1.64/1.83 tff(5196,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(5197,plain,
% 1.64/1.83 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(5198,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[5197])).
% 1.64/1.83 tff(5199,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[5198, 5196])).
% 1.64/1.83 tff(5200,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(5201,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[5200, 5199])).
% 1.64/1.83 tff(5202,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[5201, 128, 30, 876, 1842, 2718, 1841])).
% 1.64/1.83 tff(5203,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(5204,plain,
% 1.64/1.83 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[5203, 5195, 5193, 4470, 197])).
% 1.64/1.83 tff(5205,plain,
% 1.64/1.83 (r(s(s(s(s(elem!1)))), s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1828, 5204])).
% 1.64/1.83 tff(5206,plain,
% 1.64/1.83 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[803, 4473])).
% 1.64/1.83 tff(5207,plain,
% 1.64/1.83 (~b(z, s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4526, 5195, 197, 4474, 171, 5206])).
% 1.64/1.83 tff(5208,plain,
% 1.64/1.83 (r(z, s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[415, 5207])).
% 1.64/1.83 tff(5209,plain,
% 1.64/1.83 (~r(z, s(s(s(s(elem!1)))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4413, 45, 5208, 5205])).
% 1.64/1.83 tff(5210,plain,
% 1.64/1.83 (~r(z, s(s(s(elem!1))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[854, 5191, 171])).
% 1.64/1.83 tff(5211,plain,
% 1.64/1.83 (b(z, s(s(s(elem!1))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[858, 5210])).
% 1.64/1.83 tff(5212,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(5213,plain,
% 1.64/1.83 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(5214,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[5213])).
% 1.64/1.83 tff(5215,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[5214, 5212])).
% 1.64/1.83 tff(5216,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(5217,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[5216, 5215])).
% 1.64/1.83 tff(5218,plain,
% 1.64/1.83 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[5217, 128, 5195, 5193, 197])).
% 1.64/1.83 tff(5219,plain,
% 1.64/1.83 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[889, 5218, 5206])).
% 1.64/1.83 tff(5220,plain,
% 1.64/1.83 (~r(s(s(s(s(elem!1)))), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1745, 5205, 171])).
% 1.64/1.83 tff(5221,plain,
% 1.64/1.83 (b(s(s(s(s(elem!1)))), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[2081, 5220])).
% 1.64/1.83 tff(5222,plain,
% 1.64/1.83 (~r(z, s(s(elem!1)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4546, 5221, 4470, 5219])).
% 1.64/1.83 tff(5223,plain,
% 1.64/1.83 (b(z, s(s(elem!1)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[160, 5222])).
% 1.64/1.83 tff(5224,plain,
% 1.64/1.83 (~b(z, s(s(s(s(elem!1)))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4563, 128, 5223, 5193, 4470, 197, 5211])).
% 1.64/1.83 tff(5225,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[2047, 21, 5224, 5209, 178])).
% 1.64/1.83 tff(5226,plain,(b(s(s(elem!1)), s(s(s(elem!1)))) | b(s(z), z) | r(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(5227,plain,
% 1.64/1.83 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[5226, 172, 164])).
% 1.64/1.83 tff(5228,plain,
% 1.64/1.83 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[228])).
% 1.64/1.83 tff(5229,plain,
% 1.64/1.83 (b(elem!1, s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.64/1.83 inference(symmetry,[status(thm)],[5228])).
% 1.64/1.83 tff(5230,plain,
% 1.64/1.83 (b(elem!1, s(s(s(elem!1))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[2106, 266])).
% 1.64/1.83 tff(5231,plain,
% 1.64/1.83 (b(elem!1, s(elem!1))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[5230, 264])).
% 1.64/1.83 tff(5232,plain,
% 1.64/1.83 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[5231, 5229])).
% 1.64/1.83 tff(5233,plain,
% 1.64/1.83 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[226])).
% 1.64/1.83 tff(5234,plain,
% 1.64/1.83 ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) <=> (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[5233])).
% 1.64/1.83 tff(5235,plain,
% 1.64/1.83 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[4264, 5234])).
% 1.64/1.83 tff(5236,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[5235, 5232])).
% 1.64/1.83 tff(5237,plain,((~(s(s(elem!1)) = elem!1)) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(5238,plain,
% 1.64/1.83 (~(s(s(elem!1)) = elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[5237, 4264, 2106])).
% 1.64/1.83 tff(5239,plain,
% 1.64/1.83 (~(z = elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4250, 5238, 164])).
% 1.64/1.83 tff(5240,plain,
% 1.64/1.83 (~(s(s(elem!1)) = s(s(z)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[4260, 5239])).
% 1.64/1.83 tff(5241,assumption,(~b(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.64/1.83 tff(5242,plain,
% 1.64/1.83 (r(z, elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1549, 4251, 455])).
% 1.64/1.83 tff(5243,plain,
% 1.64/1.83 (~r(s(s(elem!1)), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1962, 325, 171])).
% 1.64/1.83 tff(5244,plain,
% 1.64/1.83 (b(s(s(elem!1)), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[2018, 21, 154, 5243])).
% 1.64/1.83 tff(5245,plain,
% 1.64/1.83 (~r(z, s(s(elem!1)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[2545, 323, 272, 325, 1063])).
% 1.64/1.83 tff(5246,plain,
% 1.64/1.83 (b(z, s(s(elem!1)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[160, 5245])).
% 1.64/1.83 tff(5247,plain,
% 1.64/1.83 (~b(s(s(s(elem!1))), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[3460, 1836, 2106, 5246])).
% 1.64/1.83 tff(5248,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[547, 21, 382, 2447, 5247])).
% 1.64/1.83 tff(5249,plain,((~r(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (s(s(s(s(elem!1)))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(5250,plain,
% 1.64/1.83 (~r(s(z), s(s(s(elem!1))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[5249, 1664, 171, 325, 2106])).
% 1.64/1.83 tff(5251,plain,
% 1.64/1.83 (b(s(z), s(s(s(elem!1))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[339, 5250])).
% 1.64/1.83 tff(5252,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(5253,plain,
% 1.64/1.83 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(5254,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[5253])).
% 1.64/1.83 tff(5255,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[5254, 5252])).
% 1.64/1.83 tff(5256,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(5257,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[5256, 5255])).
% 1.64/1.83 tff(5258,plain,
% 1.64/1.83 (~b(s(z), s(s(elem!1)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[5257, 128, 2106, 5251, 2718])).
% 1.64/1.83 tff(5259,plain,
% 1.64/1.83 (r(s(z), s(s(elem!1)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[117, 5258])).
% 1.64/1.83 tff(5260,plain,
% 1.64/1.83 (~r(z, s(s(elem!1)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1383, 5259, 171])).
% 1.64/1.83 tff(5261,plain,
% 1.64/1.83 (b(z, s(s(elem!1)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[160, 5260])).
% 1.64/1.83 tff(5262,plain,
% 1.64/1.83 (r(s(s(elem!1)), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1934, 4659, 1086])).
% 1.64/1.83 tff(5263,plain,
% 1.64/1.83 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), elem!1)),
% 1.64/1.83 inference(monotonicity,[status(thm)],[710])).
% 1.64/1.83 tff(5264,plain,
% 1.64/1.83 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.64/1.83 inference(symmetry,[status(thm)],[5263])).
% 1.64/1.83 tff(5265,plain,
% 1.64/1.83 ((~b(s(s(elem!1)), elem!1)) <=> (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[5264])).
% 1.64/1.83 tff(5266,plain,
% 1.64/1.83 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[4659, 5265])).
% 1.64/1.83 tff(5267,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[2106, 5266])).
% 1.64/1.83 tff(5268,plain,((~(s(s(s(elem!1))) = elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | b(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(5269,plain,
% 1.64/1.83 (~(s(s(s(elem!1))) = elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[5268, 4659, 2106])).
% 1.64/1.83 tff(5270,plain,
% 1.64/1.83 (r(s(s(s(elem!1))), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[742, 5269, 5241])).
% 1.64/1.83 tff(5271,plain,
% 1.64/1.83 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[3820, 5270, 5262])).
% 1.64/1.83 tff(5272,plain,
% 1.64/1.83 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[889, 5271, 4492])).
% 1.64/1.83 tff(5273,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(5274,plain,
% 1.64/1.83 (((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(5275,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[5274])).
% 1.64/1.83 tff(5276,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[5275, 5273])).
% 1.64/1.83 tff(5277,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(5278,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[5277, 5276])).
% 1.64/1.84 tff(5279,plain,
% 1.64/1.84 (~b(z, s(s(s(elem!1))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5278, 128, 453, 2006, 5272])).
% 1.64/1.84 tff(5280,plain,
% 1.64/1.84 (((~![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(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(5281,plain,
% 1.64/1.84 (((~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(5282,plain,
% 1.64/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[5281])).
% 1.64/1.84 tff(5283,plain,
% 1.64/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.64/1.84 inference(transitivity,[status(thm)],[5282, 5280])).
% 1.64/1.84 tff(5284,plain,
% 1.64/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(5285,plain,
% 1.64/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[5284, 5283])).
% 1.64/1.84 tff(5286,plain,
% 1.64/1.84 (~r(z, s(s(s(elem!1))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5285, 45, 1416, 5270])).
% 1.64/1.84 tff(5287,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[858, 5286, 5279])).
% 1.64/1.84 tff(5288,plain,(b(s(s(elem!1)), elem!1) | (~r(z, elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | b(s(s(s(elem!1))), elem!1) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(5289,plain,
% 1.64/1.84 (b(s(s(elem!1)), elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5288, 5244, 2106, 5242, 5261, 5241, 1086])).
% 1.64/1.84 tff(5290,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(5291,plain,
% 1.64/1.84 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(5292,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[5291])).
% 1.64/1.84 tff(5293,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 1.64/1.84 inference(transitivity,[status(thm)],[5292, 5290])).
% 1.64/1.84 tff(5294,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(5295,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[5294, 5293])).
% 1.64/1.84 tff(5296,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5295, 128, 453, 1681, 2006, 2106, 3452])).
% 1.64/1.84 tff(5297,plain,((~b(s(s(s(elem!1))), 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(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(5298,plain,
% 1.64/1.84 (~b(s(s(s(elem!1))), z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5297, 5289, 5261, 5244, 2106])).
% 1.64/1.84 tff(5299,assumption,(~b(s(s(s(elem!1))), z)), introduced(assumption)).
% 1.64/1.84 tff(5300,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[547, 21, 382, 544, 5299])).
% 1.64/1.84 tff(5301,plain,(b(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(5302,plain,
% 1.64/1.84 (r(s(s(s(elem!1))), z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5301, 5298])).
% 1.64/1.84 tff(5303,plain,
% 1.64/1.84 (((~![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(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(5304,plain,
% 1.64/1.84 (((~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z))) <=> ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(5305,plain,
% 1.64/1.84 (((~![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(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[5304])).
% 1.64/1.84 tff(5306,plain,
% 1.64/1.84 (((~![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(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.64/1.84 inference(transitivity,[status(thm)],[5305, 5303])).
% 1.64/1.84 tff(5307,plain,
% 1.64/1.84 ((~![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(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(5308,plain,
% 1.64/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[5307, 5306])).
% 1.64/1.84 tff(5309,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5308, 45, 1416, 2450, 520])).
% 1.64/1.84 tff(5310,plain,((~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(5311,plain,
% 1.64/1.84 (~r(s(s(s(elem!1))), elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5310, 5302, 5242])).
% 1.64/1.84 tff(5312,plain,
% 1.64/1.84 (s(s(s(elem!1))) = elem!1),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[742, 5311, 5241])).
% 1.64/1.84 tff(5313,plain,
% 1.64/1.84 ((s(s(s(elem!1))) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[5312])).
% 1.64/1.84 tff(5314,plain,
% 1.64/1.84 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 1.64/1.84 inference(transitivity,[status(thm)],[5313, 225])).
% 1.64/1.84 tff(5315,plain,
% 1.64/1.84 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[5314])).
% 1.64/1.84 tff(5316,plain,
% 1.64/1.84 (~(s(s(z)) = elem!1)),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[283, 5315])).
% 1.64/1.84 tff(5317,plain,
% 1.64/1.84 (s(s(s(s(elem!1)))) = s(elem!1)),
% 1.64/1.84 inference(monotonicity,[status(thm)],[5312])).
% 1.64/1.84 tff(5318,plain,
% 1.64/1.84 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.64/1.84 inference(symmetry,[status(thm)],[5317])).
% 1.64/1.84 tff(5319,plain,
% 1.64/1.84 (r(s(elem!1), elem!1) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 1.64/1.84 inference(monotonicity,[status(thm)],[5318])).
% 1.64/1.84 tff(5320,plain,
% 1.64/1.84 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(elem!1), elem!1)),
% 1.64/1.84 inference(symmetry,[status(thm)],[5319])).
% 1.64/1.84 tff(5321,plain,
% 1.64/1.84 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 1.64/1.84 inference(monotonicity,[status(thm)],[710])).
% 1.64/1.84 tff(5322,plain,
% 1.64/1.84 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.64/1.84 inference(symmetry,[status(thm)],[5321])).
% 1.64/1.84 tff(5323,plain,
% 1.64/1.84 ((~r(s(s(s(s(elem!1)))), elem!1)) <=> (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[5322])).
% 1.64/1.84 tff(5324,assumption,(~r(s(s(s(s(elem!1)))), elem!1)), introduced(assumption)).
% 1.64/1.84 tff(5325,plain,
% 1.64/1.84 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[5324, 5323])).
% 1.64/1.84 tff(5326,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1772, 5325])).
% 1.64/1.84 tff(5327,plain,((~(s(s(s(elem!1))) = elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | r(s(s(s(s(elem!1)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(5328,plain,
% 1.64/1.84 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5327, 5312, 1772])).
% 1.64/1.84 tff(5329,plain,
% 1.64/1.84 (r(s(elem!1), elem!1)),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[5328, 5320])).
% 1.64/1.84 tff(5330,plain,
% 1.64/1.84 (~r(s(elem!1), s(s(z)))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[905, 45, 1103, 3397])).
% 1.64/1.84 tff(5331,plain,
% 1.64/1.84 (b(s(elem!1), s(s(z)))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[473, 21, 759, 5330])).
% 1.64/1.84 tff(5332,plain,
% 1.64/1.84 (((~![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(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(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(5333,plain,
% 1.64/1.84 (((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z))) <=> ((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(5334,plain,
% 1.64/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[5333])).
% 1.64/1.84 tff(5335,plain,
% 1.64/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 1.64/1.84 inference(transitivity,[status(thm)],[5334, 5332])).
% 1.64/1.84 tff(5336,plain,
% 1.64/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z)))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(5337,plain,
% 1.64/1.84 ((~![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(s(elem!1), z))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[5336, 5335])).
% 1.64/1.84 tff(5338,plain,
% 1.64/1.84 (~r(s(elem!1), z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5337, 45, 1416, 3397])).
% 1.64/1.84 tff(5339,plain,
% 1.64/1.84 (b(s(elem!1), z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[728, 21, 109, 5338])).
% 1.64/1.84 tff(5340,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(5341,plain,
% 1.64/1.84 (((~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(z))))) <=> ((~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(5342,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[5341])).
% 1.64/1.84 tff(5343,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z)))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[5342, 5340])).
% 1.64/1.84 tff(5344,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(z)))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(5345,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), s(s(z))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[5344, 5343])).
% 1.64/1.84 tff(5346,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5345, 128, 1443, 1435, 5339, 5331])).
% 1.64/1.84 tff(5347,plain,((~r(s(s(z)), elem!1)) | (s(elem!1) = s(s(z))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(5348,plain,
% 1.64/1.84 (~r(s(s(z)), elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5347, 5329, 5242, 5016])).
% 1.64/1.84 tff(5349,plain,
% 1.64/1.84 (b(s(s(z)), elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[370, 5348, 5316])).
% 1.64/1.84 tff(5350,plain,
% 1.64/1.84 (~r(s(z), elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1544, 5242, 171])).
% 1.64/1.84 tff(5351,plain,
% 1.64/1.84 (b(s(z), elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[665, 1610, 5350])).
% 1.64/1.84 tff(5352,plain,
% 1.64/1.84 (r(s(s(s(elem!1))), elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[742, 5101, 5241])).
% 1.64/1.84 tff(5353,plain,
% 1.64/1.84 (~r(z, s(s(s(elem!1))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5285, 45, 1416, 5352])).
% 1.64/1.84 tff(5354,plain,
% 1.64/1.84 (r(elem!1, s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[305, 4883, 1642])).
% 1.64/1.84 tff(5355,plain,
% 1.64/1.84 (~r(z, s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4896, 5354, 1416])).
% 1.64/1.84 tff(5356,plain,
% 1.64/1.84 (b(z, s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[415, 5355])).
% 1.64/1.84 tff(5357,plain,
% 1.64/1.84 (~b(z, s(s(s(elem!1))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[422, 128, 5356, 549, 2718])).
% 1.64/1.84 tff(5358,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[858, 5357, 5353])).
% 1.64/1.84 tff(5359,plain,(b(elem!1, s(z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~r(z, elem!1)) | b(s(s(s(elem!1))), elem!1) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(5360,plain,
% 1.64/1.84 (b(elem!1, s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5359, 5241, 2718, 5242, 5251, 5008])).
% 1.64/1.84 tff(5361,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)), elem!1)) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)), elem!1)) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(5362,plain,
% 1.64/1.84 (((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, 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(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(5363,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, 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(s(z)), elem!1)) | (~b(s(s(elem!1)), s(s(z))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[5362])).
% 1.64/1.84 tff(5364,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, 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(s(z)), elem!1)) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[5363, 5361])).
% 1.64/1.84 tff(5365,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(5366,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)), elem!1)) | (~b(s(s(elem!1)), s(s(z))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[5365, 5364])).
% 1.64/1.84 tff(5367,plain,
% 1.64/1.84 (~b(s(s(elem!1)), s(s(z)))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5366, 128, 5360, 5289, 5351, 5349])).
% 1.64/1.84 tff(5368,plain,
% 1.64/1.84 (r(s(s(elem!1)), s(s(z)))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4339, 21, 4261, 5367])).
% 1.64/1.84 tff(5369,plain,
% 1.64/1.84 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[5318])).
% 1.64/1.84 tff(5370,plain,
% 1.64/1.84 (r(s(s(elem!1)), s(s(s(s(elem!1))))) <=> r(s(s(elem!1)), s(elem!1))),
% 1.64/1.84 inference(symmetry,[status(thm)],[5369])).
% 1.64/1.84 tff(5371,plain,
% 1.64/1.84 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[5317])).
% 1.64/1.84 tff(5372,plain,
% 1.64/1.84 (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[5371])).
% 1.64/1.84 tff(5373,plain,
% 1.64/1.84 (s(s(s(s(s(s(elem!1)))))) = elem!1),
% 1.64/1.84 inference(transitivity,[status(thm)],[5372, 5312])).
% 1.64/1.84 tff(5374,plain,
% 1.64/1.84 (s(s(s(s(s(s(s(elem!1))))))) = s(elem!1)),
% 1.64/1.84 inference(monotonicity,[status(thm)],[5373])).
% 1.64/1.84 tff(5375,plain,
% 1.64/1.84 (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(elem!1))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[5374, 5318])).
% 1.64/1.84 tff(5376,plain,
% 1.64/1.84 (s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(elem!1))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[5374])).
% 1.64/1.84 tff(5377,plain,
% 1.64/1.84 (r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(s(s(s(elem!1)))))))) <=> r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[5376, 5375])).
% 1.64/1.84 tff(5378,assumption,(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.64/1.84 tff(5379,plain,
% 1.64/1.84 (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))),
% 1.64/1.84 inference(symmetry,[status(thm)],[5378])).
% 1.64/1.84 tff(5380,plain,
% 1.64/1.84 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[5379])).
% 1.64/1.84 tff(5381,plain,
% 1.64/1.84 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[1720, 5380, 3116])).
% 1.64/1.84 tff(5382,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[698, 5381])).
% 1.64/1.84 tff(5383,plain,((~(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1)))))) | (s(s(s(elem!1))) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(5384,plain,
% 1.64/1.84 (~(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1)))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5383, 2649])).
% 1.64/1.84 tff(5385,plain,
% 1.64/1.84 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(s(s(s(elem!1))))))))) = s(s(s(s(s(s(s(elem!1))))))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(5386,plain,
% 1.64/1.84 (inj_0(s(s(s(s(s(s(s(s(elem!1))))))))) = s(s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5385, 62])).
% 1.64/1.84 tff(5387,assumption,(s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 1.64/1.84 tff(5388,plain,
% 1.64/1.84 (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(s(s(s(elem!1))))))))),
% 1.64/1.84 inference(symmetry,[status(thm)],[5387])).
% 1.64/1.84 tff(5389,plain,
% 1.64/1.84 (inj_0(s(s(s(s(s(s(s(elem!1)))))))) = inj_0(s(s(s(s(s(s(s(s(elem!1)))))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[5388])).
% 1.64/1.84 tff(5390,plain,
% 1.64/1.84 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(5391,plain,
% 1.64/1.84 (inj_0(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(s(s(s(elem!1))))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5390, 62])).
% 1.64/1.84 tff(5392,plain,
% 1.64/1.84 (s(s(s(s(s(s(elem!1)))))) = inj_0(s(s(s(s(s(s(s(elem!1))))))))),
% 1.64/1.84 inference(symmetry,[status(thm)],[5391])).
% 1.64/1.84 tff(5393,plain,
% 1.64/1.84 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[5392, 5389, 5386])).
% 1.64/1.84 tff(5394,plain,
% 1.64/1.84 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(s(s(s(s(s(s(elem!1))))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[5393])).
% 1.64/1.84 tff(5395,plain,
% 1.64/1.84 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(s(s(elem!1)))))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[3332, 5394, 5389, 5386])).
% 1.64/1.84 tff(5396,plain,
% 1.64/1.84 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(s(s(s(s(s(elem!1))))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[5395])).
% 1.64/1.84 tff(5397,plain,
% 1.64/1.84 (inj_0(s(s(s(s(s(s(s(elem!1)))))))) = inj_0(s(s(s(s(s(elem!1))))))),
% 1.64/1.84 inference(symmetry,[status(thm)],[5396])).
% 1.64/1.84 tff(5398,plain,
% 1.64/1.84 (s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[3332, 5394, 5397, 3116])).
% 1.64/1.84 tff(5399,assumption,(~(s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.64/1.84 tff(5400,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5399, 5398])).
% 1.64/1.84 tff(5401,plain,((~(s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(s(s(s(s(elem!1))))))))) | (s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(5402,plain,
% 1.64/1.84 (~(s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(s(s(s(s(elem!1))))))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5401, 5384])).
% 1.64/1.84 tff(5403,plain,
% 1.64/1.84 (b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(s(s(s(elem!1)))))))) <=> b(s(s(elem!1)), s(elem!1))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[5376, 5374])).
% 1.64/1.84 tff(5404,plain,
% 1.64/1.84 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.64/1.84 inference(symmetry,[status(thm)],[5403])).
% 1.64/1.84 tff(5405,plain,
% 1.64/1.84 ((~b(s(s(elem!1)), s(elem!1))) <=> (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(s(s(s(elem!1)))))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[5404])).
% 1.64/1.84 tff(5406,plain,
% 1.64/1.84 (~r(s(elem!1), z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5337, 45, 5242, 5329])).
% 1.64/1.84 tff(5407,plain,
% 1.64/1.84 (b(s(elem!1), z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[728, 21, 109, 5406])).
% 1.64/1.84 tff(5408,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(5409,plain,
% 1.64/1.84 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~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(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(5410,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), elem!1)) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1)))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[5409])).
% 1.64/1.84 tff(5411,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), elem!1)) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[5410, 5408])).
% 1.64/1.85 tff(5412,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), elem!1)) | (~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))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(5413,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[5412, 5411])).
% 1.64/1.85 tff(5414,plain,
% 1.64/1.85 (~b(s(s(elem!1)), s(elem!1))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[5413, 128, 5261, 5289, 5244, 5407])).
% 1.64/1.85 tff(5415,plain,
% 1.64/1.85 (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[5414, 5405])).
% 1.64/1.85 tff(5416,plain,
% 1.64/1.85 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(s(s(s(s(elem!1)))))))) | b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(s(s(s(elem!1)))))))) | r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(s(s(s(elem!1)))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(s(s(s(s(elem!1)))))))) | b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(s(s(s(elem!1)))))))) | r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(s(s(s(elem!1)))))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(5417,plain,
% 1.64/1.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(s(s(s(s(elem!1)))))))) | b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(s(s(s(elem!1)))))))) | r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(s(s(s(elem!1)))))))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(5418,plain,
% 1.64/1.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(s(s(s(s(elem!1)))))))) | b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(s(s(s(elem!1)))))))) | r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[5417, 5416])).
% 1.64/1.85 tff(5419,plain,
% 1.64/1.85 ((s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(s(s(s(s(elem!1)))))))) | b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(s(s(s(elem!1)))))))) | r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[5418, 21])).
% 1.64/1.85 tff(5420,plain,
% 1.64/1.85 (r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[5419, 5415, 5402])).
% 1.64/1.85 tff(5421,plain,
% 1.64/1.85 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[5420, 5377])).
% 1.64/1.85 tff(5422,plain,
% 1.64/1.85 (r(s(s(elem!1)), s(elem!1))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[5421, 5370])).
% 1.64/1.85 tff(5423,plain,
% 1.64/1.85 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[5318])).
% 1.64/1.85 tff(5424,plain,
% 1.64/1.85 (r(elem!1, s(s(s(s(elem!1))))) <=> r(elem!1, s(elem!1))),
% 1.64/1.85 inference(symmetry,[status(thm)],[5423])).
% 1.64/1.85 tff(5425,plain,
% 1.64/1.85 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[5312])).
% 1.64/1.85 tff(5426,plain,
% 1.64/1.85 (~b(z, s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2917, 5360, 164, 455, 5242, 1610])).
% 1.64/1.85 tff(5427,plain,
% 1.64/1.85 (r(z, s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[415, 5426])).
% 1.64/1.85 tff(5428,plain,
% 1.64/1.85 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2176, 5427, 325, 1664])).
% 1.64/1.85 tff(5429,plain,
% 1.64/1.85 (b(s(s(s(s(elem!1)))), s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1828, 5428])).
% 1.64/1.85 tff(5430,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(5431,plain,
% 1.64/1.85 (((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(5432,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[5431])).
% 1.64/1.85 tff(5433,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[5432, 5430])).
% 1.64/1.85 tff(5434,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(5435,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[5434, 5433])).
% 1.64/1.85 tff(5436,plain,
% 1.64/1.85 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[5435, 128, 5360, 5351, 2718, 5429])).
% 1.64/1.85 tff(5437,plain,
% 1.64/1.85 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1856, 5436, 2649])).
% 1.64/1.85 tff(5438,plain,
% 1.64/1.85 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[5437, 5425])).
% 1.64/1.85 tff(5439,plain,
% 1.64/1.85 (r(elem!1, s(elem!1))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[5438, 5424])).
% 1.64/1.85 tff(5440,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(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(5441,plain,
% 1.64/1.85 (((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(5442,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)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[5441])).
% 1.64/1.85 tff(5443,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)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[5442, 5440])).
% 1.64/1.85 tff(5444,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)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(5445,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(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[5444, 5443])).
% 1.64/1.85 tff(5446,plain,
% 1.64/1.85 (~r(elem!1, s(s(elem!1)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[5445, 45, 5439, 5422])).
% 1.64/1.85 tff(5447,plain,
% 1.64/1.85 (b(elem!1, s(s(elem!1)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2371, 5446, 2344])).
% 1.64/1.85 tff(5448,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))) | (~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(X0, 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(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(5449,plain,
% 1.64/1.85 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(5450,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, s(s(elem!1)))) | (~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(X0, 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(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[5449])).
% 1.64/1.85 tff(5451,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, s(s(elem!1)))) | (~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(X0, 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(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.64/1.85 inference(transitivity,[status(thm)],[5450, 5448])).
% 1.64/1.85 tff(5452,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(5453,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[5452, 5451])).
% 1.64/1.85 tff(5454,plain,
% 1.64/1.85 (~b(s(s(z)), s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[5453, 128, 5289, 5447, 5351, 5349])).
% 1.64/1.85 tff(5455,plain,
% 1.64/1.85 (r(s(s(z)), s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[86, 5454])).
% 1.64/1.85 tff(5456,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)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(5457,plain,
% 1.64/1.85 (((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(5458,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(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[5457])).
% 1.64/1.85 tff(5459,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(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[5458, 5456])).
% 1.64/1.85 tff(5460,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(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(5461,plain,
% 1.64/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[5460, 5459])).
% 1.64/1.85 tff(5462,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[5461, 45, 325, 5455, 5368])).
% 1.64/1.85 tff(5463,plain,(b(s(s(s(elem!1))), elem!1) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(elem!1)) = elem!1) | (~b(s(s(s(elem!1))), s(z))) | b(s(z), z) | b(z, elem!1) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(5464,plain,
% 1.64/1.85 (b(s(s(s(elem!1))), elem!1)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[5463, 1610, 1772, 2106, 1086, 2718, 164, 455, 325])).
% 1.64/1.85 tff(5465,plain,
% 1.64/1.85 (b(elem!1, z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2915, 550, 164, 455])).
% 1.64/1.85 tff(5466,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(5467,plain,
% 1.64/1.85 (((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(5468,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[5467])).
% 1.64/1.85 tff(5469,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[5468, 5466])).
% 1.64/1.85 tff(5470,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(5471,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z)))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[5470, 5469])).
% 1.64/1.85 tff(5472,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[5471, 128, 5465, 550, 922, 2659, 2718])).
% 1.64/1.85 tff(5473,plain,((~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | b(s(z), z) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(5474,plain,
% 1.64/1.85 (~b(z, s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[5473, 5351, 5464, 2718, 164, 455])).
% 1.64/1.85 tff(5475,plain,
% 1.64/1.85 (r(z, s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[415, 5474])).
% 1.64/1.85 tff(5476,plain,
% 1.64/1.85 (~r(elem!1, s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4896, 5475, 5242])).
% 1.64/1.85 tff(5477,plain,
% 1.64/1.85 (b(elem!1, s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[305, 5476, 5008])).
% 1.64/1.85 tff(5478,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4998, 128, 5477, 5351, 5464, 2718])).
% 1.64/1.85 tff(5479,plain,((s(z) = elem!1) | (~b(s(s(s(elem!1))), s(z))) | b(s(z), z) | b(z, elem!1) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(elem!1)) = elem!1) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(5480,plain,
% 1.64/1.85 (s(z) = elem!1),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[5479, 4265, 164, 455, 2718, 2106, 1086, 325])).
% 1.64/1.85 tff(5481,plain,
% 1.64/1.85 (s(s(z)) = s(elem!1)),
% 1.64/1.85 inference(monotonicity,[status(thm)],[5480])).
% 1.64/1.85 tff(5482,plain,
% 1.64/1.85 (s(elem!1) = s(s(z))),
% 1.64/1.85 inference(symmetry,[status(thm)],[5481])).
% 1.64/1.85 tff(5483,plain,
% 1.64/1.85 (b(s(elem!1), z) <=> b(s(s(z)), z)),
% 1.64/1.85 inference(monotonicity,[status(thm)],[5482])).
% 1.64/1.85 tff(5484,plain,
% 1.64/1.85 (b(s(s(z)), z) <=> b(s(elem!1), z)),
% 1.64/1.85 inference(symmetry,[status(thm)],[5483])).
% 1.64/1.85 tff(5485,plain,
% 1.64/1.85 (b(s(s(z)), s(z)) <=> b(s(s(z)), elem!1)),
% 1.64/1.85 inference(monotonicity,[status(thm)],[5480])).
% 1.64/1.85 tff(5486,plain,
% 1.64/1.85 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(z))),
% 1.64/1.85 inference(symmetry,[status(thm)],[5485])).
% 1.64/1.85 tff(5487,plain,
% 1.64/1.85 (b(s(s(z)), elem!1) <=> b(s(elem!1), elem!1)),
% 1.64/1.85 inference(monotonicity,[status(thm)],[5481])).
% 1.64/1.85 tff(5488,plain,
% 1.64/1.85 (b(s(elem!1), elem!1) <=> b(s(s(z)), elem!1)),
% 1.64/1.85 inference(symmetry,[status(thm)],[5487])).
% 1.64/1.85 tff(5489,plain,
% 1.64/1.85 (b(s(elem!1), elem!1) <=> b(s(s(z)), s(z))),
% 1.64/1.85 inference(transitivity,[status(thm)],[5488, 5486])).
% 1.64/1.85 tff(5490,plain,
% 1.64/1.85 ((~b(s(elem!1), elem!1)) <=> (~b(s(s(z)), s(z)))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[5489])).
% 1.64/1.85 tff(5491,plain,
% 1.64/1.85 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.64/1.85 inference(monotonicity,[status(thm)],[5480])).
% 1.64/1.85 tff(5492,plain,
% 1.64/1.85 (elem!1 = s(z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1644, 5480])).
% 1.64/1.85 tff(5493,plain,
% 1.64/1.85 (~b(z, s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1638, 5492, 455])).
% 1.64/1.85 tff(5494,plain,
% 1.64/1.85 (r(z, s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[415, 5493])).
% 1.64/1.85 tff(5495,plain,
% 1.64/1.85 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2176, 5494, 325, 1664])).
% 1.64/1.85 tff(5496,plain,
% 1.64/1.85 (b(s(s(s(s(elem!1)))), s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1828, 5495])).
% 1.64/1.85 tff(5497,plain,
% 1.64/1.85 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[5496, 5491])).
% 1.64/1.85 tff(5498,plain,
% 1.64/1.85 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
% 1.64/1.85 inference(monotonicity,[status(thm)],[5480])).
% 1.64/1.85 tff(5499,plain,
% 1.64/1.85 (b(s(s(s(elem!1))), elem!1)),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[2718, 5498])).
% 1.64/1.85 tff(5500,plain,
% 1.64/1.85 (b(s(z), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[5480])).
% 1.64/1.85 tff(5501,plain,
% 1.64/1.85 (b(elem!1, s(s(s(elem!1))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[5251, 5500])).
% 1.64/1.85 tff(5502,plain,
% 1.64/1.85 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[5481])).
% 1.64/1.85 tff(5503,plain,
% 1.64/1.85 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[5502, 1712])).
% 1.64/1.85 tff(5504,plain,
% 1.64/1.85 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 1.64/1.85 inference(transitivity,[status(thm)],[5503, 1748])).
% 1.64/1.85 tff(5505,plain,
% 1.64/1.85 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[5504])).
% 1.64/1.85 tff(5506,plain,
% 1.64/1.85 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[239, 5505])).
% 1.64/1.85 tff(5507,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(5508,plain,
% 1.64/1.85 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(5509,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[5508])).
% 1.64/1.86 tff(5510,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[5509, 5507])).
% 1.64/1.86 tff(5511,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(5512,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[5511, 5510])).
% 1.64/1.86 tff(5513,plain,
% 1.64/1.86 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[5512, 128, 5501, 5499, 5497])).
% 1.64/1.86 tff(5514,plain,
% 1.64/1.86 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1856, 5513, 2649])).
% 1.64/1.86 tff(5515,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(5516,plain,
% 1.64/1.86 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(5517,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[5516])).
% 1.64/1.86 tff(5518,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[5517, 5515])).
% 1.64/1.86 tff(5519,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(5520,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[5519, 5518])).
% 1.64/1.86 tff(5521,plain,
% 1.64/1.86 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[5520, 128, 4193, 2659, 4791])).
% 1.64/1.86 tff(5522,plain,
% 1.64/1.86 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | r(s(s(s(elem!1))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | r(s(s(s(elem!1))), s(elem!1)))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(5523,plain,
% 1.64/1.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | r(s(s(s(elem!1))), s(elem!1)))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(5524,plain,
% 1.64/1.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | r(s(s(s(elem!1))), s(elem!1))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[5523, 5522])).
% 1.64/1.86 tff(5525,plain,
% 1.64/1.86 (r(s(s(s(elem!1))), s(elem!1))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[5524, 21, 4789, 5521])).
% 1.64/1.86 tff(5526,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(5527,plain,
% 1.64/1.86 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(5528,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[5527])).
% 1.64/1.86 tff(5529,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[5528, 5526])).
% 1.64/1.86 tff(5530,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(5531,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[5530, 5529])).
% 1.64/1.86 tff(5532,plain,
% 1.64/1.86 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[5531, 128, 4193, 2659, 2656, 4791])).
% 1.64/1.86 tff(5533,plain,
% 1.64/1.86 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1920, 5532, 1918])).
% 1.64/1.86 tff(5534,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(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(5535,plain,
% 1.64/1.86 (((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(5536,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(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[5535])).
% 1.64/1.86 tff(5537,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(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[5536, 5534])).
% 1.64/1.86 tff(5538,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(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(5539,plain,
% 1.64/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[5538, 5537])).
% 1.64/1.86 tff(5540,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[5539, 45, 1866, 5533, 5525])).
% 1.64/1.86 tff(5541,plain,((~b(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (s(s(s(elem!1))) = s(elem!1)) | (s(s(s(s(elem!1)))) = s(elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(5542,plain,
% 1.64/1.86 (~b(s(elem!1), elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[5541, 5514, 4603, 5506, 5501, 5499, 5497])).
% 1.64/1.86 tff(5543,plain,
% 1.64/1.86 (~b(s(s(z)), s(z))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[5542, 5490])).
% 1.64/1.86 tff(5544,plain,
% 1.64/1.86 (r(s(s(z)), s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[86, 5543])).
% 1.64/1.86 tff(5545,plain,
% 1.64/1.86 (~r(s(s(z)), z)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1509, 5544, 171])).
% 1.64/1.86 tff(5546,plain,
% 1.64/1.86 (b(s(s(z)), z)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[25, 5545])).
% 1.64/1.86 tff(5547,plain,
% 1.64/1.86 (b(s(elem!1), z)),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[5546, 5484])).
% 1.64/1.86 tff(5548,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(elem!1))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(5549,plain,
% 1.64/1.86 (((~b(s(s(elem!1)), z)) | (~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(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(5550,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~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(X0, 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)), s(elem!1)))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[5549])).
% 1.64/1.86 tff(5551,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~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(X0, 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)), s(elem!1))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[5550, 5548])).
% 1.64/1.86 tff(5552,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~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))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(5553,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(elem!1)))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[5552, 5551])).
% 1.64/1.86 tff(5554,plain,
% 1.64/1.86 ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[5553, 128, 5261, 5244])).
% 1.64/1.86 tff(5555,plain,
% 1.64/1.86 (~b(s(s(elem!1)), s(elem!1))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[5554, 5547])).
% 1.64/1.86 tff(5556,plain,
% 1.64/1.86 (r(s(s(z)), elem!1) <=> r(s(elem!1), elem!1)),
% 1.64/1.86 inference(monotonicity,[status(thm)],[5481])).
% 1.64/1.86 tff(5557,plain,
% 1.64/1.86 (r(s(s(z)), s(z)) <=> r(s(s(z)), elem!1)),
% 1.64/1.86 inference(monotonicity,[status(thm)],[5480])).
% 1.64/1.86 tff(5558,plain,
% 1.64/1.86 (r(s(s(z)), s(z)) <=> r(s(elem!1), elem!1)),
% 1.64/1.86 inference(transitivity,[status(thm)],[5557, 5556])).
% 1.64/1.86 tff(5559,plain,
% 1.64/1.86 (r(s(elem!1), elem!1)),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[5544, 5558])).
% 1.64/1.86 tff(5560,plain,
% 1.64/1.86 (r(s(s(elem!1)), s(z)) <=> r(s(s(elem!1)), elem!1)),
% 1.64/1.86 inference(monotonicity,[status(thm)],[5480])).
% 1.64/1.86 tff(5561,plain,
% 1.64/1.86 (r(s(s(elem!1)), elem!1)),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[325, 5560])).
% 1.64/1.86 tff(5562,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(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))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(5563,plain,
% 1.64/1.86 (((~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))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(5564,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), 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)))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[5563])).
% 1.64/1.86 tff(5565,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), 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))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[5564, 5562])).
% 1.64/1.86 tff(5566,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), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(5567,plain,
% 1.64/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[5566, 5565])).
% 1.64/1.86 tff(5568,plain,
% 1.64/1.86 (~r(s(s(elem!1)), s(elem!1))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[5567, 45, 5561, 5559])).
% 1.64/1.86 tff(5569,plain,
% 1.64/1.86 ((s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4835, 21, 5568])).
% 1.64/1.86 tff(5570,plain,
% 1.64/1.86 (s(s(elem!1)) = s(elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[5569, 5555])).
% 1.64/1.86 tff(5571,plain,
% 1.64/1.86 (s(s(elem!1)) = s(s(z))),
% 1.64/1.86 inference(transitivity,[status(thm)],[5570, 5482])).
% 1.64/1.86 tff(5572,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4261, 5571])).
% 1.64/1.86 tff(5573,plain,((s(s(elem!1)) = elem!1) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | b(z, elem!1) | b(s(z), z) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(5574,plain,
% 1.64/1.86 (b(z, elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[5573, 5238, 325, 2718, 164, 2106, 4264])).
% 1.64/1.86 tff(5575,plain,
% 1.64/1.86 (~(elem!1 = z)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4554, 5239])).
% 1.64/1.86 tff(5576,plain,
% 1.64/1.86 (~r(s(z), s(s(s(elem!1))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[5249, 1664, 272, 325, 2106])).
% 1.64/1.86 tff(5577,plain,
% 1.64/1.86 (b(s(z), s(s(s(elem!1))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[339, 5576])).
% 1.64/1.86 tff(5578,plain,
% 1.64/1.86 (~b(s(z), s(s(elem!1)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[5257, 128, 2106, 5577, 2718])).
% 1.64/1.86 tff(5579,plain,
% 1.64/1.86 (r(s(z), s(s(elem!1)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[117, 5578])).
% 1.64/1.86 tff(5580,plain,
% 1.64/1.86 (~r(z, s(s(elem!1)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1383, 5579, 272])).
% 1.64/1.86 tff(5581,plain,
% 1.64/1.86 (b(z, s(s(elem!1)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[160, 5580])).
% 1.64/1.86 tff(5582,plain,
% 1.64/1.86 (~r(s(s(elem!1)), z)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1962, 325, 272])).
% 1.64/1.86 tff(5583,plain,
% 1.64/1.86 (b(s(s(elem!1)), z)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[2018, 21, 154, 5582])).
% 1.64/1.86 tff(5584,plain,
% 1.64/1.86 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[2176, 27, 325, 1664])).
% 1.64/1.86 tff(5585,plain,
% 1.64/1.86 (b(s(s(s(s(elem!1)))), s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1828, 5584])).
% 1.64/1.86 tff(5586,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(5587,plain,
% 1.64/1.86 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(5588,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[5587])).
% 1.64/1.86 tff(5589,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[5588, 5586])).
% 1.64/1.86 tff(5590,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(5591,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[5590, 5589])).
% 1.64/1.86 tff(5592,plain,
% 1.64/1.86 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[5591, 128, 5577, 2718, 5585])).
% 1.64/1.86 tff(5593,plain,
% 1.64/1.86 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1856, 5592, 2649])).
% 1.64/1.86 tff(5594,plain,
% 1.64/1.86 (~r(elem!1, z)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[569, 45, 313, 27])).
% 1.64/1.86 tff(5595,plain,
% 1.64/1.86 (b(elem!1, z)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[574, 5594, 5065])).
% 1.64/1.86 tff(5596,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[5109, 5595, 4959, 498, 2006])).
% 1.64/1.86 tff(5597,plain,((~r(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (elem!1 = z) | (s(s(elem!1)) = elem!1) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(5598,plain,
% 1.64/1.86 (~r(elem!1, s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[5597, 5583, 498, 5065, 1086, 27, 325])).
% 1.64/1.86 tff(5599,plain,
% 1.64/1.86 (b(elem!1, s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[305, 5598, 5008])).
% 1.64/1.86 tff(5600,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(5601,plain,
% 1.64/1.86 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z))) <=> ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(5602,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[5601])).
% 1.64/1.86 tff(5603,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[5602, 5600])).
% 1.64/1.86 tff(5604,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(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(5605,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[5604, 5603])).
% 1.64/1.87 tff(5606,plain,
% 1.64/1.87 (~b(s(s(elem!1)), elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5605, 128, 498, 5599, 5583, 2106, 5577])).
% 1.64/1.87 tff(5607,plain,
% 1.64/1.87 (r(s(s(elem!1)), elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1934, 5606, 1086])).
% 1.64/1.87 tff(5608,plain,
% 1.64/1.87 (~(s(s(s(elem!1))) = elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5268, 5606, 2106])).
% 1.64/1.87 tff(5609,plain,
% 1.64/1.87 (r(s(s(s(elem!1))), elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[742, 5608, 5241])).
% 1.64/1.87 tff(5610,plain,
% 1.64/1.87 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[3820, 5609, 5607])).
% 1.64/1.87 tff(5611,plain,
% 1.64/1.87 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[889, 5610, 4492])).
% 1.64/1.87 tff(5612,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(5613,plain,
% 1.64/1.87 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(5614,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[5613])).
% 1.64/1.87 tff(5615,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[5614, 5612])).
% 1.64/1.87 tff(5616,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(5617,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z)))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[5616, 5615])).
% 1.64/1.87 tff(5618,plain,
% 1.64/1.87 ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5617, 128, 5581, 2106, 2718])).
% 1.64/1.87 tff(5619,plain,
% 1.64/1.87 (~b(s(s(s(elem!1))), z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5618, 5611])).
% 1.64/1.87 tff(5620,plain,
% 1.64/1.87 (r(s(s(s(elem!1))), z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5301, 5619])).
% 1.64/1.87 tff(5621,plain,
% 1.64/1.87 (~r(s(s(s(s(elem!1)))), z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1874, 5620, 5593])).
% 1.64/1.87 tff(5622,plain,
% 1.64/1.87 (b(s(s(s(s(elem!1)))), z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[2081, 5621])).
% 1.64/1.87 tff(5623,plain,
% 1.64/1.87 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[2092, 5622, 5583, 5581])).
% 1.64/1.87 tff(5624,plain,
% 1.64/1.87 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1897, 5623, 1664])).
% 1.64/1.87 tff(5625,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(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(5626,plain,
% 1.64/1.87 (((~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(5627,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(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[5626])).
% 1.64/1.87 tff(5628,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(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.64/1.87 inference(transitivity,[status(thm)],[5627, 5625])).
% 1.64/1.87 tff(5629,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(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(5630,plain,
% 1.64/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[5629, 5628])).
% 1.64/1.87 tff(5631,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5630, 45, 1004, 2450, 520])).
% 1.64/1.87 tff(5632,plain,((~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(5633,plain,
% 1.64/1.87 (~r(elem!1, z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5632, 5609, 5620])).
% 1.64/1.87 tff(5634,plain,
% 1.64/1.87 (b(elem!1, z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[574, 5633, 5065])).
% 1.64/1.87 tff(5635,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(5636,plain,
% 1.64/1.87 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(5637,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1))))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[5636])).
% 1.64/1.87 tff(5638,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[5637, 5635])).
% 1.64/1.87 tff(5639,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(5640,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[5639, 5638])).
% 1.64/1.87 tff(5641,plain,
% 1.64/1.87 ((~b(elem!1, z)) | (~b(elem!1, s(s(elem!1))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5640, 128, 498, 5599, 5583])).
% 1.64/1.87 tff(5642,plain,
% 1.64/1.87 (~b(elem!1, s(s(elem!1)))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5641, 5634])).
% 1.64/1.87 tff(5643,plain,
% 1.64/1.87 (r(elem!1, s(s(elem!1)))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[2371, 5642, 2344])).
% 1.64/1.87 tff(5644,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(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(5645,plain,
% 1.64/1.87 (((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(5646,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(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[5645])).
% 1.64/1.87 tff(5647,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(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[5646, 5644])).
% 1.64/1.87 tff(5648,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(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(5649,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(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[5648, 5647])).
% 1.64/1.87 tff(5650,plain,
% 1.64/1.87 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5649, 45, 5643, 5624])).
% 1.64/1.87 tff(5651,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(5652,plain,
% 1.64/1.87 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(5653,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[5652])).
% 1.64/1.87 tff(5654,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[5653, 5651])).
% 1.64/1.87 tff(5655,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(5656,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[5655, 5654])).
% 1.64/1.87 tff(5657,plain,
% 1.64/1.87 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5656, 128, 5599, 5577, 2718, 5585])).
% 1.64/1.87 tff(5658,plain,
% 1.64/1.87 ((s(s(s(s(elem!1)))) = elem!1) | r(s(s(s(s(elem!1)))), elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5088, 21, 5657])).
% 1.64/1.87 tff(5659,plain,
% 1.64/1.87 (s(s(s(s(elem!1)))) = elem!1),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5658, 5650])).
% 1.64/1.87 tff(5660,plain,
% 1.64/1.87 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[5659])).
% 1.64/1.87 tff(5661,plain,
% 1.64/1.87 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 1.64/1.87 inference(transitivity,[status(thm)],[5660, 225])).
% 1.64/1.87 tff(5662,plain,
% 1.64/1.87 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[5661])).
% 1.64/1.87 tff(5663,plain,
% 1.64/1.87 (~(s(s(z)) = elem!1)),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[239, 5662])).
% 1.64/1.87 tff(5664,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(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(s(elem!1)), s(z))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(5665,plain,
% 1.64/1.87 (((~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(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(5666,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(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(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z)))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[5665])).
% 1.64/1.87 tff(5667,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(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(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[5666, 5664])).
% 1.64/1.87 tff(5668,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(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(5669,plain,
% 1.64/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z)))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[5668, 5667])).
% 1.64/1.87 tff(5670,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5669, 45, 325, 2349, 1340])).
% 1.64/1.87 tff(5671,plain,((~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(5672,plain,
% 1.64/1.87 (~r(s(z), elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5671, 5607, 325])).
% 1.64/1.87 tff(5673,plain,
% 1.64/1.87 (b(s(z), elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[665, 5672, 1610])).
% 1.64/1.87 tff(5674,plain,
% 1.64/1.87 (~b(z, s(s(z)))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[3026, 591, 498, 297, 922])).
% 1.64/1.87 tff(5675,plain,
% 1.64/1.87 (r(z, s(s(z)))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[516, 5674])).
% 1.64/1.87 tff(5676,plain,
% 1.64/1.87 (~b(s(s(z)), s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1337, 591, 498, 272, 297, 577])).
% 1.64/1.87 tff(5677,plain,
% 1.64/1.87 (r(s(s(z)), s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[86, 5676])).
% 1.64/1.87 tff(5678,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[2946, 5677, 5675, 27])).
% 1.64/1.87 tff(5679,plain,((~b(s(s(z)), elem!1)) | (~r(z, s(z))) | (~b(z, elem!1)) | (~r(s(z), z)) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(5680,plain,
% 1.64/1.87 (~b(s(s(z)), elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5679, 27, 498, 272, 5599, 5634, 5673])).
% 1.64/1.87 tff(5681,plain,
% 1.64/1.87 (r(s(s(z)), elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[370, 5680, 5663])).
% 1.64/1.87 tff(5682,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)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(5683,plain,
% 1.64/1.87 (((~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(5684,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)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(elem!1))))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[5683])).
% 1.64/1.87 tff(5685,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)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[5684, 5682])).
% 1.64/1.87 tff(5686,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)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(5687,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)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(elem!1))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[5686, 5685])).
% 1.64/1.87 tff(5688,plain,
% 1.64/1.87 (~r(s(s(z)), s(s(elem!1)))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5687, 45, 325, 5607, 5681])).
% 1.64/1.87 tff(5689,plain,
% 1.64/1.87 ((s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1)))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[138, 21, 5688])).
% 1.64/1.87 tff(5690,plain,
% 1.64/1.87 (b(s(s(z)), s(s(elem!1)))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5689, 34])).
% 1.64/1.87 tff(5691,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(z)), elem!1)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(5692,plain,
% 1.64/1.87 (((~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), s(s(z))))) <=> ((~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(5693,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(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), elem!1))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[5692])).
% 1.64/1.88 tff(5694,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(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.64/1.88 inference(transitivity,[status(thm)],[5693, 5691])).
% 1.64/1.88 tff(5695,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(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(5696,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(z)), elem!1)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), elem!1))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[5695, 5694])).
% 1.64/1.88 tff(5697,plain,
% 1.64/1.88 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5696, 45, 5609, 5681])).
% 1.64/1.88 tff(5698,plain,
% 1.64/1.88 (b(s(s(s(elem!1))), s(s(z)))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4350, 21, 5697, 283])).
% 1.64/1.88 tff(5699,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), 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(X0, 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(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(5700,plain,
% 1.64/1.88 (((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(5701,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[5700])).
% 1.64/1.88 tff(5702,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[5701, 5699])).
% 1.64/1.88 tff(5703,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(5704,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[5703, 5702])).
% 1.64/1.88 tff(5705,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5704, 128, 5581, 5583, 5611, 5698, 5690])).
% 1.64/1.88 tff(5706,plain,((~r(z, s(z))) | (s(s(elem!1)) = s(s(z))) | (~r(s(s(elem!1)), s(z))) | (~b(z, elem!1)) | (~r(s(z), z)) | (elem!1 = z) | (s(z) = elem!1) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | b(s(s(s(elem!1))), elem!1) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(5707,plain,
% 1.64/1.88 (~r(z, s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5706, 1610, 325, 498, 272, 5065, 1, 2106, 2718, 5241, 1086])).
% 1.64/1.88 tff(5708,plain,
% 1.64/1.88 (b(z, s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[415, 5707])).
% 1.64/1.88 tff(5709,plain,
% 1.64/1.88 (~b(s(s(s(elem!1))), z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4498, 128, 5708, 5577, 2718])).
% 1.64/1.88 tff(5710,plain,
% 1.64/1.88 (r(s(s(s(elem!1))), z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5301, 5709])).
% 1.64/1.88 tff(5711,plain,
% 1.64/1.88 (~r(s(s(elem!1)), elem!1)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4957, 45, 325, 5354])).
% 1.64/1.88 tff(5712,plain,
% 1.64/1.88 (b(s(s(elem!1)), elem!1)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1934, 5711, 1086])).
% 1.64/1.88 tff(5713,plain,
% 1.64/1.88 (~r(elem!1, z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5632, 5352, 520])).
% 1.64/1.88 tff(5714,plain,
% 1.64/1.88 (b(elem!1, z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[574, 5713, 5065])).
% 1.64/1.88 tff(5715,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))) | (~b(z, elem!1)))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(5716,plain,
% 1.64/1.88 (((~b(z, elem!1)) | (~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(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(5717,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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(X0, 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(elem!1)))) | (~b(z, elem!1))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[5716])).
% 1.64/1.88 tff(5718,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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(X0, 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(elem!1)))) | (~b(z, elem!1)))),
% 1.64/1.88 inference(transitivity,[status(thm)],[5717, 5715])).
% 1.64/1.88 tff(5719,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~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)))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(5720,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[5719, 5718])).
% 1.64/1.88 tff(5721,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5720, 128, 498, 5714, 453, 5712])).
% 1.64/1.88 tff(5722,plain,(b(elem!1, s(z)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (s(s(elem!1)) = elem!1) | (~r(s(s(elem!1)), s(z))) | (elem!1 = z) | (~r(s(s(s(elem!1))), z)) | b(s(s(s(elem!1))), elem!1) | (elem!1 = s(z)) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(5723,plain,
% 1.64/1.88 (b(elem!1, s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5722, 5710, 5581, 1086, 325, 5065, 498, 5241, 5008, 2718])).
% 1.64/1.88 tff(5724,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(5725,plain,
% 1.64/1.88 (((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1))) <=> ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(5726,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[5725])).
% 1.64/1.88 tff(5727,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[5726, 5724])).
% 1.64/1.88 tff(5728,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(5729,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[5728, 5727])).
% 1.64/1.88 tff(5730,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5729, 128, 498, 5723, 5708, 5577, 2718])).
% 1.64/1.88 tff(5731,plain,((s(z) = elem!1) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (s(s(elem!1)) = elem!1) | (~r(s(s(elem!1)), s(z))) | (elem!1 = z) | b(s(s(s(elem!1))), elem!1) | (~r(s(z), z)) | (s(s(elem!1)) = s(s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(5732,plain,
% 1.64/1.88 (s(z) = elem!1),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5731, 5241, 2718, 1086, 325, 5065, 498, 272, 1, 2106])).
% 1.64/1.88 tff(5733,plain,
% 1.64/1.88 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
% 1.64/1.88 inference(monotonicity,[status(thm)],[5732])).
% 1.64/1.88 tff(5734,plain,
% 1.64/1.88 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(z))),
% 1.64/1.88 inference(symmetry,[status(thm)],[5733])).
% 1.64/1.88 tff(5735,plain,
% 1.64/1.88 ((~b(s(s(s(elem!1))), elem!1)) <=> (~b(s(s(s(elem!1))), s(z)))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[5734])).
% 1.64/1.88 tff(5736,plain,
% 1.64/1.88 (~b(s(s(s(elem!1))), s(z))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[5241, 5735])).
% 1.64/1.88 tff(5737,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[2718, 5736])).
% 1.64/1.88 tff(5738,plain,(b(s(s(s(elem!1))), elem!1) | (~b(s(s(s(elem!1))), s(z))) | (s(s(elem!1)) = elem!1) | (~r(s(s(elem!1)), s(z))) | (elem!1 = z) | (~b(z, elem!1)) | (~r(s(z), z)) | (s(s(elem!1)) = s(s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(5739,plain,
% 1.64/1.88 (b(s(s(s(elem!1))), elem!1)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5738, 5238, 2718, 325, 5575, 5574, 171, 5240, 2106])).
% 1.64/1.88 tff(5740,plain,
% 1.64/1.88 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1089, 5238])).
% 1.64/1.88 tff(5741,plain,
% 1.64/1.88 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1073, 5740])).
% 1.64/1.88 tff(5742,plain,
% 1.64/1.88 (~r(s(z), s(s(s(elem!1))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5249, 5741, 171, 325, 2106])).
% 1.64/1.88 tff(5743,plain,
% 1.64/1.88 (b(s(z), s(s(s(elem!1))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[339, 5742])).
% 1.64/1.88 tff(5744,plain,
% 1.64/1.88 (~b(s(z), s(s(elem!1)))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5257, 128, 2106, 5743, 2718])).
% 1.64/1.88 tff(5745,plain,
% 1.64/1.88 (r(s(z), s(s(elem!1)))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[117, 5744])).
% 1.64/1.88 tff(5746,plain,
% 1.64/1.88 (~r(z, s(s(elem!1)))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1383, 5745, 171])).
% 1.64/1.88 tff(5747,plain,
% 1.64/1.88 (b(z, s(s(elem!1)))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[160, 5746])).
% 1.64/1.88 tff(5748,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z, elem!1)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z, elem!1)) | (~b(elem!1, s(s(elem!1)))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(5749,plain,
% 1.64/1.88 (((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(5750,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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, s(s(elem!1)))) | (~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(X0, 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(z, elem!1)) | (~b(elem!1, s(s(elem!1))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[5749])).
% 1.64/1.88 tff(5751,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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, s(s(elem!1)))) | (~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(X0, 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(z, elem!1)) | (~b(elem!1, s(s(elem!1)))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[5750, 5748])).
% 1.64/1.88 tff(5752,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(5753,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[5752, 5751])).
% 1.64/1.88 tff(5754,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5753, 128, 498, 453, 4959, 4951])).
% 1.64/1.88 tff(5755,plain,((~r(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))) | (s(s(elem!1)) = elem!1) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(5756,plain,
% 1.64/1.88 (~r(elem!1, s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5755, 5574, 5747, 5238, 325])).
% 1.64/1.88 tff(5757,plain,
% 1.64/1.88 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1065, 5741])).
% 1.64/1.88 tff(5758,plain,
% 1.64/1.88 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[693, 5757])).
% 1.64/1.88 tff(5759,plain,
% 1.64/1.88 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[700, 5758])).
% 1.64/1.88 tff(5760,plain,
% 1.64/1.88 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1820, 5759, 4264])).
% 1.64/1.88 tff(5761,plain,
% 1.64/1.88 (s(elem!1) = s(s(z))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[1633])).
% 1.64/1.88 tff(5762,plain,
% 1.64/1.88 (s(s(elem!1)) = s(s(s(z)))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[5761])).
% 1.64/1.88 tff(5763,plain,
% 1.64/1.88 (s(s(s(z))) = s(s(elem!1))),
% 1.64/1.88 inference(symmetry,[status(thm)],[5762])).
% 1.64/1.88 tff(5764,plain,
% 1.64/1.88 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[5762])).
% 1.64/1.88 tff(5765,plain,
% 1.64/1.88 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[5764])).
% 1.64/1.88 tff(5766,plain,
% 1.64/1.88 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 1.64/1.88 inference(symmetry,[status(thm)],[5765])).
% 1.64/1.88 tff(5767,plain,
% 1.64/1.88 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[5766, 5763])).
% 1.64/1.88 tff(5768,plain,
% 1.64/1.88 (b(s(s(s(s(elem!1)))), s(s(elem!1))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.64/1.88 inference(symmetry,[status(thm)],[5767])).
% 1.64/1.88 tff(5769,plain,
% 1.64/1.88 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[5766])).
% 1.64/1.88 tff(5770,plain,
% 1.64/1.88 ((~b(s(s(s(s(s(z))))), s(z))) <=> (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[5769])).
% 1.64/1.88 tff(5771,plain,
% 1.64/1.88 ((z = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = z)),
% 1.64/1.88 inference(commutativity,[status(thm)],[])).
% 1.64/1.88 tff(5772,plain,
% 1.64/1.88 ((s(s(s(s(s(z))))) = z) <=> (z = s(s(s(s(s(z))))))),
% 1.64/1.88 inference(symmetry,[status(thm)],[5771])).
% 1.64/1.88 tff(5773,plain,
% 1.64/1.88 ((~(s(s(s(s(s(z))))) = z)) <=> (~(z = s(s(s(s(s(z)))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[5772])).
% 1.64/1.88 tff(5774,plain,
% 1.64/1.88 (~(z = s(s(s(s(s(z))))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[1036, 5773])).
% 1.64/1.88 tff(5775,plain,
% 1.64/1.88 (r(z, s(s(s(s(s(z)))))) <=> r(z, s(s(s(s(elem!1)))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[5766])).
% 1.64/1.88 tff(5776,plain,
% 1.64/1.88 (r(z, s(s(s(s(elem!1))))) <=> r(z, s(s(s(s(s(z))))))),
% 1.64/1.88 inference(symmetry,[status(thm)],[5775])).
% 1.64/1.88 tff(5777,plain,
% 1.64/1.88 ((~r(z, s(s(s(s(elem!1)))))) <=> (~r(z, s(s(s(s(s(z)))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[5776])).
% 1.64/1.88 tff(5778,plain,
% 1.64/1.88 (b(z, s(z))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[498, 1634])).
% 1.64/1.88 tff(5779,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(5780,plain,
% 1.64/1.88 (((~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(5781,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1)))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[5780])).
% 1.64/1.88 tff(5782,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[5781, 5779])).
% 1.64/1.88 tff(5783,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(5784,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1)))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[5783, 5782])).
% 1.64/1.88 tff(5785,plain,
% 1.64/1.88 ((~b(z, s(z))) | (~b(z, s(s(s(elem!1)))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5784, 128, 498, 549, 2659, 2718])).
% 1.64/1.88 tff(5786,plain,
% 1.64/1.88 (~b(z, s(s(s(elem!1))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5785, 5778])).
% 1.64/1.88 tff(5787,plain,
% 1.64/1.88 (r(z, s(s(s(elem!1))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[858, 5786])).
% 1.64/1.88 tff(5788,plain,
% 1.64/1.88 (~r(z, s(s(s(s(elem!1)))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1790, 5787, 1772])).
% 1.64/1.88 tff(5789,plain,
% 1.64/1.88 (~r(z, s(s(s(s(s(z))))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[5788, 5777])).
% 1.64/1.88 tff(5790,plain,
% 1.64/1.88 (((~![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)))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(5791,plain,
% 1.64/1.88 ((~![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)))))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(5792,plain,
% 1.64/1.89 ((~![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))))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[5791, 5790])).
% 1.64/1.89 tff(5793,plain,
% 1.64/1.89 ((z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z))))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5792, 21, 5789])).
% 1.64/1.89 tff(5794,plain,
% 1.64/1.89 (b(z, s(s(s(s(s(z))))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5793, 5774])).
% 1.64/1.89 tff(5795,plain,
% 1.64/1.89 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.64/1.89 inference(symmetry,[status(thm)],[5764])).
% 1.64/1.89 tff(5796,plain,
% 1.64/1.89 (b(s(z), s(s(s(s(z))))) <=> b(s(z), s(s(s(elem!1))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5795])).
% 1.64/1.89 tff(5797,plain,
% 1.64/1.89 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(s(s(s(z)))))),
% 1.64/1.89 inference(symmetry,[status(thm)],[5796])).
% 1.64/1.89 tff(5798,plain,
% 1.64/1.89 (b(s(z), s(s(s(s(z)))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[549, 5797])).
% 1.64/1.89 tff(5799,plain,
% 1.64/1.89 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5764])).
% 1.64/1.89 tff(5800,plain,
% 1.64/1.89 (b(s(s(s(s(z)))), s(z))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[2718, 5799])).
% 1.64/1.89 tff(5801,assumption,(b(s(s(s(s(s(z))))), s(z))), introduced(assumption)).
% 1.64/1.89 tff(5802,assumption,(b(z, s(s(s(s(s(z))))))), introduced(assumption)).
% 1.64/1.89 tff(5803,assumption,(b(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 1.64/1.89 tff(5804,assumption,(b(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.64/1.89 tff(5805,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(5806,plain,
% 1.64/1.89 (((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(5807,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5806])).
% 1.64/1.89 tff(5808,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[5807, 5805])).
% 1.64/1.89 tff(5809,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(5810,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[5809, 5808])).
% 1.64/1.89 tff(5811,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5810, 128, 550, 5804, 5803, 5802, 5801])).
% 1.64/1.89 tff(5812,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(5813,plain,
% 1.64/1.89 (~b(s(s(s(s(s(z))))), s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5812, 5778, 5800, 5798, 5794])).
% 1.64/1.89 tff(5814,plain,
% 1.64/1.89 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[5813, 5770])).
% 1.64/1.89 tff(5815,plain,
% 1.64/1.89 (r(s(s(s(s(elem!1)))), s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1828, 5814])).
% 1.64/1.89 tff(5816,plain,
% 1.64/1.89 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[2141, 5815, 325])).
% 1.64/1.89 tff(5817,plain,
% 1.64/1.89 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1897, 5816, 1063])).
% 1.64/1.89 tff(5818,plain,
% 1.64/1.89 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[5817, 5768])).
% 1.64/1.89 tff(5819,plain,
% 1.64/1.89 (b(z, s(s(s(z)))) <=> b(z, s(s(elem!1)))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5763])).
% 1.64/1.89 tff(5820,plain,
% 1.64/1.89 (b(z, s(s(elem!1))) <=> b(z, s(s(s(z))))),
% 1.64/1.89 inference(symmetry,[status(thm)],[5819])).
% 1.64/1.89 tff(5821,plain,
% 1.64/1.89 (b(z, s(s(s(z))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[453, 5820])).
% 1.64/1.89 tff(5822,plain,
% 1.64/1.89 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5763, 5795])).
% 1.64/1.89 tff(5823,plain,
% 1.64/1.89 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.89 inference(symmetry,[status(thm)],[5822])).
% 1.64/1.89 tff(5824,plain,
% 1.64/1.89 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[2106, 5823])).
% 1.64/1.89 tff(5825,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(5826,plain,
% 1.64/1.89 (((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(5827,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z)))))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5826])).
% 1.64/1.89 tff(5828,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[5827, 5825])).
% 1.64/1.89 tff(5829,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(5830,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z)))))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[5829, 5828])).
% 1.64/1.89 tff(5831,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5830, 128, 5778, 5800, 5824, 5821, 5794, 5818])).
% 1.64/1.89 tff(5832,plain,((~(elem!1 = s(z))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(5833,plain,
% 1.64/1.89 (~(elem!1 = s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5832, 5741, 325, 5747, 2106, 5743, 5760, 5574, 5739, 2718])).
% 1.64/1.89 tff(5834,plain,
% 1.64/1.89 (b(elem!1, s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[305, 5833, 5756])).
% 1.64/1.89 tff(5835,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(5836,plain,
% 1.64/1.89 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(5837,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5836])).
% 1.64/1.89 tff(5838,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[5837, 5835])).
% 1.64/1.89 tff(5839,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(5840,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[5839, 5838])).
% 1.64/1.89 tff(5841,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5840, 128, 5834, 5743, 5739, 2718])).
% 1.64/1.89 tff(5842,plain,(b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(5843,plain,
% 1.64/1.89 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5842, 293, 197, 5227, 164])).
% 1.64/1.89 tff(5844,plain,
% 1.64/1.89 (~r(s(z), s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5249, 1063, 272, 325, 2106])).
% 1.64/1.89 tff(5845,plain,
% 1.64/1.89 (b(s(z), s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[339, 5844])).
% 1.64/1.89 tff(5846,plain,
% 1.64/1.89 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4479, 128, 5845, 1842, 2718])).
% 1.64/1.89 tff(5847,plain,
% 1.64/1.89 (r(s(s(s(s(elem!1)))), s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1828, 5846])).
% 1.64/1.89 tff(5848,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(5849,plain,
% 1.64/1.89 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(5850,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5849])).
% 1.64/1.89 tff(5851,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[5850, 5848])).
% 1.64/1.89 tff(5852,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(5853,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[5852, 5851])).
% 1.64/1.89 tff(5854,plain,
% 1.64/1.89 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5853, 128, 2106, 5845, 1842, 2718])).
% 1.64/1.89 tff(5855,plain,
% 1.64/1.89 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1897, 5854, 1063])).
% 1.64/1.89 tff(5856,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[2141, 5855, 5847, 325])).
% 1.64/1.89 tff(5857,plain,((s(s(s(s(elem!1)))) = s(s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(5858,plain,
% 1.64/1.89 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5857, 293, 5227, 5843, 197, 171])).
% 1.64/1.89 tff(5859,plain,
% 1.64/1.89 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1073, 5858])).
% 1.64/1.89 tff(5860,plain,
% 1.64/1.89 (s(s(elem!1)) = elem!1),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1089, 5859])).
% 1.64/1.89 tff(5861,plain,
% 1.64/1.89 (s(s(s(elem!1))) = s(elem!1)),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5860])).
% 1.64/1.89 tff(5862,plain,
% 1.64/1.89 (b(s(s(s(elem!1))), elem!1) <=> b(s(elem!1), elem!1)),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5861])).
% 1.64/1.89 tff(5863,plain,
% 1.64/1.89 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), elem!1)),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5860])).
% 1.64/1.89 tff(5864,plain,
% 1.64/1.89 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(elem!1), elem!1)),
% 1.64/1.89 inference(transitivity,[status(thm)],[5863, 5862])).
% 1.64/1.89 tff(5865,plain,
% 1.64/1.89 (r(s(s(elem!1)), s(z)) <=> r(elem!1, s(z))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5860])).
% 1.64/1.89 tff(5866,plain,
% 1.64/1.89 (r(elem!1, s(z))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[293, 5865])).
% 1.64/1.89 tff(5867,plain,
% 1.64/1.89 (r(s(s(s(elem!1))), s(z)) <=> r(s(elem!1), s(z))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5861])).
% 1.64/1.89 tff(5868,plain,
% 1.64/1.89 ((~r(s(s(s(elem!1))), s(z))) <=> (~r(s(elem!1), s(z)))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5867])).
% 1.64/1.89 tff(5869,plain,
% 1.64/1.89 (~r(s(elem!1), s(z))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[172, 5868])).
% 1.64/1.89 tff(5870,plain,
% 1.64/1.89 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[316, 5869, 5866, 5860])).
% 1.64/1.89 tff(5871,plain,
% 1.64/1.89 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[803, 5870])).
% 1.64/1.89 tff(5872,plain,
% 1.64/1.89 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(elem!1))), elem!1)),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5860])).
% 1.64/1.89 tff(5873,plain,
% 1.64/1.89 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.64/1.89 inference(symmetry,[status(thm)],[5872])).
% 1.64/1.89 tff(5874,plain,
% 1.64/1.89 (s(elem!1) = s(s(s(elem!1)))),
% 1.64/1.89 inference(symmetry,[status(thm)],[5861])).
% 1.64/1.89 tff(5875,plain,
% 1.64/1.89 (r(s(elem!1), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5874])).
% 1.64/1.89 tff(5876,plain,
% 1.64/1.89 (r(s(elem!1), elem!1) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.64/1.89 inference(transitivity,[status(thm)],[5875, 5873])).
% 1.64/1.89 tff(5877,plain,
% 1.64/1.89 ((~r(s(elem!1), elem!1)) <=> (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5876])).
% 1.64/1.89 tff(5878,plain,
% 1.64/1.89 (~r(s(s(elem!1)), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1962, 293, 171])).
% 1.64/1.89 tff(5879,plain,
% 1.64/1.89 (~r(elem!1, z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1534, 5860, 5878])).
% 1.64/1.89 tff(5880,plain,
% 1.64/1.89 ((s(s(elem!1)) = z) <=> (elem!1 = z)),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5860])).
% 1.64/1.89 tff(5881,plain,
% 1.64/1.89 ((s(s(elem!1)) = z) <=> (z = elem!1)),
% 1.64/1.89 inference(transitivity,[status(thm)],[5880, 247])).
% 1.64/1.89 tff(5882,plain,
% 1.64/1.89 ((s(s(elem!1)) = z) <=> (elem!1 = z)),
% 1.64/1.89 inference(transitivity,[status(thm)],[5881, 459])).
% 1.64/1.89 tff(5883,plain,
% 1.64/1.89 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = z))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5882])).
% 1.64/1.89 tff(5884,plain,
% 1.64/1.89 (~(elem!1 = z)),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[154, 5883])).
% 1.64/1.89 tff(5885,plain,
% 1.64/1.89 (b(elem!1, z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[574, 5884, 5879])).
% 1.64/1.89 tff(5886,plain,
% 1.64/1.89 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5861])).
% 1.64/1.89 tff(5887,plain,
% 1.64/1.89 (s(s(s(s(elem!1)))) = elem!1),
% 1.64/1.89 inference(transitivity,[status(thm)],[5886, 5860])).
% 1.64/1.89 tff(5888,plain,
% 1.64/1.89 (r(s(s(s(s(elem!1)))), z) <=> r(elem!1, z)),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5887])).
% 1.64/1.89 tff(5889,plain,
% 1.64/1.89 (r(elem!1, z) <=> r(s(s(s(s(elem!1)))), z)),
% 1.64/1.89 inference(symmetry,[status(thm)],[5888])).
% 1.64/1.89 tff(5890,plain,
% 1.64/1.89 ((~r(elem!1, z)) <=> (~r(s(s(s(s(elem!1)))), z))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5889])).
% 1.64/1.89 tff(5891,plain,
% 1.64/1.89 (~r(s(s(s(s(elem!1)))), z)),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[5879, 5890])).
% 1.64/1.89 tff(5892,plain,
% 1.64/1.89 (b(s(s(s(s(elem!1)))), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[2081, 5891])).
% 1.64/1.89 tff(5893,plain,
% 1.64/1.89 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), elem!1)),
% 1.64/1.89 inference(monotonicity,[status(thm)],[199])).
% 1.64/1.89 tff(5894,plain,
% 1.64/1.89 (~b(z, s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[457, 455, 378])).
% 1.64/1.89 tff(5895,plain,
% 1.64/1.89 (r(z, s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[160, 5894])).
% 1.64/1.89 tff(5896,plain,
% 1.64/1.89 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4546, 5895, 1842, 2083])).
% 1.64/1.89 tff(5897,plain,
% 1.64/1.89 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[889, 5896, 1691])).
% 1.64/1.89 tff(5898,plain,
% 1.64/1.89 (b(s(s(s(elem!1))), elem!1)),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[5897, 5893])).
% 1.64/1.89 tff(5899,plain,
% 1.64/1.89 (~r(elem!1, s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4896, 1609, 27])).
% 1.64/1.89 tff(5900,plain,
% 1.64/1.89 (b(elem!1, s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[305, 5899, 295])).
% 1.64/1.89 tff(5901,plain,
% 1.64/1.89 (b(s(s(elem!1)), s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[300, 5900, 199])).
% 1.64/1.89 tff(5902,plain,
% 1.64/1.89 (~r(s(z), s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[97, 5895, 27])).
% 1.64/1.89 tff(5903,plain,
% 1.64/1.89 (b(s(z), s(s(elem!1)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[117, 5902])).
% 1.64/1.89 tff(5904,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[2726, 5903, 5901, 2106, 2718])).
% 1.64/1.89 tff(5905,plain,(b(z, elem!1) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~(s(s(elem!1)) = elem!1)) | (~r(z, s(z))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(5906,plain,
% 1.64/1.89 (~r(z, s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5905, 455, 2718, 2106, 199, 251])).
% 1.64/1.89 tff(5907,plain,
% 1.64/1.89 (b(z, s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[415, 5906])).
% 1.64/1.89 tff(5908,plain,
% 1.64/1.89 (r(z, elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1549, 455, 251])).
% 1.64/1.89 tff(5909,plain,
% 1.64/1.89 (~r(s(z), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1544, 5908, 171])).
% 1.64/1.89 tff(5910,plain,
% 1.64/1.89 (b(s(z), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[665, 5909, 257])).
% 1.64/1.89 tff(5911,plain,
% 1.64/1.89 (~b(s(s(s(elem!1))), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5473, 5910, 455, 2718, 164, 5907])).
% 1.64/1.89 tff(5912,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5911, 5898])).
% 1.64/1.89 tff(5913,plain,(b(z, elem!1) | (~(s(s(elem!1)) = elem!1)) | (~b(s(s(s(elem!1))), s(z))) | b(s(z), z) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(5914,plain,
% 1.64/1.89 (b(z, elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5913, 5860, 197, 164, 5871, 5843, 5892, 5227])).
% 1.64/1.89 tff(5915,plain,
% 1.64/1.89 (b(s(s(s(elem!1))), s(z)) <=> b(s(elem!1), s(z))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5861])).
% 1.64/1.89 tff(5916,plain,
% 1.64/1.89 (b(s(elem!1), s(z))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[197, 5915])).
% 1.64/1.89 tff(5917,plain,
% 1.64/1.89 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(elem!1))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5861])).
% 1.64/1.89 tff(5918,plain,
% 1.64/1.89 (b(z, s(s(elem!1))) <=> b(z, elem!1)),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5860])).
% 1.64/1.89 tff(5919,plain,
% 1.64/1.89 (b(z, elem!1) <=> b(z, s(s(elem!1)))),
% 1.64/1.89 inference(symmetry,[status(thm)],[5918])).
% 1.64/1.89 tff(5920,plain,
% 1.64/1.89 (b(z, s(s(elem!1)))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[5914, 5919])).
% 1.64/1.89 tff(5921,plain,
% 1.64/1.89 (b(s(s(s(elem!1))), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5301, 2447])).
% 1.64/1.89 tff(5922,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[3460, 1836, 5921, 2106, 453])).
% 1.64/1.89 tff(5923,plain,((~r(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(5924,plain,
% 1.64/1.89 (~r(s(z), s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5923, 5920, 5227, 171])).
% 1.64/1.89 tff(5925,plain,
% 1.64/1.89 (b(s(z), s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[339, 5924])).
% 1.64/1.89 tff(5926,plain,
% 1.64/1.89 (b(s(z), s(elem!1))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[5925, 5917])).
% 1.64/1.89 tff(5927,plain,
% 1.64/1.89 ((s(s(elem!1)) = s(z)) <=> (elem!1 = s(z))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5860])).
% 1.64/1.89 tff(5928,plain,
% 1.64/1.89 ((s(s(elem!1)) = s(z)) <=> (s(z) = elem!1)),
% 1.64/1.89 inference(transitivity,[status(thm)],[5927, 253])).
% 1.64/1.89 tff(5929,plain,
% 1.64/1.89 ((~(s(s(elem!1)) = s(z))) <=> (~(s(z) = elem!1))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5928])).
% 1.64/1.89 tff(5930,plain,
% 1.64/1.89 (~(s(z) = elem!1)),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[111, 5929])).
% 1.64/1.89 tff(5931,plain,
% 1.64/1.89 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(elem!1))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5861])).
% 1.64/1.89 tff(5932,plain,
% 1.64/1.89 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5860])).
% 1.64/1.89 tff(5933,plain,
% 1.64/1.89 (b(elem!1, s(s(s(elem!1))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[5227, 5932])).
% 1.64/1.89 tff(5934,plain,
% 1.64/1.89 (b(elem!1, s(elem!1))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[5933, 5931])).
% 1.64/1.89 tff(5935,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(5936,plain,
% 1.64/1.89 (((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(5937,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1)))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5936])).
% 1.64/1.89 tff(5938,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[5937, 5935])).
% 1.64/1.89 tff(5939,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(5940,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1)))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[5939, 5938])).
% 1.64/1.89 tff(5941,plain,
% 1.64/1.89 (~b(s(z), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5940, 128, 5934, 5926, 5916])).
% 1.64/1.89 tff(5942,plain,
% 1.64/1.89 (r(s(z), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[665, 5941, 5930])).
% 1.64/1.89 tff(5943,plain,
% 1.64/1.89 (~r(s(s(z)), s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1557, 5942, 171, 5860])).
% 1.64/1.89 tff(5944,plain,
% 1.64/1.89 (b(s(s(z)), s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[86, 5943])).
% 1.64/1.89 tff(5945,plain,
% 1.64/1.89 (~b(s(elem!1), s(s(z)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[469, 128, 5944, 5926, 5916])).
% 1.64/1.89 tff(5946,plain,
% 1.64/1.89 ((s(s(s(elem!1))) = s(s(z))) <=> (s(elem!1) = s(s(z)))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5861])).
% 1.64/1.89 tff(5947,plain,
% 1.64/1.89 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(elem!1) = s(s(z))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5946])).
% 1.64/1.89 tff(5948,plain,
% 1.64/1.89 (~(s(elem!1) = s(s(z)))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[283, 5947])).
% 1.64/1.89 tff(5949,plain,
% 1.64/1.89 (r(s(elem!1), s(s(z)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[473, 21, 5948, 5945])).
% 1.64/1.89 tff(5950,plain,
% 1.64/1.89 (r(z, s(s(s(elem!1)))) <=> r(z, s(elem!1))),
% 1.64/1.89 inference(symmetry,[status(thm)],[530])).
% 1.64/1.89 tff(5951,plain,
% 1.64/1.89 (b(z, s(s(elem!1))) <=> b(z, elem!1)),
% 1.64/1.89 inference(monotonicity,[status(thm)],[199])).
% 1.64/1.89 tff(5952,plain,
% 1.64/1.89 (b(z, elem!1) <=> b(z, s(s(elem!1)))),
% 1.64/1.89 inference(symmetry,[status(thm)],[5951])).
% 1.64/1.89 tff(5953,plain,
% 1.64/1.89 (b(z, s(s(elem!1)))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[498, 5952])).
% 1.64/1.89 tff(5954,assumption,(r(s(elem!1), s(s(z)))), introduced(assumption)).
% 1.64/1.89 tff(5955,plain,
% 1.64/1.89 (r(s(s(s(elem!1))), s(s(z)))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[5954, 463])).
% 1.64/1.89 tff(5956,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[905, 45, 1103, 3397, 5954])).
% 1.64/1.89 tff(5957,plain,((~r(s(s(z)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(5958,plain,
% 1.64/1.89 (~r(s(s(z)), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5957, 3397, 5954])).
% 1.64/1.89 tff(5959,plain,
% 1.64/1.89 (b(s(s(z)), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[370, 5958, 240])).
% 1.64/1.89 tff(5960,plain,
% 1.64/1.89 (~b(z, s(s(z)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5126, 128, 498, 577, 5959])).
% 1.64/1.89 tff(5961,plain,
% 1.64/1.89 (r(z, s(s(z)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[516, 5960])).
% 1.64/1.89 tff(5962,plain,
% 1.64/1.89 (~r(s(s(s(elem!1))), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[528, 5961, 5955])).
% 1.64/1.89 tff(5963,plain,
% 1.64/1.89 (b(s(s(s(elem!1))), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5301, 5962])).
% 1.64/1.89 tff(5964,plain,
% 1.64/1.89 (~b(z, s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[3460, 5963, 2106, 5953])).
% 1.64/1.89 tff(5965,plain,
% 1.64/1.89 (r(z, s(s(s(elem!1))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[858, 5964])).
% 1.64/1.89 tff(5966,plain,
% 1.64/1.89 (r(z, s(elem!1))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[5965, 5950])).
% 1.64/1.89 tff(5967,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), elem!1)) | (~r(z, s(s(z)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(z, s(s(z)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(z)))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(5968,plain,
% 1.74/1.90 (((~r(s(elem!1), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(z, s(s(z)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(z)))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(5969,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), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, s(s(z)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(z))))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[5968])).
% 1.74/1.90 tff(5970,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), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(z, s(s(z)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(z)))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[5969, 5967])).
% 1.74/1.90 tff(5971,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), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(5972,plain,
% 1.74/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(z, s(s(z)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(s(z))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[5971, 5970])).
% 1.74/1.90 tff(5973,plain,
% 1.74/1.90 (~r(z, s(elem!1))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[5972, 45, 5961, 3397, 5954])).
% 1.74/1.90 tff(5974,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[5973, 5966])).
% 1.74/1.90 tff(5975,plain,((~r(s(elem!1), elem!1)) | (~(s(s(elem!1)) = elem!1)) | (~r(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(5976,plain,
% 1.74/1.90 (~r(s(elem!1), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[5975, 5860, 5949, 5227, 5914, 5885])).
% 1.74/1.90 tff(5977,plain,
% 1.74/1.90 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[5976, 5877])).
% 1.74/1.90 tff(5978,plain,
% 1.74/1.90 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[889, 5977, 5871])).
% 1.74/1.90 tff(5979,plain,
% 1.74/1.90 (b(s(elem!1), elem!1)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[5978, 5864])).
% 1.74/1.90 tff(5980,plain,
% 1.74/1.90 (~(s(s(s(s(z)))) = elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[242, 5860])).
% 1.74/1.90 tff(5981,plain,
% 1.74/1.90 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[5887])).
% 1.74/1.90 tff(5982,plain,
% 1.74/1.90 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 1.74/1.90 inference(transitivity,[status(thm)],[5981, 225])).
% 1.74/1.90 tff(5983,plain,
% 1.74/1.90 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[5982])).
% 1.74/1.90 tff(5984,plain,
% 1.74/1.90 (~(s(s(z)) = elem!1)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[239, 5983])).
% 1.74/1.90 tff(5985,plain,
% 1.74/1.90 (~b(elem!1, s(z))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[300, 5860, 287])).
% 1.74/1.90 tff(5986,plain,
% 1.74/1.90 (~(s(s(s(elem!1))) = elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[5100, 5985, 197])).
% 1.74/1.90 tff(5987,plain,
% 1.74/1.90 ((~r(s(elem!1), elem!1)) <=> (~r(s(s(s(elem!1))), elem!1))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[5875])).
% 1.74/1.90 tff(5988,plain,
% 1.74/1.90 (~r(s(s(s(elem!1))), elem!1)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[5976, 5987])).
% 1.74/1.90 tff(5989,plain,
% 1.74/1.90 (b(s(s(s(elem!1))), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[742, 5988, 5986])).
% 1.74/1.90 tff(5990,plain,
% 1.74/1.90 (b(s(elem!1), z) <=> b(s(s(s(elem!1))), z)),
% 1.74/1.90 inference(monotonicity,[status(thm)],[5874])).
% 1.74/1.90 tff(5991,plain,
% 1.74/1.90 ((~b(s(elem!1), z)) <=> (~b(s(s(s(elem!1))), z))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[5990])).
% 1.74/1.90 tff(5992,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(5993,plain,
% 1.74/1.90 (((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(5994,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[5993])).
% 1.74/1.90 tff(5995,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)))),
% 1.74/1.90 inference(transitivity,[status(thm)],[5994, 5992])).
% 1.74/1.90 tff(5996,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(5997,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[5996, 5995])).
% 1.74/1.90 tff(5998,plain,
% 1.74/1.90 (~b(s(elem!1), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[5997, 128, 5914, 5885, 5979])).
% 1.74/1.90 tff(5999,plain,
% 1.74/1.90 (~b(s(s(s(elem!1))), z)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[5998, 5991])).
% 1.74/1.90 tff(6000,plain,
% 1.74/1.90 (r(s(s(s(elem!1))), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[5301, 5999])).
% 1.74/1.90 tff(6001,plain,
% 1.74/1.90 (~b(s(s(z)), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[5131, 6000, 5885, 5914, 5989])).
% 1.74/1.90 tff(6002,plain,
% 1.74/1.90 (r(s(s(z)), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[370, 6001, 5984])).
% 1.74/1.90 tff(6003,plain,
% 1.74/1.90 (~r(s(s(s(s(z)))), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1356, 6002, 171, 5942])).
% 1.74/1.90 tff(6004,plain,
% 1.74/1.90 (b(s(s(s(s(z)))), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[632, 6003, 5980])).
% 1.74/1.90 tff(6005,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(6006,plain,
% 1.74/1.90 (((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, 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(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(6007,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[6006])).
% 1.74/1.90 tff(6008,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[6007, 6005])).
% 1.74/1.90 tff(6009,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(6010,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z))))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[6009, 6008])).
% 1.74/1.90 tff(6011,plain,
% 1.74/1.90 (~b(s(elem!1), s(s(s(s(z)))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[6010, 128, 5914, 5885, 6004, 5979])).
% 1.74/1.90 tff(6012,plain,
% 1.74/1.90 (~(s(elem!1) = s(s(s(s(z)))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[761, 5948, 5860])).
% 1.74/1.90 tff(6013,plain,
% 1.74/1.90 (r(s(elem!1), s(s(s(s(z)))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[765, 21, 6012, 6011])).
% 1.74/1.90 tff(6014,plain,
% 1.74/1.90 (r(s(elem!1), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[728, 21, 109, 5998])).
% 1.74/1.90 tff(6015,plain,
% 1.74/1.90 (~b(s(s(s(s(z)))), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[583, 128, 5914, 5885, 6004])).
% 1.74/1.90 tff(6016,plain,
% 1.74/1.90 (r(s(s(s(s(z)))), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[589, 21, 586, 6015])).
% 1.74/1.90 tff(6017,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(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(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(6018,plain,
% 1.74/1.90 (((~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(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(6019,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(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(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[6018])).
% 1.74/1.90 tff(6020,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(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(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[6019, 6017])).
% 1.74/1.90 tff(6021,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(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)))))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(6022,plain,
% 1.74/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z))))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[6021, 6020])).
% 1.74/1.90 tff(6023,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[6022, 45, 6016, 6014, 6013])).
% 1.74/1.90 tff(6024,plain,(b(s(s(elem!1)), s(z)) | b(s(z), z) | r(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(6025,plain,
% 1.74/1.90 (b(s(s(elem!1)), s(z))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[6024, 172, 164])).
% 1.74/1.90 tff(6026,plain,
% 1.74/1.90 (~b(s(z), s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2726, 6025, 197, 5227])).
% 1.74/1.90 tff(6027,plain,
% 1.74/1.90 (r(s(z), s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[117, 6026])).
% 1.74/1.90 tff(6028,plain,
% 1.74/1.90 (~r(z, s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1383, 6027, 171])).
% 1.74/1.90 tff(6029,plain,
% 1.74/1.90 (b(z, s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[160, 6028])).
% 1.74/1.90 tff(6030,plain,
% 1.74/1.90 (~r(s(z), s(s(s(elem!1))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[5923, 6029, 5227, 171])).
% 1.74/1.90 tff(6031,plain,
% 1.74/1.90 (b(s(z), s(s(s(elem!1))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[339, 6030])).
% 1.74/1.90 tff(6032,plain,
% 1.74/1.90 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2132, 6031, 171, 5227, 6025, 6027])).
% 1.74/1.90 tff(6033,plain,
% 1.74/1.90 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(s(elem!1)))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[6032])).
% 1.74/1.90 tff(6034,plain,
% 1.74/1.90 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(elem!1))))),
% 1.74/1.90 inference(symmetry,[status(thm)],[6033])).
% 1.74/1.90 tff(6035,plain,
% 1.74/1.90 ((~b(s(z), s(s(elem!1)))) <=> (~b(s(z), s(s(s(elem!1)))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[6034])).
% 1.74/1.90 tff(6036,plain,
% 1.74/1.90 (~b(s(z), s(s(s(elem!1))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[6026, 6035])).
% 1.74/1.90 tff(6037,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[6031, 6036])).
% 1.74/1.90 tff(6038,plain,(r(s(s(s(elem!1))), s(z)) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(6039,plain,
% 1.74/1.90 (r(s(s(s(elem!1))), s(z))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[6038, 164])).
% 1.74/1.90 tff(6040,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), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(6041,plain,
% 1.74/1.90 (((~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(6042,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), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z)))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[6041])).
% 1.74/1.90 tff(6043,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), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[6042, 6040])).
% 1.74/1.90 tff(6044,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), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(6045,plain,
% 1.74/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z)))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[6044, 6043])).
% 1.74/1.90 tff(6046,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[6045, 45, 272, 385, 520])).
% 1.74/1.90 tff(6047,plain,((~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(6048,plain,
% 1.74/1.90 (~r(s(s(s(elem!1))), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[6047, 171, 6039])).
% 1.74/1.90 tff(6049,plain,
% 1.74/1.90 (b(s(s(s(elem!1))), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[5301, 6048])).
% 1.74/1.90 tff(6050,plain,
% 1.74/1.90 (~b(s(z), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2380, 1086, 164, 455, 88])).
% 1.74/1.90 tff(6051,plain,
% 1.74/1.90 (s(z) = elem!1),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[665, 5350, 6050])).
% 1.74/1.90 tff(6052,plain,
% 1.74/1.90 (s(s(z)) = s(elem!1)),
% 1.74/1.90 inference(monotonicity,[status(thm)],[6051])).
% 1.74/1.90 tff(6053,plain,
% 1.74/1.90 (s(elem!1) = s(s(z))),
% 1.74/1.90 inference(symmetry,[status(thm)],[6052])).
% 1.74/1.90 tff(6054,plain,
% 1.74/1.90 (b(s(elem!1), z) <=> b(s(s(z)), z)),
% 1.74/1.90 inference(monotonicity,[status(thm)],[6053])).
% 1.74/1.90 tff(6055,plain,
% 1.74/1.90 (b(s(s(z)), z) <=> b(s(elem!1), z)),
% 1.74/1.90 inference(symmetry,[status(thm)],[6054])).
% 1.74/1.90 tff(6056,plain,
% 1.74/1.90 (r(s(elem!1), z) <=> r(s(s(z)), z)),
% 1.74/1.90 inference(monotonicity,[status(thm)],[6053])).
% 1.74/1.90 tff(6057,plain,
% 1.74/1.90 ((~r(s(elem!1), z)) <=> (~r(s(s(z)), z))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[6056])).
% 1.74/1.90 tff(6058,plain,
% 1.74/1.90 ((s(elem!1) = s(s(elem!1))) <=> (s(s(z)) = s(s(elem!1)))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[6053])).
% 1.74/1.90 tff(6059,plain,
% 1.74/1.90 ((s(elem!1) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(z)))),
% 1.74/1.90 inference(transitivity,[status(thm)],[6058, 31])).
% 1.74/1.90 tff(6060,plain,
% 1.74/1.90 ((s(s(elem!1)) = s(s(z))) <=> (s(elem!1) = s(s(elem!1)))),
% 1.74/1.90 inference(symmetry,[status(thm)],[6059])).
% 1.74/1.90 tff(6061,plain,
% 1.74/1.90 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[6060])).
% 1.74/1.90 tff(6062,plain,
% 1.74/1.90 (~(s(elem!1) = s(s(elem!1)))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[4261, 6061])).
% 1.74/1.90 tff(6063,plain,
% 1.74/1.90 (b(s(s(z)), elem!1) <=> b(s(elem!1), elem!1)),
% 1.74/1.90 inference(monotonicity,[status(thm)],[6052])).
% 1.74/1.90 tff(6064,plain,
% 1.74/1.90 (~(s(s(z)) = elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4620, 6051])).
% 1.74/1.90 tff(6065,plain,
% 1.74/1.90 (s(s(s(z))) = s(s(elem!1))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[6052])).
% 1.74/1.90 tff(6066,plain,
% 1.74/1.90 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[6065])).
% 1.74/1.90 tff(6067,plain,
% 1.74/1.90 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 1.74/1.90 inference(monotonicity,[status(thm)],[6066])).
% 1.74/1.90 tff(6068,plain,
% 1.74/1.90 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 1.74/1.90 inference(symmetry,[status(thm)],[6067])).
% 1.74/1.90 tff(6069,plain,
% 1.74/1.90 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), elem!1)),
% 1.74/1.90 inference(monotonicity,[status(thm)],[6051])).
% 1.74/1.90 tff(6070,plain,
% 1.74/1.90 (r(s(s(s(elem!1))), elem!1)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[6039, 6069])).
% 1.74/1.90 tff(6071,plain,
% 1.74/1.90 (r(s(s(s(s(z)))), elem!1)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[6070, 6068])).
% 1.74/1.90 tff(6072,plain,
% 1.74/1.90 (~r(s(s(z)), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1469, 6071, 5242])).
% 1.74/1.90 tff(6073,plain,
% 1.74/1.90 (b(s(s(z)), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[370, 6072, 6064])).
% 1.74/1.90 tff(6074,plain,
% 1.74/1.90 (b(s(elem!1), elem!1)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[6073, 6063])).
% 1.74/1.90 tff(6075,plain,
% 1.74/1.90 (b(s(z), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[6051])).
% 1.74/1.90 tff(6076,plain,
% 1.74/1.90 (b(elem!1, s(s(elem!1)))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[2346, 6075])).
% 1.74/1.90 tff(6077,plain,
% 1.74/1.90 (~r(s(s(elem!1)), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2357, 5242, 88])).
% 1.74/1.90 tff(6078,plain,
% 1.74/1.90 (b(s(s(elem!1)), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1934, 6077, 1086])).
% 1.74/1.90 tff(6079,plain,
% 1.74/1.90 (~b(s(elem!1), s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4864, 128, 6078, 6076, 6074])).
% 1.74/1.90 tff(6080,plain,
% 1.74/1.90 ((s(elem!1) = s(s(elem!1))) | r(s(elem!1), s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[4819, 21, 6079])).
% 1.74/1.90 tff(6081,plain,
% 1.74/1.90 (r(s(elem!1), s(s(elem!1)))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[6080, 6062])).
% 1.74/1.90 tff(6082,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, elem!1)) | (~r(z, s(s(elem!1)))) | (~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(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(6083,plain,
% 1.74/1.90 (((~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(elem!1), z))) <=> ((~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(6084,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(elem!1), s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1))))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[6083])).
% 1.74/1.90 tff(6085,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(elem!1), s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[6084, 6082])).
% 1.74/1.90 tff(6086,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(elem!1), s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(elem!1), z)))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(6087,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, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[6086, 6085])).
% 1.74/1.90 tff(6088,plain,
% 1.74/1.90 (~r(s(elem!1), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[6087, 45, 5242, 88, 6081])).
% 1.74/1.90 tff(6089,plain,
% 1.74/1.90 (~r(s(s(z)), z)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[6088, 6057])).
% 1.74/1.90 tff(6090,plain,
% 1.74/1.90 (b(s(s(z)), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[25, 6089])).
% 1.74/1.90 tff(6091,plain,
% 1.74/1.90 (b(s(elem!1), z)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[6090, 6055])).
% 1.74/1.90 tff(6092,plain,
% 1.74/1.90 (b(z, s(s(z))) <=> b(z, s(elem!1))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[6052])).
% 1.74/1.90 tff(6093,plain,
% 1.74/1.90 (r(z, s(elem!1)) <=> r(z, s(s(z)))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[6053])).
% 1.74/1.90 tff(6094,plain,
% 1.74/1.90 ((~r(z, s(elem!1))) <=> (~r(z, s(s(z))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[6093])).
% 1.74/1.91 tff(6095,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(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(6096,plain,
% 1.74/1.91 (((~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1)))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(6097,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(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1)))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[6096])).
% 1.74/1.91 tff(6098,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(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[6097, 6095])).
% 1.74/1.91 tff(6099,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(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(6100,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(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1)))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[6099, 6098])).
% 1.74/1.91 tff(6101,plain,
% 1.74/1.91 (~r(z, s(elem!1))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[6100, 45, 88, 6081])).
% 1.74/1.91 tff(6102,plain,
% 1.74/1.91 (~r(z, s(s(z)))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[6101, 6094])).
% 1.74/1.91 tff(6103,plain,
% 1.74/1.91 (b(z, s(s(z)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[516, 6102])).
% 1.74/1.91 tff(6104,plain,
% 1.74/1.91 (b(z, s(elem!1))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[6103, 6092])).
% 1.74/1.91 tff(6105,plain,
% 1.74/1.91 (~r(s(s(s(elem!1))), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[5308, 45, 5242, 6070])).
% 1.74/1.91 tff(6106,plain,
% 1.74/1.91 (b(s(s(s(elem!1))), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[5301, 6105])).
% 1.74/1.91 tff(6107,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(6108,plain,
% 1.74/1.91 (((~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(6109,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[6108])).
% 1.74/1.91 tff(6110,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)))),
% 1.74/1.91 inference(transitivity,[status(thm)],[6109, 6107])).
% 1.74/1.91 tff(6111,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(6112,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[6111, 6110])).
% 1.74/1.91 tff(6113,plain,
% 1.74/1.91 ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[6112, 128, 6106, 6104])).
% 1.74/1.91 tff(6114,plain,
% 1.74/1.91 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[6113, 6091])).
% 1.74/1.91 tff(6115,plain,
% 1.74/1.91 (r(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[5524, 21, 4603, 6114])).
% 1.74/1.91 tff(6116,plain,
% 1.74/1.91 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(elem!1)) = s(s(z)))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[6053])).
% 1.74/1.91 tff(6117,plain,
% 1.74/1.91 ((s(s(elem!1)) = s(s(z))) <=> (s(s(elem!1)) = s(elem!1))),
% 1.74/1.91 inference(symmetry,[status(thm)],[6116])).
% 1.74/1.91 tff(6118,plain,
% 1.74/1.91 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[6117])).
% 1.74/1.91 tff(6119,plain,
% 1.74/1.91 (~(s(s(elem!1)) = s(elem!1))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[4261, 6118])).
% 1.74/1.91 tff(6120,plain,
% 1.74/1.91 (~b(s(s(elem!1)), s(elem!1))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4873, 128, 6078, 6076, 6074])).
% 1.74/1.91 tff(6121,plain,
% 1.74/1.91 ((s(s(elem!1)) = s(elem!1)) | r(s(s(elem!1)), s(elem!1))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4835, 21, 6120])).
% 1.74/1.91 tff(6122,plain,
% 1.74/1.91 (r(s(s(elem!1)), s(elem!1))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[6121, 6119])).
% 1.74/1.91 tff(6123,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(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, 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(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(6124,plain,
% 1.74/1.91 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(6125,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(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1)))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[6124])).
% 1.74/1.91 tff(6126,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(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[6125, 6123])).
% 1.74/1.91 tff(6127,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(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(6128,plain,
% 1.74/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[6127, 6126])).
% 1.74/1.91 tff(6129,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[6128, 45, 4263, 6122, 6115])).
% 1.74/1.91 tff(6130,plain,((s(s(elem!1)) = elem!1) | (~r(z, s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | b(z, elem!1) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(6131,plain,
% 1.74/1.91 (s(s(elem!1)) = elem!1),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[6130, 88, 198, 455, 164])).
% 1.74/1.91 tff(6132,plain,
% 1.74/1.91 (s(s(s(elem!1))) = s(elem!1)),
% 1.74/1.91 inference(monotonicity,[status(thm)],[6131])).
% 1.74/1.91 tff(6133,plain,
% 1.74/1.91 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(elem!1), s(s(z)))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[6132])).
% 1.74/1.91 tff(6134,plain,
% 1.74/1.91 (r(s(elem!1), s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 1.74/1.91 inference(symmetry,[status(thm)],[6133])).
% 1.74/1.91 tff(6135,plain,
% 1.74/1.91 (r(s(s(s(elem!1))), s(z)) <=> r(s(elem!1), s(z))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[6132])).
% 1.74/1.91 tff(6136,plain,
% 1.74/1.91 (r(s(elem!1), s(z))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[6039, 6135])).
% 1.74/1.91 tff(6137,plain,
% 1.74/1.91 ((s(s(elem!1)) = s(z)) <=> (elem!1 = s(z))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[6131])).
% 1.74/1.91 tff(6138,plain,
% 1.74/1.91 ((~(s(s(elem!1)) = s(z))) <=> (~(elem!1 = s(z)))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[6137])).
% 1.74/1.91 tff(6139,plain,
% 1.74/1.91 (~(elem!1 = s(z))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[111, 6138])).
% 1.74/1.91 tff(6140,plain,
% 1.74/1.91 ((s(s(elem!1)) = z) <=> (elem!1 = z)),
% 1.74/1.91 inference(monotonicity,[status(thm)],[6131])).
% 1.74/1.91 tff(6141,plain,
% 1.74/1.91 ((s(s(elem!1)) = z) <=> (z = elem!1)),
% 1.74/1.91 inference(transitivity,[status(thm)],[6140, 247])).
% 1.74/1.91 tff(6142,plain,
% 1.74/1.91 ((~(s(s(elem!1)) = z)) <=> (~(z = elem!1))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[6141])).
% 1.74/1.91 tff(6143,plain,
% 1.74/1.91 (~(z = elem!1)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[154, 6142])).
% 1.74/1.91 tff(6144,plain,
% 1.74/1.91 ((s(s(elem!1)) = s(z)) <=> (s(z) = elem!1)),
% 1.74/1.91 inference(transitivity,[status(thm)],[6137, 253])).
% 1.74/1.91 tff(6145,plain,
% 1.74/1.91 ((~(s(s(elem!1)) = s(z))) <=> (~(s(z) = elem!1))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[6144])).
% 1.74/1.91 tff(6146,plain,
% 1.74/1.91 (~(s(z) = elem!1)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[111, 6145])).
% 1.74/1.91 tff(6147,plain,
% 1.74/1.91 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[6132])).
% 1.74/1.91 tff(6148,plain,
% 1.74/1.91 (s(s(s(s(elem!1)))) = elem!1),
% 1.74/1.91 inference(transitivity,[status(thm)],[6147, 6131])).
% 1.74/1.91 tff(6149,plain,
% 1.74/1.91 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[6148])).
% 1.74/1.91 tff(6150,plain,
% 1.74/1.91 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 1.74/1.91 inference(transitivity,[status(thm)],[6149, 225])).
% 1.74/1.91 tff(6151,plain,
% 1.74/1.91 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[6150])).
% 1.74/1.91 tff(6152,plain,
% 1.74/1.91 (~(s(s(z)) = elem!1)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[239, 6151])).
% 1.74/1.91 tff(6153,plain,
% 1.74/1.91 (r(z, s(s(elem!1))) <=> r(z, elem!1)),
% 1.74/1.91 inference(monotonicity,[status(thm)],[6131])).
% 1.74/1.91 tff(6154,plain,
% 1.74/1.91 (r(z, elem!1)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[88, 6153])).
% 1.74/1.91 tff(6155,plain,
% 1.74/1.91 (~(s(s(s(s(z)))) = elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[242, 6131])).
% 1.74/1.91 tff(6156,plain,
% 1.74/1.91 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[245, 6131])).
% 1.74/1.91 tff(6157,plain,
% 1.74/1.91 (b(s(z), s(s(elem!1))) <=> b(s(z), elem!1)),
% 1.74/1.91 inference(monotonicity,[status(thm)],[6131])).
% 1.74/1.91 tff(6158,plain,
% 1.74/1.91 (b(s(z), elem!1)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[2346, 6157])).
% 1.74/1.91 tff(6159,plain,
% 1.74/1.91 (~r(s(s(z)), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[3007, 297, 455, 2953, 2956, 484, 922, 164, 1610, 1608])).
% 1.74/1.91 tff(6160,plain,
% 1.74/1.91 (b(s(s(z)), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[86, 6159])).
% 1.74/1.91 tff(6161,plain,
% 1.74/1.91 (~b(s(s(z)), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[897, 128, 297, 922, 6160])).
% 1.74/1.91 tff(6162,plain,
% 1.74/1.91 (r(s(s(z)), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[370, 6161, 484])).
% 1.74/1.91 tff(6163,plain,
% 1.74/1.91 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1451, 6162, 1416])).
% 1.74/1.91 tff(6164,plain,
% 1.74/1.91 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1055, 6163, 2956])).
% 1.74/1.91 tff(6165,plain,
% 1.74/1.91 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1485, 128, 297, 922, 6164])).
% 1.74/1.91 tff(6166,plain,
% 1.74/1.91 (r(s(z), s(s(s(s(s(s(z)))))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1041, 21, 1038, 6165])).
% 1.74/1.91 tff(6167,plain,
% 1.74/1.91 (~r(s(s(s(s(z)))), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1469, 6162, 1416])).
% 1.74/1.91 tff(6168,plain,
% 1.74/1.91 (b(s(s(s(s(z)))), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[632, 6167, 2953])).
% 1.74/1.91 tff(6169,plain,
% 1.74/1.91 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1477, 128, 297, 922, 6168, 6164])).
% 1.74/1.91 tff(6170,plain,
% 1.74/1.91 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1215, 21, 1212, 6169])).
% 1.74/1.91 tff(6171,plain,
% 1.74/1.91 (~b(s(z), s(s(s(s(z)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[928, 128, 297, 922, 6168])).
% 1.74/1.91 tff(6172,plain,
% 1.74/1.91 (r(s(z), s(s(s(s(z)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[684, 21, 681, 6171])).
% 1.74/1.91 tff(6173,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1495, 45, 6172, 6170, 6166])).
% 1.74/1.91 tff(6174,plain,((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (s(s(s(s(s(s(z)))))) = elem!1) | (s(s(s(s(z)))) = elem!1) | (~r(z, elem!1)) | (s(s(z)) = elem!1) | b(z, elem!1) | b(s(z), z) | (s(z) = elem!1) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(6175,plain,
% 1.74/1.91 (~b(elem!1, s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[6174, 6158, 6156, 6155, 6154, 6152, 455, 164, 6146, 6143])).
% 1.74/1.91 tff(6176,plain,
% 1.74/1.91 (r(elem!1, s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[305, 6175, 6139])).
% 1.74/1.91 tff(6177,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(elem!1, s(z))) | (~r(elem!1, 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(elem!1, s(z))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(6178,plain,
% 1.74/1.91 (((~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(6179,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(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z)))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[6178])).
% 1.74/1.91 tff(6180,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(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[6179, 6177])).
% 1.74/1.91 tff(6181,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(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(elem!1))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(6182,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(elem!1, s(z))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z)))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[6181, 6180])).
% 1.74/1.91 tff(6183,plain,
% 1.74/1.91 (~r(elem!1, s(elem!1))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[6182, 45, 6176, 6136])).
% 1.74/1.91 tff(6184,plain,
% 1.74/1.91 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(elem!1))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[6132])).
% 1.74/1.91 tff(6185,plain,
% 1.74/1.91 ((~b(elem!1, s(s(s(elem!1))))) <=> (~b(elem!1, s(elem!1)))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[6184])).
% 1.74/1.91 tff(6186,plain,
% 1.74/1.91 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[6131])).
% 1.74/1.91 tff(6187,plain,
% 1.74/1.91 ((~b(s(s(elem!1)), s(s(s(elem!1))))) <=> (~b(elem!1, s(s(s(elem!1)))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[6186])).
% 1.74/1.91 tff(6188,plain,
% 1.74/1.91 (~b(elem!1, s(s(s(elem!1))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[198, 6187])).
% 1.74/1.91 tff(6189,plain,
% 1.74/1.91 (~b(elem!1, s(elem!1))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[6188, 6185])).
% 1.74/1.91 tff(6190,plain,
% 1.74/1.91 ((elem!1 = s(elem!1)) | r(elem!1, s(elem!1))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1403, 21, 6189])).
% 1.74/1.91 tff(6191,plain,
% 1.74/1.91 (elem!1 = s(elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[6190, 6183])).
% 1.74/1.91 tff(6192,plain,
% 1.74/1.91 (r(elem!1, s(s(z))) <=> r(s(elem!1), s(s(z)))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[6191])).
% 1.74/1.91 tff(6193,plain,
% 1.74/1.91 (r(elem!1, s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 1.74/1.91 inference(transitivity,[status(thm)],[6192, 6134])).
% 1.74/1.91 tff(6194,plain,
% 1.74/1.91 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 1.74/1.91 inference(transitivity,[status(thm)],[6150, 650])).
% 1.74/1.91 tff(6195,plain,
% 1.74/1.91 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(elem!1 = s(s(z))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[6194])).
% 1.74/1.91 tff(6196,plain,
% 1.74/1.91 (~(elem!1 = s(s(z)))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[239, 6195])).
% 1.74/1.91 tff(6197,plain,
% 1.74/1.91 (~r(z, s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4896, 6176, 6154])).
% 1.74/1.91 tff(6198,plain,
% 1.74/1.91 (b(z, s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[415, 6197])).
% 1.74/1.91 tff(6199,plain,
% 1.74/1.91 (b(elem!1, z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2915, 6198, 164, 455])).
% 1.74/1.91 tff(6200,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(6201,plain,
% 1.74/1.91 (((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(6202,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(z))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[6201])).
% 1.74/1.91 tff(6203,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(z))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 1.74/1.91 inference(transitivity,[status(thm)],[6202, 6200])).
% 1.74/1.91 tff(6204,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(6205,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[6204, 6203])).
% 1.74/1.91 tff(6206,plain,
% 1.74/1.91 (~b(s(s(z)), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[6205, 128, 577, 550, 922, 591])).
% 1.74/1.91 tff(6207,plain,
% 1.74/1.91 (r(s(s(z)), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[25, 6206])).
% 1.74/1.91 tff(6208,plain,
% 1.74/1.91 (~r(s(s(z)), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1509, 6207, 272])).
% 1.74/1.91 tff(6209,plain,
% 1.74/1.91 (b(s(s(z)), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[86, 6208])).
% 1.74/1.91 tff(6210,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(6211,plain,
% 1.74/1.91 (((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~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(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(6212,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[6211])).
% 1.74/1.91 tff(6213,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.74/1.91 inference(transitivity,[status(thm)],[6212, 6210])).
% 1.74/1.91 tff(6214,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(6215,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[6214, 6213])).
% 1.74/1.91 tff(6216,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[6215, 128, 577, 550, 922, 591, 6209])).
% 1.74/1.91 tff(6217,plain,((~b(s(s(z)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(6218,plain,
% 1.74/1.91 (~b(s(s(z)), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[6217, 6199, 6198, 6158, 171])).
% 1.74/1.91 tff(6219,plain,
% 1.74/1.91 (r(s(s(z)), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[370, 6218, 6152])).
% 1.74/1.91 tff(6220,plain,
% 1.74/1.91 (~r(s(s(z)), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1433, 45, 6154, 6219])).
% 1.74/1.91 tff(6221,plain,
% 1.74/1.91 (b(s(s(z)), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[25, 6220])).
% 1.74/1.91 tff(6222,plain,
% 1.74/1.91 (~r(z, s(s(z)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1441, 45, 6154, 6219])).
% 1.74/1.91 tff(6223,plain,
% 1.74/1.91 (b(z, s(s(z)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[516, 6222])).
% 1.74/1.91 tff(6224,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(6225,plain,
% 1.74/1.91 (((~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z))))) <=> ((~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(6226,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z))))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[6225])).
% 1.74/1.91 tff(6227,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[6226, 6224])).
% 1.74/1.91 tff(6228,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(6229,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[6228, 6227])).
% 1.74/1.91 tff(6230,plain,
% 1.74/1.91 (~b(elem!1, s(s(z)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[6229, 128, 6199, 6223, 6221])).
% 1.74/1.91 tff(6231,plain,
% 1.74/1.91 (r(elem!1, s(s(z)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[493, 6230, 6196])).
% 1.74/1.91 tff(6232,plain,
% 1.74/1.91 (r(s(s(s(elem!1))), s(s(z)))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[6231, 6193])).
% 1.74/1.91 tff(6233,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(6234,plain,
% 1.74/1.92 (((~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(6235,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(z), elem!1)) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[6234])).
% 1.74/1.92 tff(6236,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(z), elem!1)) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[6235, 6233])).
% 1.74/1.92 tff(6237,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(6238,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[6237, 6236])).
% 1.74/1.92 tff(6239,plain,
% 1.74/1.92 (~b(s(s(z)), s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[6238, 128, 6199, 6198, 6158, 6221])).
% 1.74/1.92 tff(6240,plain,
% 1.74/1.92 (r(s(s(z)), s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[86, 6239])).
% 1.74/1.92 tff(6241,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)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(6242,plain,
% 1.74/1.92 (((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(6243,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)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z)))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[6242])).
% 1.74/1.92 tff(6244,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)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[6243, 6241])).
% 1.74/1.92 tff(6245,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)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(6246,plain,
% 1.74/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z)))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[6245, 6244])).
% 1.74/1.92 tff(6247,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[6246, 45, 385, 35, 518])).
% 1.74/1.92 tff(6248,plain,((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(6249,plain,
% 1.74/1.92 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[6248, 6240, 6039])).
% 1.74/1.92 tff(6250,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[6249, 6232])).
% 1.74/1.92 tff(6251,plain,((~r(z, s(s(elem!1)))) | b(s(z), z) | b(z, elem!1) | b(s(s(elem!1)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(6252,plain,
% 1.74/1.92 (~r(z, s(s(elem!1)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[6251, 198, 455, 164])).
% 1.74/1.92 tff(6253,plain,
% 1.74/1.92 (b(z, s(s(elem!1)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[160, 6252])).
% 1.74/1.92 tff(6254,plain,
% 1.74/1.92 (~(elem!1 = s(s(elem!1)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[457, 6253, 455])).
% 1.74/1.92 tff(6255,plain,
% 1.74/1.92 (~(s(s(elem!1)) = elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[377, 6254])).
% 1.74/1.92 tff(6256,plain,
% 1.74/1.92 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4602, 6255])).
% 1.74/1.92 tff(6257,plain,
% 1.74/1.92 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[6256, 4597])).
% 1.74/1.92 tff(6258,assumption,(~b(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 1.74/1.92 tff(6259,plain,
% 1.74/1.92 (~(z = elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4250, 6255, 164])).
% 1.74/1.92 tff(6260,plain,
% 1.74/1.92 (r(z, elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1549, 6259, 455])).
% 1.74/1.92 tff(6261,plain,
% 1.74/1.92 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1089, 6255])).
% 1.74/1.92 tff(6262,plain,
% 1.74/1.92 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1073, 6261])).
% 1.74/1.92 tff(6263,plain,
% 1.74/1.92 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1065, 6262])).
% 1.74/1.92 tff(6264,plain,
% 1.74/1.92 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[321, 6263, 198])).
% 1.74/1.92 tff(6265,plain,
% 1.74/1.92 (~r(s(s(elem!1)), s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[393, 6264, 6039])).
% 1.74/1.92 tff(6266,plain,
% 1.74/1.92 (b(s(s(elem!1)), s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[292, 6265])).
% 1.74/1.92 tff(6267,plain,
% 1.74/1.92 (~(s(s(elem!1)) = elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[377, 4901])).
% 1.74/1.92 tff(6268,plain,
% 1.74/1.92 (~(z = elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4250, 6267, 164])).
% 1.74/1.92 tff(6269,plain,
% 1.74/1.92 (r(z, elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1549, 6268, 455])).
% 1.74/1.92 tff(6270,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4926, 5465, 550, 453, 6269, 30, 455])).
% 1.74/1.92 tff(6271,plain,((~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | b(z, elem!1) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(6272,plain,
% 1.74/1.92 (~b(z, s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[6271, 6253, 6266, 455, 164])).
% 1.74/1.92 tff(6273,plain,
% 1.74/1.92 (r(z, s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[415, 6272])).
% 1.74/1.92 tff(6274,plain,
% 1.74/1.92 (~(s(s(elem!1)) = s(s(z)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4260, 6259])).
% 1.74/1.92 tff(6275,plain,
% 1.74/1.92 (b(s(s(s(elem!1))), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5301, 3936])).
% 1.74/1.92 tff(6276,plain,
% 1.74/1.92 (b(z, s(s(s(elem!1))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[858, 3612])).
% 1.74/1.92 tff(6277,plain,
% 1.74/1.92 (~(s(s(elem!1)) = elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[377, 375])).
% 1.74/1.92 tff(6278,plain,
% 1.74/1.92 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1089, 6277])).
% 1.74/1.92 tff(6279,plain,
% 1.74/1.92 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1073, 6278])).
% 1.74/1.92 tff(6280,plain,
% 1.74/1.92 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1065, 6279])).
% 1.74/1.92 tff(6281,plain,
% 1.74/1.92 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[693, 6280])).
% 1.74/1.92 tff(6282,plain,
% 1.74/1.92 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[700, 6281])).
% 1.74/1.92 tff(6283,plain,
% 1.74/1.92 (~r(elem!1, s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4896, 27, 1416])).
% 1.74/1.92 tff(6284,plain,
% 1.74/1.92 (b(elem!1, s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[305, 5008, 6283])).
% 1.74/1.92 tff(6285,plain,
% 1.74/1.92 (b(s(s(s(elem!1))), s(z))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[297, 5096])).
% 1.74/1.92 tff(6286,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[6258, 6285])).
% 1.74/1.92 tff(6287,plain,((~(s(s(s(elem!1))) = elem!1)) | b(s(s(s(elem!1))), s(z)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(6288,plain,
% 1.74/1.92 (~(s(s(s(elem!1))) = elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[6287, 6284, 6258])).
% 1.74/1.92 tff(6289,plain,
% 1.74/1.92 (~r(s(z), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1544, 1416, 272])).
% 1.74/1.92 tff(6290,plain,
% 1.74/1.92 (b(s(z), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[665, 1610, 6289])).
% 1.74/1.92 tff(6291,plain,
% 1.74/1.92 (~r(s(s(elem!1)), s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[393, 324, 385])).
% 1.74/1.92 tff(6292,plain,
% 1.74/1.92 (b(s(s(elem!1)), s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[292, 6291])).
% 1.74/1.92 tff(6293,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)), s(z))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(6294,plain,
% 1.74/1.92 (((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(6295,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(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(X0, 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(s(elem!1)), s(z)))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[6294])).
% 1.74/1.92 tff(6296,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(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(X0, 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(s(elem!1)), s(z))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[6295, 6293])).
% 1.74/1.92 tff(6297,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(6298,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)), s(z)))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[6297, 6296])).
% 1.74/1.92 tff(6299,plain,
% 1.74/1.92 (~b(s(s(elem!1)), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[6298, 128, 6292, 6284, 6290])).
% 1.74/1.92 tff(6300,plain,
% 1.74/1.92 (r(s(s(elem!1)), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1934, 6299, 6277])).
% 1.74/1.92 tff(6301,plain,
% 1.74/1.92 (~r(s(s(s(elem!1))), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4990, 6300, 324])).
% 1.74/1.92 tff(6302,plain,
% 1.74/1.92 (b(s(s(s(elem!1))), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[742, 6301, 6288])).
% 1.74/1.92 tff(6303,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(6304,plain,
% 1.74/1.92 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(6305,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[6304])).
% 1.74/1.92 tff(6306,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[6305, 6303])).
% 1.74/1.92 tff(6307,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(6308,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1)))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[6307, 6306])).
% 1.74/1.92 tff(6309,plain,
% 1.74/1.92 (~b(s(z), s(s(s(elem!1))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[6308, 128, 6284, 6290, 6302])).
% 1.74/1.92 tff(6310,plain,
% 1.74/1.92 (r(s(z), s(s(s(elem!1))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[339, 6309])).
% 1.74/1.92 tff(6311,plain,
% 1.74/1.92 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[803, 6280])).
% 1.74/1.92 tff(6312,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(6313,plain,
% 1.74/1.92 (((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(6314,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[6313])).
% 1.74/1.92 tff(6315,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 1.74/1.92 inference(transitivity,[status(thm)],[6314, 6312])).
% 1.74/1.92 tff(6316,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(6317,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[6316, 6315])).
% 1.74/1.92 tff(6318,plain,
% 1.74/1.92 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[6317, 128, 6292, 453, 6290, 6302, 6275])).
% 1.74/1.92 tff(6319,plain,
% 1.74/1.92 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[889, 6318, 6311])).
% 1.74/1.92 tff(6320,plain,
% 1.74/1.92 (~r(s(z), s(s(elem!1)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1802, 6319, 6310])).
% 1.74/1.92 tff(6321,plain,
% 1.74/1.92 (b(s(z), s(s(elem!1)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[117, 6320])).
% 1.74/1.92 tff(6322,plain,
% 1.74/1.92 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2519, 1772, 272, 323])).
% 1.74/1.92 tff(6323,plain,
% 1.74/1.92 (b(s(s(s(s(elem!1)))), s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1828, 6322])).
% 1.74/1.92 tff(6324,plain,
% 1.74/1.92 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1897, 4266, 1063])).
% 1.74/1.92 tff(6325,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2608, 6324, 6323, 876, 30])).
% 1.74/1.92 tff(6326,plain,((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(6327,plain,
% 1.74/1.92 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[6326, 6321, 6292, 6279, 324, 272, 6310])).
% 1.74/1.92 tff(6328,plain,
% 1.74/1.92 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1820, 6327, 6282])).
% 1.74/1.92 tff(6329,plain,
% 1.74/1.92 (((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(6330,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[6329])).
% 1.74/1.92 tff(6331,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.74/1.92 inference(transitivity,[status(thm)],[6330, 4539])).
% 1.74/1.92 tff(6332,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(6333,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[6332, 6331])).
% 1.74/1.92 tff(6334,plain,
% 1.74/1.92 (~b(s(s(s(s(elem!1)))), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[6333, 128, 6328, 6276, 6275])).
% 1.74/1.92 tff(6335,plain,
% 1.74/1.92 (r(s(s(s(s(elem!1)))), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2081, 6334])).
% 1.74/1.92 tff(6336,plain,
% 1.74/1.92 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1745, 6335, 272])).
% 1.74/1.92 tff(6337,plain,
% 1.74/1.92 (b(s(s(s(s(elem!1)))), s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1828, 6336])).
% 1.74/1.92 tff(6338,plain,
% 1.74/1.92 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2608, 6337, 6321, 6292])).
% 1.74/1.92 tff(6339,plain,
% 1.74/1.92 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1897, 6338, 6279])).
% 1.74/1.92 tff(6340,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(6341,plain,
% 1.74/1.93 (((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(6342,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~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(X0, 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(elem!1)))) | (~b(s(s(elem!1)), s(z)))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[6341])).
% 1.74/1.93 tff(6343,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~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(X0, 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(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[6342, 6340])).
% 1.74/1.93 tff(6344,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(6345,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))) | (~b(s(s(elem!1)), s(z)))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[6344, 6343])).
% 1.74/1.93 tff(6346,plain,
% 1.74/1.93 ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[6345, 128])).
% 1.74/1.93 tff(6347,plain,
% 1.74/1.93 (~b(elem!1, s(s(elem!1)))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[6346, 6284, 6292, 6290])).
% 1.74/1.93 tff(6348,plain,
% 1.74/1.93 (r(elem!1, s(s(elem!1)))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[2371, 6347, 375])).
% 1.74/1.93 tff(6349,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(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(6350,plain,
% 1.74/1.93 (((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(elem!1, s(s(s(s(elem!1))))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(6351,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(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[6350])).
% 1.74/1.93 tff(6352,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(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[6351, 6349])).
% 1.74/1.93 tff(6353,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(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(6354,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(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[6353, 6352])).
% 1.74/1.93 tff(6355,plain,
% 1.74/1.93 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[6354, 45, 6348, 6339, 6335])).
% 1.74/1.93 tff(6356,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(6357,plain,
% 1.74/1.93 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(elem!1))))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(6358,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[6357])).
% 1.74/1.93 tff(6359,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[6358, 6356])).
% 1.74/1.93 tff(6360,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(6361,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[6360, 6359])).
% 1.74/1.93 tff(6362,plain,
% 1.74/1.93 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[6361, 128, 6284, 6290, 6337])).
% 1.74/1.93 tff(6363,plain,
% 1.74/1.93 (elem!1 = s(s(s(s(elem!1))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1766, 6362, 6355])).
% 1.74/1.93 tff(6364,plain,
% 1.74/1.93 (s(elem!1) = s(s(s(s(s(elem!1)))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[6363])).
% 1.74/1.93 tff(6365,plain,
% 1.74/1.93 (s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[6364])).
% 1.74/1.93 tff(6366,plain,
% 1.74/1.93 (s(s(s(elem!1))) = s(s(s(s(s(s(s(elem!1)))))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[6365])).
% 1.74/1.93 tff(6367,plain,
% 1.74/1.93 (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(elem!1)))),
% 1.74/1.93 inference(symmetry,[status(thm)],[6366])).
% 1.74/1.93 tff(6368,plain,
% 1.74/1.93 (r(s(s(s(s(s(s(s(elem!1))))))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[6367])).
% 1.74/1.93 tff(6369,plain,
% 1.74/1.93 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))),
% 1.74/1.93 inference(symmetry,[status(thm)],[6368])).
% 1.74/1.93 tff(6370,plain,
% 1.74/1.93 ((~r(s(s(s(elem!1))), s(s(z)))) <=> (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(z))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[6369])).
% 1.74/1.93 tff(6371,plain,
% 1.74/1.93 (b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1)))))))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[6367])).
% 1.74/1.93 tff(6372,plain,
% 1.74/1.93 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.74/1.93 inference(symmetry,[status(thm)],[6371])).
% 1.74/1.93 tff(6373,plain,
% 1.74/1.93 (b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[6328, 6372])).
% 1.74/1.93 tff(6374,plain,
% 1.74/1.93 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[6367])).
% 1.74/1.93 tff(6375,plain,
% 1.74/1.93 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))),
% 1.74/1.93 inference(symmetry,[status(thm)],[6374])).
% 1.74/1.93 tff(6376,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(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(6377,plain,
% 1.74/1.93 (((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(6378,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(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[6377])).
% 1.74/1.93 tff(6379,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(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[6378, 6376])).
% 1.74/1.93 tff(6380,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(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(6381,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(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[6380, 6379])).
% 1.74/1.93 tff(6382,plain,
% 1.74/1.93 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[6381, 45, 6339, 6319, 6335])).
% 1.74/1.93 tff(6383,plain,
% 1.74/1.93 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1856, 6382, 6281])).
% 1.74/1.93 tff(6384,plain,
% 1.74/1.93 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[6383, 6375])).
% 1.74/1.93 tff(6385,plain,
% 1.74/1.93 (s(s(s(s(elem!1)))) = elem!1),
% 1.74/1.93 inference(symmetry,[status(thm)],[6363])).
% 1.74/1.93 tff(6386,plain,
% 1.74/1.93 (b(s(s(z)), s(s(s(s(elem!1))))) <=> b(s(s(z)), elem!1)),
% 1.74/1.93 inference(monotonicity,[status(thm)],[6385])).
% 1.74/1.93 tff(6387,plain,
% 1.74/1.93 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.74/1.93 inference(symmetry,[status(thm)],[6386])).
% 1.74/1.93 tff(6388,plain,
% 1.74/1.93 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[6385])).
% 1.74/1.93 tff(6389,plain,
% 1.74/1.93 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 1.74/1.93 inference(transitivity,[status(thm)],[6388, 225])).
% 1.74/1.93 tff(6390,plain,
% 1.74/1.93 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[6389])).
% 1.74/1.93 tff(6391,plain,
% 1.74/1.93 (~(s(s(z)) = elem!1)),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[239, 6390])).
% 1.74/1.93 tff(6392,plain,
% 1.74/1.93 (r(s(s(z)), s(s(s(s(elem!1))))) <=> r(s(s(z)), elem!1)),
% 1.74/1.93 inference(monotonicity,[status(thm)],[6385])).
% 1.74/1.93 tff(6393,plain,
% 1.74/1.93 ((~r(s(s(z)), s(s(s(s(elem!1)))))) <=> (~r(s(s(z)), elem!1))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[6392])).
% 1.74/1.93 tff(6394,plain,
% 1.74/1.93 (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))),
% 1.74/1.93 inference(symmetry,[status(thm)],[6365])).
% 1.74/1.93 tff(6395,plain,
% 1.74/1.93 (r(s(s(s(s(s(s(elem!1)))))), elem!1) <=> r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[6394, 6363])).
% 1.74/1.93 tff(6396,plain,
% 1.74/1.93 (r(s(s(elem!1)), s(s(s(s(elem!1))))) <=> r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.74/1.93 inference(symmetry,[status(thm)],[6395])).
% 1.74/1.93 tff(6397,plain,
% 1.74/1.93 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[6363])).
% 1.74/1.93 tff(6398,plain,
% 1.74/1.93 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[6300, 6397])).
% 1.74/1.93 tff(6399,plain,
% 1.74/1.93 (r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[6398, 6396])).
% 1.74/1.93 tff(6400,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(6401,plain,
% 1.74/1.93 (((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1))))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(6402,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1))))))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[6401])).
% 1.74/1.93 tff(6403,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[6402, 6400])).
% 1.74/1.93 tff(6404,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(6405,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1))))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[6404, 6403])).
% 1.74/1.93 tff(6406,plain,
% 1.74/1.93 (~b(z, s(s(s(s(elem!1)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[6405, 128, 453, 6328, 6276, 6275])).
% 1.74/1.93 tff(6407,plain,
% 1.74/1.93 (r(z, s(s(s(s(elem!1)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[2047, 21, 6406, 178])).
% 1.74/1.93 tff(6408,plain,
% 1.74/1.93 (~r(s(s(elem!1)), z)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[2004, 45, 1416, 6300])).
% 1.74/1.93 tff(6409,plain,
% 1.74/1.93 (b(s(s(elem!1)), z)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[2018, 21, 154, 6408])).
% 1.74/1.93 tff(6410,assumption,(elem!1 = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.74/1.93 tff(6411,plain,
% 1.74/1.93 (s(elem!1) = s(s(s(s(s(elem!1)))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[6410])).
% 1.74/1.93 tff(6412,plain,
% 1.74/1.93 (s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[6411])).
% 1.74/1.93 tff(6413,plain,
% 1.74/1.93 (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))),
% 1.74/1.93 inference(symmetry,[status(thm)],[6412])).
% 1.74/1.93 tff(6414,plain,
% 1.74/1.93 ((s(s(s(s(s(s(elem!1)))))) = s(s(z))) <=> (s(s(elem!1)) = s(s(z)))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[6413])).
% 1.74/1.93 tff(6415,plain,
% 1.74/1.93 ((s(s(elem!1)) = s(s(z))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(z)))),
% 1.74/1.93 inference(symmetry,[status(thm)],[6414])).
% 1.74/1.93 tff(6416,plain,
% 1.74/1.93 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(s(s(s(s(s(elem!1)))))) = s(s(z))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[6415])).
% 1.74/1.93 tff(6417,plain,
% 1.74/1.93 (~(s(s(s(s(s(s(elem!1)))))) = s(s(z)))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[1, 6416])).
% 1.74/1.93 tff(6418,plain,
% 1.74/1.93 (b(s(s(s(s(s(s(elem!1)))))), z) <=> b(s(s(elem!1)), z)),
% 1.74/1.93 inference(monotonicity,[status(thm)],[6413])).
% 1.74/1.93 tff(6419,plain,
% 1.74/1.93 (b(s(s(elem!1)), z) <=> b(s(s(s(s(s(s(elem!1)))))), z)),
% 1.74/1.93 inference(symmetry,[status(thm)],[6418])).
% 1.74/1.93 tff(6420,plain,
% 1.74/1.93 (b(s(s(s(s(s(s(elem!1)))))), z)),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[2006, 6419])).
% 1.74/1.93 tff(6421,assumption,(r(s(s(z)), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.74/1.93 tff(6422,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(z, s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(6423,plain,
% 1.74/1.93 (((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(s(s(z)), z))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(6424,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(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(elem!1))))))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[6423])).
% 1.74/1.93 tff(6425,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(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[6424, 6422])).
% 1.74/1.93 tff(6426,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(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(s(s(z)), z)))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(6427,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(z, s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(elem!1))))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[6426, 6425])).
% 1.74/1.93 tff(6428,plain,
% 1.74/1.93 ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(elem!1))))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[6427, 45, 27, 1782])).
% 1.74/1.93 tff(6429,plain,
% 1.74/1.93 (~r(s(s(z)), z)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[6428, 6421])).
% 1.74/1.93 tff(6430,plain,
% 1.74/1.93 (b(s(s(z)), z)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[25, 6429])).
% 1.74/1.93 tff(6431,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(z, s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(6432,plain,
% 1.74/1.93 (((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(6433,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(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1))))))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[6432])).
% 1.74/1.93 tff(6434,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(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[6433, 6431])).
% 1.74/1.94 tff(6435,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(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(6436,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(z)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1))))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[6435, 6434])).
% 1.74/1.94 tff(6437,plain,
% 1.74/1.94 ((~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1))))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6436, 45, 1782])).
% 1.74/1.94 tff(6438,plain,
% 1.74/1.94 (~r(z, s(s(z)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6437, 6421])).
% 1.74/1.94 tff(6439,plain,
% 1.74/1.94 (b(z, s(s(z)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[516, 6438])).
% 1.74/1.94 tff(6440,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(6441,plain,
% 1.74/1.94 (((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z))))) <=> ((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(6442,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z))))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[6441])).
% 1.74/1.94 tff(6443,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[6442, 6440])).
% 1.74/1.94 tff(6444,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(6445,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[6444, 6443])).
% 1.74/1.94 tff(6446,plain,
% 1.74/1.94 ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6445, 128, 6439, 6430])).
% 1.74/1.94 tff(6447,plain,
% 1.74/1.94 (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6446, 6420])).
% 1.74/1.94 tff(6448,plain,
% 1.74/1.94 (s(s(s(s(elem!1)))) = elem!1),
% 1.74/1.94 inference(symmetry,[status(thm)],[6410])).
% 1.74/1.94 tff(6449,plain,
% 1.74/1.94 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))) <=> r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.74/1.94 inference(monotonicity,[status(thm)],[6448])).
% 1.74/1.94 tff(6450,plain,
% 1.74/1.94 (r(s(s(s(s(s(s(elem!1)))))), elem!1) <=> r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.74/1.94 inference(symmetry,[status(thm)],[6449])).
% 1.74/1.94 tff(6451,plain,
% 1.74/1.94 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[3393, 6450])).
% 1.74/1.94 tff(6452,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(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(6453,plain,
% 1.74/1.94 (((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(6454,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(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z))))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[6453])).
% 1.74/1.94 tff(6455,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(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[6454, 6452])).
% 1.74/1.94 tff(6456,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(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(6457,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(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[6456, 6455])).
% 1.74/1.94 tff(6458,plain,
% 1.74/1.94 ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6457, 45])).
% 1.74/1.94 tff(6459,plain,
% 1.74/1.94 (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6458, 6451, 6421])).
% 1.74/1.94 tff(6460,plain,
% 1.74/1.94 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(z))) | b(s(s(s(s(s(s(elem!1)))))), s(s(z))) | r(s(s(s(s(s(s(elem!1)))))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(z))) | b(s(s(s(s(s(s(elem!1)))))), s(s(z))) | r(s(s(s(s(s(s(elem!1)))))), s(s(z))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(6461,plain,
% 1.74/1.94 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(z))) | b(s(s(s(s(s(s(elem!1)))))), s(s(z))) | r(s(s(s(s(s(s(elem!1)))))), s(s(z))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(6462,plain,
% 1.74/1.94 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(z))) | b(s(s(s(s(s(s(elem!1)))))), s(s(z))) | r(s(s(s(s(s(s(elem!1)))))), s(s(z)))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[6461, 6460])).
% 1.74/1.94 tff(6463,plain,
% 1.74/1.94 ((s(s(s(s(s(s(elem!1)))))) = s(s(z))) | b(s(s(s(s(s(s(elem!1)))))), s(s(z)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6462, 21, 6459])).
% 1.74/1.94 tff(6464,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6463, 6447, 6417])).
% 1.74/1.94 tff(6465,plain,((~r(s(s(z)), s(s(s(s(elem!1)))))) | (s(s(elem!1)) = s(s(z))) | (~(elem!1 = s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), z)) | (~r(z, s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(6466,plain,
% 1.74/1.94 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6465, 6363, 1, 6409, 27, 6407, 6399])).
% 1.74/1.94 tff(6467,plain,
% 1.74/1.94 (~r(s(s(z)), elem!1)),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[6466, 6393])).
% 1.74/1.94 tff(6468,plain,
% 1.74/1.94 (b(s(s(z)), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[370, 6467, 6391])).
% 1.74/1.94 tff(6469,plain,
% 1.74/1.94 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[6468, 6387])).
% 1.74/1.94 tff(6470,plain,
% 1.74/1.94 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2266, 45, 272, 6335])).
% 1.74/1.94 tff(6471,plain,
% 1.74/1.94 ((s(z) = s(s(s(s(elem!1))))) | b(s(z), s(s(s(s(elem!1)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2258, 21, 6470])).
% 1.74/1.94 tff(6472,plain,
% 1.74/1.94 (b(s(z), s(s(s(s(elem!1)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6471, 2248])).
% 1.74/1.94 tff(6473,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(6474,plain,
% 1.74/1.94 (((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(6475,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1)))))))))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[6474])).
% 1.74/1.94 tff(6476,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[6475, 6473])).
% 1.74/1.94 tff(6477,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(6478,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1)))))))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[6477, 6476])).
% 1.74/1.94 tff(6479,plain,
% 1.74/1.94 ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1)))))))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6478, 128, 6472])).
% 1.74/1.94 tff(6480,plain,
% 1.74/1.94 (~b(s(s(z)), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6479, 6469, 6384, 6373])).
% 1.74/1.94 tff(6481,plain,
% 1.74/1.94 (r(s(s(z)), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[86, 6480])).
% 1.74/1.94 tff(6482,plain,
% 1.74/1.94 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6248, 6481, 385])).
% 1.74/1.94 tff(6483,plain,
% 1.74/1.94 (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[6482, 6370])).
% 1.74/1.94 tff(6484,plain,
% 1.74/1.94 ((s(s(s(s(s(s(s(elem!1))))))) = s(s(z))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[6367])).
% 1.74/1.94 tff(6485,plain,
% 1.74/1.94 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(s(s(s(s(s(elem!1))))))) = s(s(z)))),
% 1.74/1.94 inference(symmetry,[status(thm)],[6484])).
% 1.74/1.94 tff(6486,plain,
% 1.74/1.94 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(s(s(s(s(s(s(elem!1))))))) = s(s(z))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[6485])).
% 1.74/1.94 tff(6487,plain,
% 1.74/1.94 (~(s(s(s(s(s(s(s(elem!1))))))) = s(s(z)))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[283, 6486])).
% 1.74/1.94 tff(6488,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(6489,plain,
% 1.74/1.94 (((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(6490,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1)))))))))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[6489])).
% 1.74/1.94 tff(6491,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[6490, 6488])).
% 1.74/1.94 tff(6492,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(6493,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1)))))))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[6492, 6491])).
% 1.74/1.94 tff(6494,plain,
% 1.74/1.94 ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1)))))))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6493, 128])).
% 1.74/1.94 tff(6495,plain,
% 1.74/1.94 (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6494, 6469, 6384, 6373])).
% 1.74/1.94 tff(6496,plain,
% 1.74/1.94 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(elem!1))))))) = s(s(z))) | b(s(s(s(s(s(s(s(elem!1))))))), s(s(z))) | r(s(s(s(s(s(s(s(elem!1))))))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(elem!1))))))) = s(s(z))) | b(s(s(s(s(s(s(s(elem!1))))))), s(s(z))) | r(s(s(s(s(s(s(s(elem!1))))))), s(s(z))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(6497,plain,
% 1.74/1.94 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(elem!1))))))) = s(s(z))) | b(s(s(s(s(s(s(s(elem!1))))))), s(s(z))) | r(s(s(s(s(s(s(s(elem!1))))))), s(s(z))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(6498,plain,
% 1.74/1.94 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(elem!1))))))) = s(s(z))) | b(s(s(s(s(s(s(s(elem!1))))))), s(s(z))) | r(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[6497, 6496])).
% 1.74/1.94 tff(6499,plain,
% 1.74/1.94 ((s(s(s(s(s(s(s(elem!1))))))) = s(s(z))) | r(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6498, 21, 6495])).
% 1.74/1.94 tff(6500,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6499, 6487, 6483])).
% 1.74/1.94 tff(6501,plain,((s(z) = elem!1) | (~r(s(s(s(elem!1))), s(z))) | (s(s(elem!1)) = s(s(z))) | (~r(z, s(z))) | (~r(s(z), z)) | (~b(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, elem!1)) | (elem!1 = s(s(elem!1))) | b(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(6502,plain,
% 1.74/1.94 (s(z) = elem!1),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6501, 6274, 6039, 6273, 171, 6253, 6264, 6260, 6254, 6258])).
% 1.74/1.94 tff(6503,plain,
% 1.74/1.94 (s(s(z)) = s(elem!1)),
% 1.74/1.94 inference(monotonicity,[status(thm)],[6502])).
% 1.74/1.94 tff(6504,plain,
% 1.74/1.94 (s(elem!1) = s(s(z))),
% 1.74/1.94 inference(symmetry,[status(thm)],[6503])).
% 1.74/1.94 tff(6505,plain,
% 1.74/1.94 ((s(elem!1) = s(s(elem!1))) <=> (s(s(z)) = s(s(elem!1)))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[6504])).
% 1.74/1.94 tff(6506,plain,
% 1.74/1.94 ((s(elem!1) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(z)))),
% 1.74/1.94 inference(transitivity,[status(thm)],[6505, 31])).
% 1.74/1.94 tff(6507,plain,
% 1.74/1.94 ((s(s(elem!1)) = s(s(z))) <=> (s(elem!1) = s(s(elem!1)))),
% 1.74/1.94 inference(symmetry,[status(thm)],[6506])).
% 1.74/1.94 tff(6508,plain,
% 1.74/1.94 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[6507])).
% 1.74/1.94 tff(6509,plain,
% 1.74/1.94 (~(s(elem!1) = s(s(elem!1)))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[6274, 6508])).
% 1.74/1.94 tff(6510,plain,
% 1.74/1.94 (b(s(s(z)), elem!1) <=> b(s(elem!1), elem!1)),
% 1.74/1.94 inference(monotonicity,[status(thm)],[6503])).
% 1.74/1.94 tff(6511,plain,
% 1.74/1.94 (~(s(s(z)) = elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4620, 6502])).
% 1.74/1.94 tff(6512,plain,
% 1.74/1.94 (s(s(s(z))) = s(s(elem!1))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[6503])).
% 1.74/1.94 tff(6513,plain,
% 1.74/1.94 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[6512])).
% 1.74/1.94 tff(6514,plain,
% 1.74/1.94 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 1.74/1.94 inference(monotonicity,[status(thm)],[6513])).
% 1.74/1.94 tff(6515,plain,
% 1.74/1.94 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 1.74/1.94 inference(symmetry,[status(thm)],[6514])).
% 1.74/1.94 tff(6516,plain,
% 1.74/1.94 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), elem!1)),
% 1.74/1.94 inference(monotonicity,[status(thm)],[6502])).
% 1.74/1.94 tff(6517,plain,
% 1.74/1.94 (r(s(s(s(elem!1))), elem!1)),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[6039, 6516])).
% 1.74/1.94 tff(6518,plain,
% 1.74/1.94 (r(s(s(s(s(z)))), elem!1)),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[6517, 6515])).
% 1.74/1.94 tff(6519,plain,
% 1.74/1.94 (~r(s(s(z)), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1469, 6518, 6260])).
% 1.74/1.94 tff(6520,plain,
% 1.74/1.94 (b(s(s(z)), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[370, 6519, 6511])).
% 1.74/1.94 tff(6521,plain,
% 1.74/1.94 (b(s(elem!1), elem!1)),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[6520, 6510])).
% 1.74/1.94 tff(6522,plain,
% 1.74/1.94 (b(s(z), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[6502])).
% 1.74/1.94 tff(6523,plain,
% 1.74/1.94 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[803, 6263])).
% 1.74/1.94 tff(6524,plain,
% 1.74/1.94 (~r(s(s(s(elem!1))), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[3935, 45, 6273, 6039])).
% 1.74/1.94 tff(6525,plain,
% 1.74/1.94 (b(s(s(s(elem!1))), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5301, 6524])).
% 1.74/1.94 tff(6526,plain,
% 1.74/1.94 (~r(z, s(s(s(elem!1))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[3611, 45, 6273, 6039])).
% 1.74/1.94 tff(6527,plain,
% 1.74/1.94 (b(z, s(s(s(elem!1))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[858, 6526])).
% 1.74/1.94 tff(6528,plain,
% 1.74/1.94 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4602, 6277])).
% 1.74/1.94 tff(6529,plain,
% 1.74/1.94 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[6528, 4597])).
% 1.74/1.94 tff(6530,plain,
% 1.74/1.94 (r(s(z), s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[1640])).
% 1.74/1.94 tff(6531,plain,
% 1.74/1.94 (r(elem!1, s(s(s(elem!1))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[323, 6530])).
% 1.74/1.94 tff(6532,plain,
% 1.74/1.94 (~r(elem!1, s(s(elem!1)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4721, 45, 6531, 324])).
% 1.74/1.94 tff(6533,plain,
% 1.74/1.94 (b(elem!1, s(s(elem!1)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2371, 6532, 375])).
% 1.74/1.94 tff(6534,plain,
% 1.74/1.94 (b(s(s(elem!1)), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4662, 1640, 30])).
% 1.74/1.94 tff(6535,plain,
% 1.74/1.94 (~b(s(elem!1), s(s(elem!1)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4864, 128, 6534, 6533, 4791])).
% 1.74/1.94 tff(6536,plain,
% 1.74/1.94 ((s(elem!1) = s(s(elem!1))) | r(s(elem!1), s(s(elem!1)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4819, 21, 6535])).
% 1.74/1.94 tff(6537,plain,
% 1.74/1.94 (r(s(elem!1), s(s(elem!1)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6536, 4809])).
% 1.74/1.94 tff(6538,plain,
% 1.74/1.94 (b(s(z), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[1640])).
% 1.74/1.94 tff(6539,plain,
% 1.74/1.94 (b(elem!1, s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 1.74/1.94 inference(symmetry,[status(thm)],[6538])).
% 1.74/1.94 tff(6540,plain,
% 1.74/1.94 (b(s(z), s(s(elem!1)))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[6533, 6539])).
% 1.74/1.94 tff(6541,plain,
% 1.74/1.94 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[884, 6540, 453, 874, 30])).
% 1.74/1.94 tff(6542,plain,
% 1.74/1.94 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[889, 6541, 6311])).
% 1.74/1.94 tff(6543,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(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(6544,plain,
% 1.74/1.94 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1)))))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(6545,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(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1))))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[6544])).
% 1.74/1.94 tff(6546,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(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[6545, 6543])).
% 1.74/1.94 tff(6547,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(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(6548,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(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[6547, 6546])).
% 1.74/1.94 tff(6549,plain,
% 1.74/1.94 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6548, 45, 6542, 6537])).
% 1.74/1.94 tff(6550,plain,
% 1.74/1.94 ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4801, 21, 6549])).
% 1.74/1.95 tff(6551,plain,
% 1.74/1.95 (b(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6550, 6529])).
% 1.74/1.95 tff(6552,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(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(6553,plain,
% 1.74/1.95 (((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1)))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(6554,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(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[6553])).
% 1.74/1.95 tff(6555,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(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[6554, 6552])).
% 1.74/1.95 tff(6556,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(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(6557,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(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[6556, 6555])).
% 1.74/1.95 tff(6558,plain,
% 1.74/1.95 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6557, 45, 6542, 6537])).
% 1.74/1.95 tff(6559,plain,
% 1.74/1.95 (b(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5524, 21, 6528, 6558])).
% 1.74/1.95 tff(6560,plain,
% 1.74/1.95 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6326, 6540, 30, 6279, 324, 272, 323])).
% 1.74/1.95 tff(6561,plain,
% 1.74/1.95 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1820, 6560, 6282])).
% 1.74/1.95 tff(6562,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(6563,plain,
% 1.74/1.95 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(6564,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[6563])).
% 1.74/1.95 tff(6565,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[6564, 6562])).
% 1.74/1.95 tff(6566,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(6567,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[6566, 6565])).
% 1.74/1.95 tff(6568,plain,
% 1.74/1.95 ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6567, 128, 6561, 4791, 6559])).
% 1.74/1.95 tff(6569,plain,
% 1.74/1.95 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6568, 6551])).
% 1.74/1.95 tff(6570,plain,
% 1.74/1.95 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1727, 21, 4674, 6569])).
% 1.74/1.95 tff(6571,plain,
% 1.74/1.95 (~b(s(s(s(s(elem!1)))), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6333, 128, 6561, 874, 3452])).
% 1.74/1.95 tff(6572,plain,
% 1.74/1.95 (r(s(s(s(s(elem!1)))), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2081, 6571])).
% 1.74/1.95 tff(6573,plain,
% 1.74/1.95 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1745, 6572, 272])).
% 1.74/1.95 tff(6574,plain,
% 1.74/1.95 (b(s(s(s(s(elem!1)))), s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1828, 6573])).
% 1.74/1.95 tff(6575,plain,
% 1.74/1.95 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2608, 6574, 6540, 30])).
% 1.74/1.95 tff(6576,plain,
% 1.74/1.95 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1897, 6575, 6279])).
% 1.74/1.95 tff(6577,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1904, 45, 6576, 6537, 6570])).
% 1.74/1.95 tff(6578,plain,((~r(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (s(s(elem!1)) = s(s(z))) | (~(s(z) = elem!1)) | (~b(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(6579,plain,
% 1.74/1.95 (~r(s(z), s(s(s(elem!1))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6578, 6521, 6274, 6502, 6266, 171, 6527, 6525, 6264, 6253, 6254])).
% 1.74/1.95 tff(6580,plain,
% 1.74/1.95 (b(s(z), s(s(s(elem!1))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[339, 6579])).
% 1.74/1.95 tff(6581,plain,
% 1.74/1.95 (~r(s(z), s(s(elem!1)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[3623, 6580, 6039, 6266, 6253, 6523, 171, 6273])).
% 1.74/1.95 tff(6582,plain,
% 1.74/1.95 (b(s(z), s(s(elem!1)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[117, 6581])).
% 1.74/1.95 tff(6583,plain,
% 1.74/1.95 (b(elem!1, s(s(elem!1)))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[6582, 6522])).
% 1.74/1.95 tff(6584,plain,
% 1.74/1.95 (b(s(s(elem!1)), elem!1)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[4662, 6502, 6266])).
% 1.74/1.95 tff(6585,plain,
% 1.74/1.95 (~b(s(elem!1), s(s(elem!1)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[4864, 128, 6584, 6583, 6521])).
% 1.74/1.95 tff(6586,plain,
% 1.74/1.95 ((s(elem!1) = s(s(elem!1))) | r(s(elem!1), s(s(elem!1)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[4819, 21, 6585])).
% 1.74/1.95 tff(6587,plain,
% 1.74/1.95 (r(s(elem!1), s(s(elem!1)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6586, 6509])).
% 1.74/1.95 tff(6588,plain,
% 1.74/1.95 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[884, 6582, 6253, 6527, 6266])).
% 1.74/1.95 tff(6589,plain,
% 1.74/1.95 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[889, 6588, 6523])).
% 1.74/1.95 tff(6590,plain,
% 1.74/1.95 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6557, 45, 6589, 6587])).
% 1.74/1.95 tff(6591,plain,
% 1.74/1.95 (b(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5524, 21, 6256, 6590])).
% 1.74/1.95 tff(6592,plain,
% 1.74/1.95 (b(s(z), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[6502])).
% 1.74/1.95 tff(6593,plain,
% 1.74/1.95 (b(elem!1, s(s(s(elem!1))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[6580, 6592])).
% 1.74/1.95 tff(6594,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(6595,plain,
% 1.74/1.95 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(6596,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[6595])).
% 1.74/1.95 tff(6597,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[6596, 6594])).
% 1.74/1.95 tff(6598,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(6599,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[6598, 6597])).
% 1.74/1.95 tff(6600,plain,
% 1.74/1.95 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6599, 128, 6593, 6521, 6591])).
% 1.74/1.95 tff(6601,plain,
% 1.74/1.95 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6548, 45, 6589, 6587])).
% 1.74/1.95 tff(6602,plain,
% 1.74/1.95 ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[4801, 21, 6601])).
% 1.74/1.95 tff(6603,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6602, 6600, 6257])).
% 1.74/1.95 tff(6604,plain,(b(s(s(elem!1)), s(s(s(elem!1)))) | b(s(s(s(elem!1))), s(z)) | b(z, elem!1) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(6605,plain,
% 1.74/1.95 (b(s(s(s(elem!1))), s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6604, 198, 455, 164])).
% 1.74/1.95 tff(6606,plain,
% 1.74/1.95 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[4469, 6605, 164, 1086, 198])).
% 1.74/1.95 tff(6607,plain,
% 1.74/1.95 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[321, 198, 2648])).
% 1.74/1.95 tff(6608,plain,
% 1.74/1.95 (~b(s(z), s(s(s(elem!1))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5189, 1842, 2718, 324, 164, 1086])).
% 1.74/1.95 tff(6609,plain,
% 1.74/1.95 (r(s(z), s(s(s(elem!1))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[339, 6608])).
% 1.74/1.95 tff(6610,plain,
% 1.74/1.95 (~r(s(z), s(s(elem!1)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[4323, 45, 324, 6609])).
% 1.74/1.95 tff(6611,plain,
% 1.74/1.95 (b(s(z), s(s(elem!1)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[117, 6610])).
% 1.74/1.95 tff(6612,plain,
% 1.74/1.95 (~b(s(s(elem!1)), elem!1)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2736, 4980, 4491, 6611])).
% 1.74/1.95 tff(6613,plain,
% 1.74/1.95 (r(s(s(elem!1)), elem!1)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1934, 6612, 1086])).
% 1.74/1.95 tff(6614,plain,
% 1.74/1.95 (~r(s(s(s(elem!1))), elem!1)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[4990, 6613, 324])).
% 1.74/1.95 tff(6615,plain,
% 1.74/1.95 (b(s(z), elem!1)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[665, 4594, 4879])).
% 1.74/1.95 tff(6616,plain,
% 1.74/1.95 (~b(s(s(s(elem!1))), elem!1)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[4998, 128, 4980, 6615, 2718])).
% 1.74/1.95 tff(6617,plain,
% 1.74/1.95 (s(s(s(elem!1))) = elem!1),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[742, 6616, 6614])).
% 1.74/1.95 tff(6618,plain,
% 1.74/1.95 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), elem!1)),
% 1.74/1.95 inference(monotonicity,[status(thm)],[6617])).
% 1.74/1.95 tff(6619,plain,
% 1.74/1.95 (b(s(z), elem!1) <=> b(s(z), s(s(s(elem!1))))),
% 1.74/1.95 inference(symmetry,[status(thm)],[6618])).
% 1.74/1.95 tff(6620,plain,
% 1.74/1.95 (b(s(z), s(s(s(elem!1))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[6615, 6619])).
% 1.74/1.95 tff(6621,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6608, 6620])).
% 1.74/1.95 tff(6622,plain,(b(z, elem!1) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(elem!1)) = elem!1) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(6623,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6622, 6607, 6605, 1086, 455, 6606, 164])).
% 1.74/1.95 tff(6624,plain,(b(s(s(elem!1)), s(s(s(elem!1)))) | (s(s(elem!1)) = elem!1) | b(z, elem!1) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(6625,plain,
% 1.74/1.95 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6624, 1086, 455, 164])).
% 1.74/1.95 tff(6626,plain,
% 1.74/1.95 (r(s(z), s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[6051])).
% 1.74/1.95 tff(6627,plain,
% 1.74/1.95 (elem!1 = s(z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1644, 6051])).
% 1.74/1.95 tff(6628,plain,
% 1.74/1.95 (~b(z, s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1638, 6627, 455])).
% 1.74/1.95 tff(6629,plain,
% 1.74/1.95 (r(z, s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[415, 6628])).
% 1.74/1.95 tff(6630,plain,
% 1.74/1.95 (~r(s(s(elem!1)), s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[405, 6629, 88])).
% 1.74/1.95 tff(6631,plain,
% 1.74/1.95 (b(s(s(elem!1)), s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[292, 6630])).
% 1.74/1.95 tff(6632,plain,
% 1.74/1.95 (~r(z, s(s(s(elem!1))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5285, 45, 5242, 6070])).
% 1.74/1.95 tff(6633,plain,
% 1.74/1.95 (b(z, s(s(s(elem!1))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[858, 6632])).
% 1.74/1.95 tff(6634,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(6635,plain,
% 1.74/1.95 (((~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(6636,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[6635])).
% 1.74/1.95 tff(6637,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[6636, 6634])).
% 1.74/1.95 tff(6638,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(6639,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[6638, 6637])).
% 1.74/1.95 tff(6640,plain,
% 1.74/1.95 (~b(s(s(elem!1)), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6639, 128, 2106, 6633, 6106])).
% 1.74/1.95 tff(6641,plain,
% 1.74/1.95 (r(s(s(elem!1)), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2018, 21, 154, 6640])).
% 1.74/1.95 tff(6642,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(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(6643,plain,
% 1.74/1.95 (((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(6644,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(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[6643])).
% 1.74/1.95 tff(6645,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(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[6644, 6642])).
% 1.74/1.95 tff(6646,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(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(6647,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(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[6646, 6645])).
% 1.74/1.95 tff(6648,plain,
% 1.74/1.95 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6647, 45, 6641, 6122, 6115])).
% 1.74/1.95 tff(6649,plain,
% 1.74/1.95 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[889, 6648, 4492])).
% 1.74/1.95 tff(6650,plain,
% 1.74/1.95 (~b(s(z), s(s(s(elem!1))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2114, 6649, 2106, 6631])).
% 1.74/1.95 tff(6651,plain,
% 1.74/1.95 (r(s(z), s(s(s(elem!1))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[339, 6650])).
% 1.74/1.95 tff(6652,plain,
% 1.74/1.95 (r(elem!1, s(s(s(elem!1))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[6651, 6626])).
% 1.74/1.95 tff(6653,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(6654,plain,
% 1.74/1.95 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(6655,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1)))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[6654])).
% 1.74/1.95 tff(6656,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[6655, 6653])).
% 1.74/1.95 tff(6657,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(6658,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[6657, 6656])).
% 1.74/1.95 tff(6659,plain,
% 1.74/1.95 ((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6658, 128, 6106, 6074, 6104])).
% 1.74/1.95 tff(6660,plain,
% 1.74/1.95 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6659, 6091])).
% 1.74/1.95 tff(6661,plain,
% 1.74/1.95 ((s(elem!1) = s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[4801, 21, 6660])).
% 1.74/1.95 tff(6662,plain,
% 1.74/1.95 (r(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6661, 4604])).
% 1.74/1.95 tff(6663,plain,
% 1.74/1.95 ((s(s(s(s(elem!1)))) = elem!1) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.74/1.95 inference(commutativity,[status(thm)],[])).
% 1.74/1.95 tff(6664,plain,
% 1.74/1.95 ((s(s(s(s(elem!1)))) = s(z)) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.74/1.95 inference(monotonicity,[status(thm)],[6051])).
% 1.74/1.95 tff(6665,plain,
% 1.74/1.95 ((s(s(s(s(elem!1)))) = s(z)) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[6664, 6663])).
% 1.74/1.95 tff(6666,plain,
% 1.74/1.95 ((~(s(s(s(s(elem!1)))) = s(z))) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[6665])).
% 1.74/1.95 tff(6667,plain,
% 1.74/1.95 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[1723, 6666])).
% 1.74/1.95 tff(6668,plain,
% 1.74/1.95 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[6052])).
% 1.74/1.95 tff(6669,plain,
% 1.74/1.95 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[6668, 1712])).
% 1.74/1.95 tff(6670,plain,
% 1.74/1.95 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 1.74/1.95 inference(transitivity,[status(thm)],[6669, 1748])).
% 1.74/1.95 tff(6671,plain,
% 1.74/1.95 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[6670])).
% 1.74/1.95 tff(6672,plain,
% 1.74/1.95 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[239, 6671])).
% 1.74/1.95 tff(6673,plain,
% 1.74/1.95 (b(elem!1, s(s(z))) <=> b(elem!1, s(elem!1))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[6052])).
% 1.74/1.95 tff(6674,plain,
% 1.74/1.95 (b(s(z), s(s(z))) <=> b(elem!1, s(s(z)))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[6051])).
% 1.74/1.95 tff(6675,plain,
% 1.74/1.95 (b(s(z), s(s(z))) <=> b(elem!1, s(elem!1))),
% 1.74/1.95 inference(transitivity,[status(thm)],[6674, 6673])).
% 1.74/1.95 tff(6676,plain,
% 1.74/1.96 (r(s(z), s(s(z))) <=> r(elem!1, s(s(z)))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6051])).
% 1.74/1.96 tff(6677,plain,
% 1.74/1.96 (r(elem!1, s(s(z))) <=> r(s(z), s(s(z)))),
% 1.74/1.96 inference(symmetry,[status(thm)],[6676])).
% 1.74/1.96 tff(6678,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)],[6053])).
% 1.74/1.96 tff(6679,plain,
% 1.74/1.96 (r(elem!1, s(elem!1)) <=> r(s(z), s(s(z)))),
% 1.74/1.96 inference(transitivity,[status(thm)],[6678, 6677])).
% 1.74/1.96 tff(6680,plain,
% 1.74/1.96 ((~r(elem!1, s(elem!1))) <=> (~r(s(z), s(s(z))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6679])).
% 1.74/1.96 tff(6681,plain,
% 1.74/1.96 (~r(elem!1, s(elem!1))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4070, 45, 6652, 6662])).
% 1.74/1.96 tff(6682,plain,
% 1.74/1.96 (~r(s(z), s(s(z)))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[6681, 6680])).
% 1.74/1.96 tff(6683,plain,
% 1.74/1.96 (b(s(z), s(s(z)))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[648, 6682])).
% 1.74/1.96 tff(6684,plain,
% 1.74/1.96 (b(elem!1, s(elem!1))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[6683, 6675])).
% 1.74/1.96 tff(6685,assumption,(r(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 1.74/1.96 tff(6686,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(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(6687,plain,
% 1.74/1.96 (((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(6688,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(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6687])).
% 1.74/1.96 tff(6689,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(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[6688, 6686])).
% 1.74/1.96 tff(6690,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(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(6691,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(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[6690, 6689])).
% 1.74/1.96 tff(6692,plain,
% 1.74/1.96 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6691, 45, 1772, 6685])).
% 1.74/1.96 tff(6693,plain,
% 1.74/1.96 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1920, 6692, 1918])).
% 1.74/1.96 tff(6694,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(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(6695,plain,
% 1.74/1.96 (((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1))))))) <=> ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(6696,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(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6695])).
% 1.74/1.96 tff(6697,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(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[6696, 6694])).
% 1.74/1.96 tff(6698,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(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(6699,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(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[6698, 6697])).
% 1.74/1.96 tff(6700,plain,
% 1.74/1.96 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6699, 45, 2458, 1772])).
% 1.74/1.96 tff(6701,plain,
% 1.74/1.96 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1766, 6700, 4935])).
% 1.74/1.96 tff(6702,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(6703,plain,
% 1.74/1.96 (((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1))))))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(6704,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1)))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6703])).
% 1.74/1.96 tff(6705,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[6704, 6702])).
% 1.74/1.96 tff(6706,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(6707,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1)))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[6706, 6705])).
% 1.74/1.96 tff(6708,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6707, 128, 1663, 6701, 6693, 1830, 4791])).
% 1.74/1.96 tff(6709,plain,((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (s(s(s(s(elem!1)))) = s(elem!1)) | (elem!1 = s(s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(6710,plain,
% 1.74/1.96 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6709, 6076, 6684, 6074, 6672, 6667, 6662, 6652])).
% 1.74/1.96 tff(6711,plain,
% 1.74/1.96 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1820, 6710, 2650])).
% 1.74/1.96 tff(6712,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(6713,plain,
% 1.74/1.96 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(6714,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6713])).
% 1.74/1.96 tff(6715,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[6714, 6712])).
% 1.74/1.96 tff(6716,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(6717,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[6716, 6715])).
% 1.74/1.96 tff(6718,plain,
% 1.74/1.96 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6717, 128, 6078, 2106, 6649, 6711])).
% 1.74/1.96 tff(6719,plain,
% 1.74/1.96 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2212, 21, 1646, 6718])).
% 1.74/1.96 tff(6720,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(6721,plain,
% 1.74/1.96 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(6722,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1))))))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6721])).
% 1.74/1.96 tff(6723,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[6722, 6720])).
% 1.74/1.96 tff(6724,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(6725,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1))))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[6724, 6723])).
% 1.74/1.96 tff(6726,plain,
% 1.74/1.96 (~b(z, s(s(s(s(elem!1)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6725, 128, 2106, 6649, 6711, 6633])).
% 1.74/1.96 tff(6727,plain,
% 1.74/1.96 (r(z, s(s(s(s(elem!1)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2047, 21, 6726, 178])).
% 1.74/1.96 tff(6728,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[3222, 6727, 6719, 88])).
% 1.74/1.96 tff(6729,plain,((s(s(elem!1)) = elem!1) | (~r(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | b(z, elem!1) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(6730,plain,
% 1.74/1.96 (s(s(elem!1)) = elem!1),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6729, 88, 2106, 455, 164])).
% 1.74/1.96 tff(6731,plain,
% 1.74/1.96 (s(s(s(elem!1))) = s(elem!1)),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6730])).
% 1.74/1.96 tff(6732,plain,
% 1.74/1.96 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6731])).
% 1.74/1.96 tff(6733,plain,
% 1.74/1.96 (s(s(s(s(elem!1)))) = elem!1),
% 1.74/1.96 inference(transitivity,[status(thm)],[6732, 6730])).
% 1.74/1.96 tff(6734,plain,
% 1.74/1.96 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6733])).
% 1.74/1.96 tff(6735,plain,
% 1.74/1.96 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 1.74/1.96 inference(transitivity,[status(thm)],[6734, 225])).
% 1.74/1.96 tff(6736,plain,
% 1.74/1.96 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6735])).
% 1.74/1.96 tff(6737,plain,
% 1.74/1.96 (~(s(s(z)) = elem!1)),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[239, 6736])).
% 1.74/1.96 tff(6738,plain,
% 1.74/1.96 (b(s(z), s(s(elem!1))) <=> b(s(z), elem!1)),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6730])).
% 1.74/1.96 tff(6739,plain,
% 1.74/1.96 (b(s(z), elem!1)),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[2346, 6738])).
% 1.74/1.96 tff(6740,plain,
% 1.74/1.96 (r(z, s(s(elem!1))) <=> r(z, elem!1)),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6730])).
% 1.74/1.96 tff(6741,plain,
% 1.74/1.96 (r(z, elem!1)),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[88, 6740])).
% 1.74/1.96 tff(6742,plain,
% 1.74/1.96 ((s(s(elem!1)) = s(z)) <=> (elem!1 = s(z))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6730])).
% 1.74/1.96 tff(6743,plain,
% 1.74/1.96 ((~(s(s(elem!1)) = s(z))) <=> (~(elem!1 = s(z)))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6742])).
% 1.74/1.96 tff(6744,plain,
% 1.74/1.96 (~(elem!1 = s(z))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[111, 6743])).
% 1.74/1.96 tff(6745,plain,
% 1.74/1.96 ((s(s(elem!1)) = z) <=> (elem!1 = z)),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6730])).
% 1.74/1.96 tff(6746,plain,
% 1.74/1.96 ((s(s(elem!1)) = z) <=> (z = elem!1)),
% 1.74/1.96 inference(transitivity,[status(thm)],[6745, 247])).
% 1.74/1.96 tff(6747,plain,
% 1.74/1.96 ((~(s(s(elem!1)) = z)) <=> (~(z = elem!1))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6746])).
% 1.74/1.96 tff(6748,plain,
% 1.74/1.96 (~(z = elem!1)),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[154, 6747])).
% 1.74/1.96 tff(6749,plain,
% 1.74/1.96 ((s(s(elem!1)) = s(z)) <=> (s(z) = elem!1)),
% 1.74/1.96 inference(transitivity,[status(thm)],[6742, 253])).
% 1.74/1.96 tff(6750,plain,
% 1.74/1.96 ((~(s(s(elem!1)) = s(z))) <=> (~(s(z) = elem!1))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6749])).
% 1.74/1.96 tff(6751,plain,
% 1.74/1.96 (~(s(z) = elem!1)),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[111, 6750])).
% 1.74/1.96 tff(6752,plain,
% 1.74/1.96 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[245, 6730])).
% 1.74/1.96 tff(6753,plain,
% 1.74/1.96 (~(s(s(s(s(z)))) = elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[242, 6730])).
% 1.74/1.96 tff(6754,plain,
% 1.74/1.96 (~b(elem!1, s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6174, 6739, 6753, 6752, 6741, 6737, 455, 164, 6751, 6748])).
% 1.74/1.96 tff(6755,plain,
% 1.74/1.96 (r(elem!1, s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[305, 6754, 6744])).
% 1.74/1.96 tff(6756,plain,
% 1.74/1.96 (~r(z, s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4896, 6755, 6741])).
% 1.74/1.96 tff(6757,plain,
% 1.74/1.96 (b(z, s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[415, 6756])).
% 1.74/1.96 tff(6758,plain,
% 1.74/1.96 (b(elem!1, z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2915, 6757, 164, 455])).
% 1.74/1.96 tff(6759,plain,
% 1.74/1.96 (~b(s(s(z)), elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6217, 6758, 6757, 6739, 171])).
% 1.74/1.96 tff(6760,plain,
% 1.74/1.96 (r(s(s(z)), elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[370, 6759, 6737])).
% 1.74/1.96 tff(6761,plain,
% 1.74/1.96 (~r(s(s(z)), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1433, 45, 6741, 6760])).
% 1.74/1.96 tff(6762,plain,
% 1.74/1.96 (b(s(s(z)), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[25, 6761])).
% 1.74/1.96 tff(6763,plain,
% 1.74/1.96 (~b(s(s(z)), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6238, 128, 6758, 6757, 6739, 6762])).
% 1.74/1.96 tff(6764,plain,
% 1.74/1.96 (r(s(s(z)), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[86, 6763])).
% 1.74/1.96 tff(6765,plain,
% 1.74/1.96 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 1.74/1.96 inference(transitivity,[status(thm)],[6735, 650])).
% 1.74/1.96 tff(6766,plain,
% 1.74/1.96 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(elem!1 = s(s(z))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6765])).
% 1.74/1.96 tff(6767,plain,
% 1.74/1.96 (~(elem!1 = s(s(z)))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[239, 6766])).
% 1.74/1.96 tff(6768,plain,
% 1.74/1.96 (~r(z, s(s(z)))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1441, 45, 6741, 6760])).
% 1.74/1.96 tff(6769,plain,
% 1.74/1.96 (b(z, s(s(z)))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[516, 6768])).
% 1.74/1.96 tff(6770,plain,
% 1.74/1.96 (~b(elem!1, s(s(z)))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6229, 128, 6758, 6769, 6762])).
% 1.74/1.96 tff(6771,plain,
% 1.74/1.96 (r(elem!1, s(s(z)))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[493, 6770, 6767])).
% 1.74/1.96 tff(6772,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(z))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(6773,plain,
% 1.74/1.96 (((~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1))) <=> ((~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(6774,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(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z))))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6773])).
% 1.74/1.96 tff(6775,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(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[6774, 6772])).
% 1.74/1.96 tff(6776,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(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(6777,plain,
% 1.74/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[6776, 6775])).
% 1.74/1.96 tff(6778,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6777, 45, 6755, 6760, 6771, 6764])).
% 1.74/1.96 tff(6779,plain,((~r(z, s(s(elem!1)))) | b(s(z), z) | b(z, elem!1) | (~b(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(6780,plain,
% 1.74/1.96 (~r(z, s(s(elem!1)))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6779, 6625, 455, 164])).
% 1.74/1.96 tff(6781,plain,
% 1.74/1.96 (b(z, s(s(elem!1)))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[160, 6780])).
% 1.74/1.96 tff(6782,plain,
% 1.74/1.96 (~r(s(z), s(s(s(elem!1))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5923, 6781, 6625, 171])).
% 1.74/1.96 tff(6783,plain,
% 1.74/1.96 (b(s(z), s(s(s(elem!1))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[339, 6782])).
% 1.74/1.96 tff(6784,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(6785,plain,
% 1.74/1.96 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(6786,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6785])).
% 1.74/1.96 tff(6787,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 1.74/1.96 inference(transitivity,[status(thm)],[6786, 6784])).
% 1.74/1.96 tff(6788,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(6789,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[6788, 6787])).
% 1.74/1.97 tff(6790,plain,
% 1.74/1.97 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6789, 128, 6781, 6625, 6049])).
% 1.74/1.97 tff(6791,plain,
% 1.74/1.97 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[889, 6790, 4492])).
% 1.74/1.97 tff(6792,plain,
% 1.74/1.97 (~r(s(z), s(s(elem!1)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[3175, 6791, 6039, 171])).
% 1.74/1.97 tff(6793,plain,
% 1.74/1.97 (b(s(z), s(s(elem!1)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[117, 6792])).
% 1.74/1.97 tff(6794,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(6795,plain,
% 1.74/1.97 (((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(6796,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[6795])).
% 1.74/1.97 tff(6797,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[6796, 6794])).
% 1.74/1.97 tff(6798,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(6799,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1)))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[6798, 6797])).
% 1.74/1.97 tff(6800,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6799, 128, 6781, 6793, 6625, 6783, 6049])).
% 1.74/1.97 tff(6801,plain,((s(s(elem!1)) = elem!1) | b(z, elem!1) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(6802,plain,
% 1.74/1.97 (s(s(elem!1)) = elem!1),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6801, 455, 164])).
% 1.74/1.97 tff(6803,plain,
% 1.74/1.97 (elem!1 = s(s(elem!1))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[377, 6802])).
% 1.74/1.97 tff(6804,plain,
% 1.74/1.97 (~b(z, s(s(elem!1)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[457, 6803, 455])).
% 1.74/1.97 tff(6805,plain,
% 1.74/1.97 (r(z, s(s(elem!1)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[160, 6804])).
% 1.74/1.97 tff(6806,plain,
% 1.74/1.97 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6251, 6805, 455, 164])).
% 1.74/1.97 tff(6807,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6779, 6806, 6805, 455, 164])).
% 1.74/1.97 tff(6808,plain,(b(z, elem!1) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(6809,plain,
% 1.74/1.97 (b(z, elem!1)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6808, 164])).
% 1.74/1.97 tff(6810,plain,
% 1.74/1.97 (~r(s(s(s(elem!1))), z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6047, 272, 385])).
% 1.74/1.97 tff(6811,plain,
% 1.74/1.97 (b(s(s(s(elem!1))), z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5301, 6810])).
% 1.74/1.97 tff(6812,plain,
% 1.74/1.97 ((~(s(s(s(elem!1))) = elem!1)) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[705])).
% 1.74/1.97 tff(6813,plain,
% 1.74/1.97 (~b(s(s(elem!1)), s(s(z)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5152, 128, 30, 876, 273])).
% 1.74/1.97 tff(6814,plain,
% 1.74/1.97 (r(s(s(elem!1)), s(s(z)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[4339, 21, 1, 6813])).
% 1.74/1.97 tff(6815,plain,
% 1.74/1.97 (~b(s(s(z)), s(s(elem!1)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[134, 128, 30, 876, 273])).
% 1.74/1.97 tff(6816,plain,
% 1.74/1.97 ((s(s(z)) = s(s(elem!1))) | r(s(s(z)), s(s(elem!1)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[138, 21, 6815])).
% 1.74/1.97 tff(6817,plain,
% 1.74/1.97 (r(s(s(z)), s(s(elem!1)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6816, 34])).
% 1.74/1.97 tff(6818,plain,
% 1.74/1.97 (~r(s(s(z)), z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[146, 45, 27, 88, 6817])).
% 1.74/1.97 tff(6819,plain,
% 1.74/1.97 (b(s(s(z)), z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[25, 6818])).
% 1.74/1.97 tff(6820,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(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(6821,plain,
% 1.74/1.97 (((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(6822,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(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(elem!1))))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[6821])).
% 1.74/1.97 tff(6823,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(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[6822, 6820])).
% 1.74/1.97 tff(6824,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(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(6825,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(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(elem!1))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[6824, 6823])).
% 1.74/1.97 tff(6826,plain,
% 1.74/1.97 (~r(z, s(s(z)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6825, 45, 88, 6817])).
% 1.74/1.97 tff(6827,plain,
% 1.74/1.97 (b(z, s(s(z)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[516, 6826])).
% 1.74/1.97 tff(6828,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(6829,plain,
% 1.74/1.97 (((~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(6830,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z))))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[6829])).
% 1.74/1.97 tff(6831,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[6830, 6828])).
% 1.74/1.97 tff(6832,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(6833,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[6832, 6831])).
% 1.74/1.97 tff(6834,plain,
% 1.74/1.97 (~b(s(s(s(elem!1))), s(s(z)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6833, 128, 3452, 6827, 6819])).
% 1.74/1.97 tff(6835,plain,
% 1.74/1.97 (r(s(s(s(elem!1))), s(s(z)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[4350, 21, 6834, 283])).
% 1.74/1.97 tff(6836,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(elem!1))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(6837,plain,
% 1.74/1.97 (((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(6838,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(elem!1))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z))))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[6837])).
% 1.74/1.97 tff(6839,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(elem!1))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[6838, 6836])).
% 1.74/1.97 tff(6840,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(elem!1))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(6841,plain,
% 1.74/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[6840, 6839])).
% 1.74/1.97 tff(6842,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6841, 45, 324, 6835, 6814])).
% 1.74/1.97 tff(6843,plain,((~b(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (s(s(elem!1)) = s(s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(6844,plain,
% 1.74/1.97 (~b(s(s(z)), s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6843, 27, 6811, 324, 88, 1, 6292, 2409])).
% 1.74/1.97 tff(6845,plain,
% 1.74/1.97 (r(s(s(z)), s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[86, 6844])).
% 1.74/1.97 tff(6846,plain,
% 1.74/1.97 (~r(s(s(z)), z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1509, 6845, 272])).
% 1.74/1.97 tff(6847,plain,
% 1.74/1.97 (b(s(s(z)), z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[25, 6846])).
% 1.74/1.97 tff(6848,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(elem!1)))) | (~r(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(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(6849,plain,
% 1.74/1.97 (((~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(z))) | (~r(elem!1, z))) <=> ((~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(6850,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(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(z))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1))))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[6849])).
% 1.74/1.97 tff(6851,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(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(z))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[6850, 6848])).
% 1.74/1.97 tff(6852,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(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(z))) | (~r(elem!1, z)))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(6853,plain,
% 1.74/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[6852, 6851])).
% 1.74/1.97 tff(6854,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6853, 45, 1004, 27, 88, 2729])).
% 1.74/1.97 tff(6855,plain,((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(6856,plain,
% 1.74/1.97 (~r(elem!1, s(s(elem!1)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6855, 1004, 88, 27])).
% 1.74/1.97 tff(6857,plain,
% 1.74/1.97 (b(elem!1, s(s(elem!1)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2371, 6856, 375])).
% 1.74/1.97 tff(6858,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(6859,plain,
% 1.74/1.97 (((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(6860,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[6859])).
% 1.74/1.97 tff(6861,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[6860, 6858])).
% 1.74/1.97 tff(6862,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(6863,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[6862, 6861])).
% 1.74/1.97 tff(6864,plain,
% 1.74/1.97 (~b(s(z), elem!1)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6863, 128, 30, 6857, 2409])).
% 1.74/1.97 tff(6865,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), elem!1)) | (~r(s(z), z)) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(elem!1, z)))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(6866,plain,
% 1.74/1.97 (((~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), elem!1))) <=> ((~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(elem!1, z)))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(6867,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(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(elem!1, z))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[6866])).
% 1.74/1.97 tff(6868,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(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(elem!1, z)))),
% 1.74/1.97 inference(transitivity,[status(thm)],[6867, 6865])).
% 1.74/1.97 tff(6869,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(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), elem!1)))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(6870,plain,
% 1.74/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(elem!1, z))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[6869, 6868])).
% 1.74/1.97 tff(6871,plain,
% 1.74/1.97 (~r(s(z), elem!1)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6870, 45, 1004, 272])).
% 1.74/1.97 tff(6872,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[665, 6871, 6864, 1610])).
% 1.74/1.97 tff(6873,plain,((~r(elem!1, z)) | (s(z) = elem!1) | (~r(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (elem!1 = s(s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(6874,plain,
% 1.74/1.97 (~r(elem!1, z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6873, 27, 272, 6292, 375, 88, 1610])).
% 1.74/1.97 tff(6875,plain,
% 1.74/1.97 (b(elem!1, z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[574, 6874, 5065])).
% 1.74/1.97 tff(6876,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(6877,plain,
% 1.74/1.97 (((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(6878,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[6877])).
% 1.74/1.97 tff(6879,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[6878, 6876])).
% 1.74/1.98 tff(6880,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(6881,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[6880, 6879])).
% 1.74/1.98 tff(6882,plain,
% 1.74/1.98 (~b(s(s(s(elem!1))), s(s(z)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6881, 128, 498, 6875, 6811, 6847])).
% 1.74/1.98 tff(6883,plain,
% 1.74/1.98 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6248, 6845, 385])).
% 1.74/1.98 tff(6884,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[4350, 21, 6883, 6882, 283])).
% 1.74/1.98 tff(6885,plain,((~r(z, s(z))) | (~b(z, elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (s(s(elem!1)) = s(s(z))) | (elem!1 = z) | (elem!1 = s(s(elem!1))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(6886,plain,
% 1.74/1.98 (~r(z, s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6885, 1610, 385, 272, 324, 88, 1, 5065, 2344, 498])).
% 1.74/1.98 tff(6887,plain,
% 1.74/1.98 (b(z, s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[415, 6886])).
% 1.74/1.98 tff(6888,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(6889,plain,
% 1.74/1.98 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(6890,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[6889])).
% 1.74/1.98 tff(6891,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[6890, 6888])).
% 1.74/1.98 tff(6892,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(6893,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[6892, 6891])).
% 1.74/1.98 tff(6894,plain,
% 1.74/1.98 (~b(s(s(elem!1)), z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6893, 128, 30, 550, 876])).
% 1.74/1.98 tff(6895,plain,
% 1.74/1.98 (r(s(s(elem!1)), z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2018, 21, 154, 6894])).
% 1.74/1.98 tff(6896,plain,
% 1.74/1.98 (r(z, s(s(s(elem!1))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[561, 550, 549, 544])).
% 1.74/1.98 tff(6897,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[4572, 45, 324, 6896, 6895])).
% 1.74/1.98 tff(6898,plain,((~b(z, s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | r(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(6899,plain,
% 1.74/1.98 (~b(s(z), s(s(s(elem!1))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6898, 6887, 6292, 2409, 324, 6810])).
% 1.74/1.98 tff(6900,plain,
% 1.74/1.98 (r(s(z), s(s(s(elem!1))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[339, 6899])).
% 1.74/1.98 tff(6901,plain,
% 1.74/1.98 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6326, 6900, 324, 1664, 6292, 272, 2409])).
% 1.74/1.98 tff(6902,plain,
% 1.74/1.98 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1820, 6901, 2650])).
% 1.74/1.98 tff(6903,plain,
% 1.74/1.98 (~b(s(s(elem!1)), z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6893, 128, 6292, 6887, 2409])).
% 1.74/1.98 tff(6904,plain,
% 1.74/1.98 (r(s(s(elem!1)), z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2018, 21, 154, 6903])).
% 1.74/1.98 tff(6905,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(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(6906,plain,
% 1.74/1.98 (((~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(6907,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(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[6906])).
% 1.74/1.98 tff(6908,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(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)))),
% 1.74/1.98 inference(transitivity,[status(thm)],[6907, 6905])).
% 1.74/1.98 tff(6909,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(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(6910,plain,
% 1.74/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[6909, 6908])).
% 1.74/1.98 tff(6911,plain,
% 1.74/1.98 (~r(s(s(elem!1)), elem!1)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6910, 45, 1004, 1519])).
% 1.74/1.98 tff(6912,plain,
% 1.74/1.98 (b(s(s(elem!1)), elem!1)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1934, 6911, 1086])).
% 1.74/1.98 tff(6913,plain,
% 1.74/1.98 (~r(elem!1, s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1987, 45, 1004, 272])).
% 1.74/1.98 tff(6914,plain,
% 1.74/1.98 (b(elem!1, s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[305, 6913, 1642])).
% 1.74/1.98 tff(6915,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2736, 6914, 6912, 30, 876])).
% 1.74/1.98 tff(6916,plain,((~r(elem!1, z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (elem!1 = s(z)) | (s(s(elem!1)) = elem!1) | (~r(s(z), z)) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(6917,plain,
% 1.74/1.98 (~r(elem!1, z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6916, 5008, 2409, 6292, 1086, 272, 6904])).
% 1.74/1.98 tff(6918,plain,
% 1.74/1.98 (b(elem!1, z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[574, 6917, 5065])).
% 1.74/1.98 tff(6919,plain,
% 1.74/1.98 (s(s(s(s(elem!1)))) = s(elem!1)),
% 1.74/1.98 inference(monotonicity,[status(thm)],[710])).
% 1.74/1.98 tff(6920,plain,
% 1.74/1.98 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.74/1.98 inference(symmetry,[status(thm)],[6919])).
% 1.74/1.98 tff(6921,plain,
% 1.74/1.98 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[6920])).
% 1.74/1.98 tff(6922,plain,
% 1.74/1.98 (r(s(s(s(s(elem!1)))), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.74/1.98 inference(symmetry,[status(thm)],[6921])).
% 1.74/1.98 tff(6923,plain,
% 1.74/1.98 (b(s(elem!1), z) <=> b(s(s(s(s(elem!1)))), z)),
% 1.74/1.98 inference(monotonicity,[status(thm)],[6920])).
% 1.74/1.98 tff(6924,plain,
% 1.74/1.98 ((~b(s(elem!1), z)) <=> (~b(s(s(s(s(elem!1)))), z))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[6923])).
% 1.74/1.98 tff(6925,plain,
% 1.74/1.98 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(elem!1), elem!1)),
% 1.74/1.98 inference(monotonicity,[status(thm)],[6919])).
% 1.74/1.98 tff(6926,plain,
% 1.74/1.98 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.74/1.98 inference(monotonicity,[status(thm)],[710])).
% 1.74/1.98 tff(6927,plain,
% 1.74/1.98 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[1842, 6926])).
% 1.74/1.98 tff(6928,plain,
% 1.74/1.98 (b(s(elem!1), elem!1)),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[6927, 6925])).
% 1.74/1.98 tff(6929,plain,
% 1.74/1.98 (~b(s(elem!1), z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5997, 128, 498, 577, 6928])).
% 1.74/1.98 tff(6930,plain,
% 1.74/1.98 (~b(s(s(s(s(elem!1)))), z)),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[6929, 6924])).
% 1.74/1.98 tff(6931,plain,
% 1.74/1.98 (r(s(s(s(s(elem!1)))), z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2081, 6930])).
% 1.74/1.98 tff(6932,plain,
% 1.74/1.98 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1745, 6931, 272])).
% 1.74/1.98 tff(6933,plain,
% 1.74/1.98 (b(s(s(s(s(elem!1)))), s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1828, 6932])).
% 1.74/1.98 tff(6934,plain,
% 1.74/1.98 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2608, 6933, 876, 30])).
% 1.74/1.98 tff(6935,plain,
% 1.74/1.98 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1897, 6934, 1063])).
% 1.74/1.98 tff(6936,plain,
% 1.74/1.98 (r(s(elem!1), s(s(elem!1)))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[6935, 6922])).
% 1.74/1.98 tff(6937,plain,
% 1.74/1.98 (r(s(elem!1), z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[728, 21, 109, 6929])).
% 1.74/1.98 tff(6938,plain,
% 1.74/1.98 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(elem!1)), elem!1)),
% 1.74/1.98 inference(monotonicity,[status(thm)],[710])).
% 1.74/1.98 tff(6939,plain,
% 1.74/1.98 (r(s(s(elem!1)), elem!1)),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[324, 6938])).
% 1.74/1.98 tff(6940,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(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(6941,plain,
% 1.74/1.98 (((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(6942,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(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[6941])).
% 1.74/1.98 tff(6943,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(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[6942, 6940])).
% 1.74/1.98 tff(6944,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(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(6945,plain,
% 1.74/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[6944, 6943])).
% 1.74/1.98 tff(6946,plain,
% 1.74/1.98 (~r(s(elem!1), s(s(elem!1)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6945, 45, 6939, 1519, 6937])).
% 1.74/1.98 tff(6947,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6946, 6936])).
% 1.74/1.98 tff(6948,plain,((~(s(s(s(elem!1))) = elem!1)) | (~r(s(s(elem!1)), z)) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(6949,plain,
% 1.74/1.98 (~(s(s(s(elem!1))) = elem!1)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6948, 6904, 1664, 2409, 6292, 272, 498, 6918, 6902, 324])).
% 1.74/1.98 tff(6950,plain,
% 1.74/1.98 (~(elem!1 = s(s(s(elem!1))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[6949, 6812])).
% 1.74/1.98 tff(6951,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(6952,plain,
% 1.74/1.98 (((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(6953,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[6952])).
% 1.74/1.98 tff(6954,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 1.74/1.98 inference(transitivity,[status(thm)],[6953, 6951])).
% 1.74/1.98 tff(6955,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(6956,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[6955, 6954])).
% 1.74/1.98 tff(6957,plain,
% 1.74/1.98 (~b(s(s(s(elem!1))), elem!1)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6956, 128, 498, 577, 3452])).
% 1.74/1.98 tff(6958,plain,
% 1.74/1.98 (r(s(s(s(elem!1))), elem!1)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[742, 6957, 817])).
% 1.74/1.98 tff(6959,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(6960,plain,
% 1.74/1.98 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(6961,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[6960])).
% 1.74/1.98 tff(6962,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[6961, 6959])).
% 1.74/1.98 tff(6963,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(6964,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[6963, 6962])).
% 1.74/1.98 tff(6965,plain,
% 1.74/1.98 (~b(elem!1, s(s(s(elem!1))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6964, 128, 498, 577, 3452])).
% 1.74/1.98 tff(6966,plain,
% 1.74/1.98 (r(elem!1, s(s(s(elem!1))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2466, 6965, 4049])).
% 1.74/1.98 tff(6967,plain,
% 1.74/1.98 (~r(s(s(elem!1)), elem!1)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[4990, 6958, 324])).
% 1.74/1.98 tff(6968,plain,
% 1.74/1.98 (b(s(s(elem!1)), elem!1)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1934, 6967, 1086])).
% 1.74/1.98 tff(6969,plain,
% 1.74/1.98 (~b(elem!1, s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2736, 6968, 6292, 876])).
% 1.74/1.98 tff(6970,plain,
% 1.74/1.98 (r(elem!1, s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[305, 6969, 1642])).
% 1.74/1.98 tff(6971,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(elem!1, s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(6972,plain,
% 1.74/1.98 (((~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(elem!1, s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(6973,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(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z)))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[6972])).
% 1.74/1.98 tff(6974,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(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[6973, 6971])).
% 1.74/1.98 tff(6975,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(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(6976,plain,
% 1.74/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z)))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[6975, 6974])).
% 1.74/1.98 tff(6977,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6976, 45, 6970, 6966, 6958, 385])).
% 1.74/1.98 tff(6978,plain,((~b(elem!1, z)) | (~r(s(s(s(elem!1))), s(z))) | (elem!1 = s(z)) | (~b(s(z), s(s(elem!1)))) | (s(s(elem!1)) = elem!1) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (elem!1 = s(s(s(elem!1)))) | (s(s(s(elem!1))) = elem!1) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(6979,plain,
% 1.74/1.98 (elem!1 = s(s(s(elem!1)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6978, 6949, 5008, 2409, 1086, 324, 385, 6918, 498, 6811])).
% 1.74/1.98 tff(6980,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6979, 6950])).
% 1.74/1.98 tff(6981,plain,((s(z) = elem!1) | (s(s(elem!1)) = elem!1) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~b(z, elem!1)) | (~r(s(z), z)) | (elem!1 = z) | (~r(z, s(s(elem!1)))) | (s(s(elem!1)) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(6982,plain,
% 1.74/1.98 (s(z) = elem!1),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6981, 88, 324, 385, 498, 272, 5065, 1086, 1])).
% 1.74/1.98 tff(6983,plain,
% 1.74/1.98 (s(s(z)) = s(elem!1)),
% 1.74/1.98 inference(monotonicity,[status(thm)],[6982])).
% 1.74/1.98 tff(6984,plain,
% 1.74/1.98 (s(elem!1) = s(s(z))),
% 1.74/1.98 inference(symmetry,[status(thm)],[6983])).
% 1.74/1.98 tff(6985,plain,
% 1.74/1.98 (b(s(elem!1), z) <=> b(s(s(z)), z)),
% 1.74/1.98 inference(monotonicity,[status(thm)],[6984])).
% 1.74/1.98 tff(6986,plain,
% 1.74/1.98 (b(s(s(z)), z) <=> b(s(elem!1), z)),
% 1.74/1.98 inference(symmetry,[status(thm)],[6985])).
% 1.74/1.98 tff(6987,plain,
% 1.74/1.98 (b(s(s(elem!1)), elem!1)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[4662, 6982, 6292])).
% 1.74/1.98 tff(6988,assumption,(s(s(elem!1)) = s(elem!1)), introduced(assumption)).
% 1.74/1.98 tff(6989,plain,
% 1.74/1.98 (s(s(elem!1)) = s(s(z))),
% 1.74/1.98 inference(transitivity,[status(thm)],[6988, 4804])).
% 1.74/1.98 tff(6990,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1, 6989])).
% 1.74/1.98 tff(6991,plain,((~(s(s(elem!1)) = s(elem!1))) | (s(s(elem!1)) = s(s(z))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(6992,plain,
% 1.74/1.98 (~(s(s(elem!1)) = s(elem!1))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6991, 6982, 1])).
% 1.74/1.98 tff(6993,plain,
% 1.74/1.98 (b(s(z), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[6982])).
% 1.74/1.98 tff(6994,plain,
% 1.74/1.98 (b(elem!1, s(s(elem!1)))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[2409, 6993])).
% 1.74/1.98 tff(6995,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(6996,plain,
% 1.74/1.98 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(6997,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[6996])).
% 1.74/1.98 tff(6998,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[6997, 6995])).
% 1.74/1.98 tff(6999,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(7000,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[6999, 6998])).
% 1.74/1.98 tff(7001,plain,
% 1.74/1.98 (~b(s(s(elem!1)), z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[7000, 128, 498, 6987, 6994])).
% 1.74/1.98 tff(7002,plain,
% 1.74/1.98 (r(s(s(elem!1)), z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2018, 21, 154, 7001])).
% 1.74/1.99 tff(7003,plain,
% 1.74/1.99 (r(s(elem!1), z) <=> r(s(s(z)), z)),
% 1.74/1.99 inference(monotonicity,[status(thm)],[4804])).
% 1.74/1.99 tff(7004,plain,
% 1.74/1.99 (r(s(s(z)), z) <=> r(s(elem!1), z)),
% 1.74/1.99 inference(symmetry,[status(thm)],[7003])).
% 1.74/1.99 tff(7005,plain,
% 1.74/1.99 (r(s(elem!1), z)),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[28, 7004])).
% 1.74/1.99 tff(7006,assumption,(~(s(s(elem!1)) = s(elem!1))), introduced(assumption)).
% 1.74/1.99 tff(7007,plain,
% 1.74/1.99 (b(s(s(z)), s(z)) <=> b(s(s(z)), elem!1)),
% 1.74/1.99 inference(monotonicity,[status(thm)],[1640])).
% 1.74/1.99 tff(7008,plain,
% 1.74/1.99 (b(s(s(z)), s(z)) <=> b(s(elem!1), elem!1)),
% 1.74/1.99 inference(transitivity,[status(thm)],[7007, 4606])).
% 1.74/1.99 tff(7009,plain,
% 1.74/1.99 (~r(s(s(z)), s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[1509, 28, 272])).
% 1.74/1.99 tff(7010,plain,
% 1.74/1.99 (b(s(s(z)), s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[86, 7009])).
% 1.74/1.99 tff(7011,plain,
% 1.74/1.99 (b(s(elem!1), elem!1)),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[7010, 7008])).
% 1.74/1.99 tff(7012,plain,
% 1.74/1.99 (b(elem!1, s(s(z))) <=> b(elem!1, s(elem!1))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[4605])).
% 1.74/1.99 tff(7013,plain,
% 1.74/1.99 (b(s(z), s(s(z))) <=> b(elem!1, s(s(z)))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[1640])).
% 1.74/1.99 tff(7014,plain,
% 1.74/1.99 (b(s(z), s(s(z))) <=> b(elem!1, s(elem!1))),
% 1.74/1.99 inference(transitivity,[status(thm)],[7013, 7012])).
% 1.74/1.99 tff(7015,plain,
% 1.74/1.99 (~r(s(z), s(s(z)))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[1327, 28, 272])).
% 1.74/1.99 tff(7016,plain,
% 1.74/1.99 (b(s(z), s(s(z)))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[648, 7015])).
% 1.74/1.99 tff(7017,plain,
% 1.74/1.99 (b(elem!1, s(elem!1))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[7016, 7014])).
% 1.74/1.99 tff(7018,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(7019,plain,
% 1.74/1.99 (((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(7020,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1)))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[7019])).
% 1.74/1.99 tff(7021,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[7020, 7018])).
% 1.74/1.99 tff(7022,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(7023,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1)))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[7022, 7021])).
% 1.74/1.99 tff(7024,plain,
% 1.74/1.99 (~b(s(s(elem!1)), s(elem!1))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[7023, 128, 1681, 7017, 7011])).
% 1.74/1.99 tff(7025,plain,
% 1.74/1.99 (r(s(s(elem!1)), s(elem!1))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[4835, 21, 7024, 7006])).
% 1.74/1.99 tff(7026,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(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(7027,plain,
% 1.74/1.99 (((~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(7028,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), z)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[7027])).
% 1.74/1.99 tff(7029,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), z)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)))),
% 1.74/1.99 inference(transitivity,[status(thm)],[7028, 7026])).
% 1.74/1.99 tff(7030,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), z)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(7031,plain,
% 1.74/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[7030, 7029])).
% 1.74/1.99 tff(7032,plain,
% 1.74/1.99 ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[7031, 45, 1519])).
% 1.74/1.99 tff(7033,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[7032, 7025, 7005])).
% 1.74/1.99 tff(7034,plain,((~r(s(s(z)), z)) | (~r(s(s(elem!1)), z)) | (s(s(elem!1)) = s(elem!1)) | (~(s(z) = elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(7035,plain,
% 1.74/1.99 (~r(s(s(z)), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[7034, 7002, 6992, 6982, 6987, 272])).
% 1.74/1.99 tff(7036,plain,
% 1.74/1.99 (b(s(s(z)), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[25, 7035])).
% 1.74/1.99 tff(7037,plain,
% 1.74/1.99 (b(s(elem!1), z)),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[7036, 6986])).
% 1.74/1.99 tff(7038,plain,
% 1.74/1.99 (b(s(s(z)), elem!1) <=> b(s(elem!1), elem!1)),
% 1.74/1.99 inference(monotonicity,[status(thm)],[6983])).
% 1.74/1.99 tff(7039,plain,
% 1.74/1.99 (b(s(s(z)), s(z)) <=> b(s(s(z)), elem!1)),
% 1.74/1.99 inference(monotonicity,[status(thm)],[6982])).
% 1.74/1.99 tff(7040,plain,
% 1.74/1.99 (b(s(s(z)), s(z)) <=> b(s(elem!1), elem!1)),
% 1.74/1.99 inference(transitivity,[status(thm)],[7039, 7038])).
% 1.74/1.99 tff(7041,plain,
% 1.74/1.99 (r(s(s(z)), s(z)) <=> r(s(s(z)), elem!1)),
% 1.74/1.99 inference(monotonicity,[status(thm)],[6982])).
% 1.74/1.99 tff(7042,plain,
% 1.74/1.99 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(z))),
% 1.74/1.99 inference(symmetry,[status(thm)],[7041])).
% 1.74/1.99 tff(7043,plain,
% 1.74/1.99 (r(s(s(z)), elem!1) <=> r(s(elem!1), elem!1)),
% 1.74/1.99 inference(monotonicity,[status(thm)],[6983])).
% 1.74/1.99 tff(7044,plain,
% 1.74/1.99 (r(s(elem!1), elem!1) <=> r(s(s(z)), elem!1)),
% 1.74/1.99 inference(symmetry,[status(thm)],[7043])).
% 1.74/1.99 tff(7045,plain,
% 1.74/1.99 (r(s(elem!1), elem!1) <=> r(s(s(z)), s(z))),
% 1.74/1.99 inference(transitivity,[status(thm)],[7044, 7042])).
% 1.74/1.99 tff(7046,plain,
% 1.74/1.99 ((~r(s(elem!1), elem!1)) <=> (~r(s(s(z)), s(z)))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[7045])).
% 1.74/1.99 tff(7047,plain,
% 1.74/1.99 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), elem!1)),
% 1.74/1.99 inference(monotonicity,[status(thm)],[6982])).
% 1.74/1.99 tff(7048,plain,
% 1.74/1.99 (r(s(s(s(elem!1))), elem!1)),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[385, 7047])).
% 1.74/1.99 tff(7049,plain,
% 1.74/1.99 (b(z, s(z)) <=> b(z, elem!1)),
% 1.74/1.99 inference(monotonicity,[status(thm)],[6982])).
% 1.74/1.99 tff(7050,plain,
% 1.74/1.99 (b(z, elem!1) <=> b(z, s(z))),
% 1.74/1.99 inference(symmetry,[status(thm)],[7049])).
% 1.74/1.99 tff(7051,plain,
% 1.74/1.99 (b(z, s(z))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[498, 7050])).
% 1.74/1.99 tff(7052,plain,
% 1.74/1.99 (~b(s(z), s(s(s(elem!1))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[6898, 7051, 6292, 2409, 324, 6810])).
% 1.74/1.99 tff(7053,plain,
% 1.74/1.99 (r(s(z), s(s(s(elem!1))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[339, 7052])).
% 1.74/1.99 tff(7054,plain,
% 1.74/1.99 (~r(z, s(s(s(elem!1))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[854, 7053, 272])).
% 1.74/1.99 tff(7055,plain,
% 1.74/1.99 (b(z, s(s(s(elem!1))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[858, 7054])).
% 1.74/1.99 tff(7056,plain,
% 1.74/1.99 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[6326, 7053, 324, 1664, 6292, 272, 2409])).
% 1.74/1.99 tff(7057,plain,
% 1.74/1.99 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[1820, 7056, 2650])).
% 1.74/1.99 tff(7058,plain,
% 1.74/1.99 (r(z, s(elem!1)) <=> r(z, s(s(z)))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[4804])).
% 1.74/1.99 tff(7059,plain,
% 1.74/1.99 (r(z, s(s(z))) <=> r(z, s(elem!1))),
% 1.74/1.99 inference(symmetry,[status(thm)],[7058])).
% 1.74/1.99 tff(7060,plain,
% 1.74/1.99 (b(z, s(s(z))) <=> b(z, s(elem!1))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[4605])).
% 1.74/1.99 tff(7061,plain,
% 1.74/1.99 (b(z, s(elem!1)) <=> b(z, s(s(z)))),
% 1.74/1.99 inference(symmetry,[status(thm)],[7060])).
% 1.74/1.99 tff(7062,plain,
% 1.74/1.99 ((~b(z, s(elem!1))) <=> (~b(z, s(s(z))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[7061])).
% 1.74/1.99 tff(7063,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), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(7064,plain,
% 1.74/1.99 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1)))))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(7065,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(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[7064])).
% 1.74/1.99 tff(7066,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(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.74/1.99 inference(transitivity,[status(thm)],[7065, 7063])).
% 1.74/1.99 tff(7067,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(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(7068,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), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[7067, 7066])).
% 1.74/1.99 tff(7069,plain,
% 1.74/1.99 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[7068, 45, 2450, 3397])).
% 1.74/1.99 tff(7070,plain,
% 1.74/1.99 ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[4801, 21, 7069])).
% 1.74/1.99 tff(7071,plain,
% 1.74/1.99 (b(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[7070, 4790])).
% 1.74/1.99 tff(7072,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(7073,plain,
% 1.74/1.99 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1)))) <=> ((~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(7074,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1)))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[7073])).
% 1.74/1.99 tff(7075,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[7074, 7072])).
% 1.74/1.99 tff(7076,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(7077,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1)))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[7076, 7075])).
% 1.74/1.99 tff(7078,plain,
% 1.74/1.99 (~b(z, s(elem!1))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[7077, 128, 498, 874, 3452, 7071])).
% 1.74/1.99 tff(7079,plain,
% 1.74/1.99 (~b(z, s(s(z)))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[7078, 7062])).
% 1.74/1.99 tff(7080,plain,
% 1.74/1.99 (r(z, s(s(z)))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[516, 7079])).
% 1.74/1.99 tff(7081,plain,
% 1.74/1.99 (r(z, s(elem!1))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[7080, 7059])).
% 1.74/1.99 tff(7082,plain,
% 1.74/1.99 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 1.74/1.99 inference(transitivity,[status(thm)],[4672, 1748])).
% 1.74/1.99 tff(7083,plain,
% 1.74/1.99 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[7082])).
% 1.74/1.99 tff(7084,plain,
% 1.74/1.99 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[239, 7083])).
% 1.74/1.99 tff(7085,plain,
% 1.74/1.99 (b(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5524, 21, 4789, 3774])).
% 1.74/1.99 tff(7086,plain,
% 1.74/1.99 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(7087,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[7086])).
% 1.74/1.99 tff(7088,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[7087, 3711])).
% 1.74/1.99 tff(7089,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(7090,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[7089, 7088])).
% 1.74/1.99 tff(7091,plain,
% 1.74/1.99 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[7090, 128, 1842, 7071, 7085])).
% 1.74/1.99 tff(7092,plain,
% 1.74/1.99 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[1920, 7091, 7084])).
% 1.74/1.99 tff(7093,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(7094,plain,
% 1.74/1.99 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1))))))) <=> ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(7095,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1))))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[7094])).
% 1.74/1.99 tff(7096,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[7095, 7093])).
% 1.74/1.99 tff(7097,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(7098,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1))))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[7097, 7096])).
% 1.74/1.99 tff(7099,plain,
% 1.74/1.99 (~b(z, s(s(s(s(elem!1)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[7098, 128, 498, 1842, 874, 3452])).
% 1.74/1.99 tff(7100,plain,
% 1.74/1.99 (r(z, s(s(s(s(elem!1)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2047, 21, 7099, 178])).
% 1.74/1.99 tff(7101,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(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(7102,plain,
% 1.74/1.99 (((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(s(s(s(elem!1))))))) <=> ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(7103,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(elem!1)))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1)))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[7102])).
% 1.74/2.00 tff(7104,plain,
% 1.74/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[7103, 7101])).
% 1.74/2.00 tff(7105,plain,
% 1.74/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(7106,plain,
% 1.74/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(z, s(elem!1)))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[7105, 7104])).
% 1.74/2.00 tff(7107,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[7106, 45, 7100, 7092, 7081])).
% 1.74/2.00 tff(7108,plain,((~r(s(elem!1), elem!1)) | (~(s(z) = elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(7109,plain,
% 1.74/2.00 (~r(s(elem!1), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[7108, 6982, 7057, 498, 7055, 6811, 4603, 7048])).
% 1.74/2.00 tff(7110,plain,
% 1.74/2.00 (~r(s(s(z)), s(z))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[7109, 7046])).
% 1.74/2.00 tff(7111,plain,
% 1.74/2.00 (b(s(s(z)), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[86, 7110])).
% 1.74/2.00 tff(7112,plain,
% 1.74/2.00 (b(s(elem!1), elem!1)),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[7111, 7040])).
% 1.74/2.00 tff(7113,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), z)))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(7114,plain,
% 1.74/2.00 (((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), z)))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(7115,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), z))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[7114])).
% 1.74/2.00 tff(7116,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), z)))),
% 1.74/2.00 inference(transitivity,[status(thm)],[7115, 7113])).
% 1.74/2.00 tff(7117,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(7118,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), z))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[7117, 7116])).
% 1.74/2.00 tff(7119,plain,
% 1.74/2.00 (~b(s(elem!1), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[7118, 128, 498, 6987, 6994, 7112])).
% 1.74/2.00 tff(7120,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[7119, 7037])).
% 1.74/2.00 tff(7121,plain,((~r(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~r(s(z), z)) | (s(s(elem!1)) = s(s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (elem!1 = z) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(7122,plain,
% 1.74/2.00 (~r(z, s(s(elem!1)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[7121, 324, 272, 1, 498, 385, 5065, 1086])).
% 1.74/2.00 tff(7123,plain,
% 1.74/2.00 (b(z, s(s(elem!1)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[160, 7122])).
% 1.74/2.00 tff(7124,plain,
% 1.74/2.00 (~b(s(z), s(s(s(elem!1))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4160, 550, 272, 385, 1691, 30, 89])).
% 1.74/2.00 tff(7125,plain,
% 1.74/2.00 (~r(s(z), s(s(s(elem!1))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2034, 550, 272, 1691, 89, 453])).
% 1.74/2.00 tff(7126,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[339, 7125, 7124])).
% 1.74/2.00 tff(7127,plain,((~b(z, s(z))) | (~r(s(z), z)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(7128,plain,
% 1.74/2.00 (~b(z, s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[7127, 89, 1691, 272, 453, 385, 6292])).
% 1.74/2.00 tff(7129,plain,
% 1.74/2.00 (r(z, s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[415, 7128])).
% 1.74/2.00 tff(7130,plain,
% 1.74/2.00 (~b(s(z), s(s(s(elem!1))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[3623, 7129, 385, 6292, 453, 1691, 272, 89])).
% 1.74/2.00 tff(7131,plain,
% 1.74/2.00 (r(s(z), s(s(s(elem!1))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[339, 7130])).
% 1.74/2.00 tff(7132,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4323, 45, 89, 324, 7131])).
% 1.74/2.00 tff(7133,plain,((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~b(z, s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(7134,plain,
% 1.74/2.00 (~r(s(z), s(s(elem!1)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[7133, 324, 385, 7123, 4492, 272])).
% 1.74/2.00 tff(7135,plain,
% 1.74/2.00 (b(s(z), s(s(elem!1)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[117, 7134])).
% 1.74/2.00 tff(7136,plain,
% 1.74/2.00 (((~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z)))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(7137,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[7136])).
% 1.74/2.00 tff(7138,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[7137, 4163])).
% 1.74/2.00 tff(7139,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(7140,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[7139, 7138])).
% 1.74/2.00 tff(7141,plain,
% 1.74/2.00 (~b(z, s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[7140, 128, 6292, 7123, 7135])).
% 1.74/2.00 tff(7142,plain,
% 1.74/2.00 (r(z, s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[415, 7141])).
% 1.74/2.00 tff(7143,plain,
% 1.74/2.00 (~r(z, s(s(s(elem!1))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[3611, 45, 7142, 385])).
% 1.74/2.00 tff(7144,plain,
% 1.74/2.00 (b(z, s(s(s(elem!1))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[858, 7143])).
% 1.74/2.00 tff(7145,plain,
% 1.74/2.00 (~(s(s(s(elem!1))) = elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1007, 1004, 544])).
% 1.74/2.00 tff(7146,plain,
% 1.74/2.00 (b(s(z), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[665, 6871, 1610])).
% 1.74/2.00 tff(7147,plain,
% 1.74/2.00 (b(elem!1, s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[305, 6913, 5008])).
% 1.74/2.00 tff(7148,plain,
% 1.74/2.00 (~b(s(s(elem!1)), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1996, 7147, 876, 7146])).
% 1.74/2.00 tff(7149,plain,
% 1.74/2.00 (r(s(s(elem!1)), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1934, 7148, 1086])).
% 1.74/2.00 tff(7150,plain,
% 1.74/2.00 (~r(s(s(s(elem!1))), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4990, 7149, 324])).
% 1.74/2.00 tff(7151,plain,
% 1.74/2.00 (b(s(s(s(elem!1))), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[742, 7150, 7145])).
% 1.74/2.00 tff(7152,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(7153,plain,
% 1.74/2.00 (((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(7154,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1)))))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[7153])).
% 1.74/2.00 tff(7155,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[7154, 7152])).
% 1.74/2.00 tff(7156,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(7157,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1)))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[7156, 7155])).
% 1.74/2.00 tff(7158,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[7157, 128, 498, 7147, 7146, 7151, 874])).
% 1.74/2.00 tff(7159,plain,((~r(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(elem!1)) = elem!1) | (~b(s(z), s(s(elem!1)))) | (s(z) = elem!1) | (~r(s(z), z)) | r(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(7160,plain,
% 1.74/2.00 (~r(elem!1, z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[7159, 1610, 7144, 324, 1086, 7135, 498, 272, 6810])).
% 1.74/2.00 tff(7161,plain,
% 1.74/2.00 (b(elem!1, z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[574, 7160, 5065])).
% 1.74/2.00 tff(7162,plain,
% 1.74/2.00 (~r(s(s(s(s(elem!1)))), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1745, 1737, 272])).
% 1.74/2.00 tff(7163,plain,
% 1.74/2.00 (~b(s(s(s(s(elem!1)))), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[3953, 1737, 385, 698, 27])).
% 1.74/2.00 tff(7164,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2081, 7163, 7162])).
% 1.74/2.00 tff(7165,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(7166,plain,
% 1.74/2.00 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[7165, 7142, 2649, 385, 272])).
% 1.74/2.00 tff(7167,plain,
% 1.74/2.00 (b(s(s(s(s(elem!1)))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1828, 7166])).
% 1.74/2.00 tff(7168,plain,
% 1.74/2.00 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2608, 7167, 7135, 6292])).
% 1.74/2.00 tff(7169,plain,
% 1.74/2.00 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1897, 7168, 1664])).
% 1.74/2.00 tff(7170,plain,
% 1.74/2.00 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2103, 7169, 324])).
% 1.74/2.00 tff(7171,plain,
% 1.74/2.00 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1820, 7170, 2650])).
% 1.74/2.00 tff(7172,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(7173,plain,
% 1.74/2.00 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(7174,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1)))))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[7173])).
% 1.74/2.00 tff(7175,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[7174, 7172])).
% 1.74/2.00 tff(7176,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(7177,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1)))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[7176, 7175])).
% 1.74/2.00 tff(7178,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[7177, 128, 498, 577, 2659, 874])).
% 1.74/2.00 tff(7179,plain,((~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(7180,plain,
% 1.74/2.00 (~b(s(s(s(elem!1))), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[7179, 577, 498, 874])).
% 1.74/2.00 tff(7181,plain,
% 1.74/2.00 (~b(s(s(s(s(elem!1)))), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[6333, 128, 1842, 874, 3452])).
% 1.74/2.00 tff(7182,plain,
% 1.74/2.00 (r(s(s(s(s(elem!1)))), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2081, 7181])).
% 1.74/2.00 tff(7183,plain,
% 1.74/2.00 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1745, 7182, 272])).
% 1.74/2.00 tff(7184,plain,
% 1.74/2.00 (b(s(s(s(s(elem!1)))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1828, 7183])).
% 1.74/2.00 tff(7185,plain,
% 1.74/2.00 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4176, 128, 30, 876, 7184])).
% 1.74/2.00 tff(7186,plain,
% 1.74/2.00 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2212, 21, 1646, 7185])).
% 1.74/2.00 tff(7187,plain,
% 1.74/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(7188,plain,
% 1.74/2.00 (((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z))) <=> ((~r(z, s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(7189,plain,
% 1.74/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(s(s(elem!1))))))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[7188])).
% 1.74/2.00 tff(7190,plain,
% 1.74/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[7189, 7187])).
% 1.74/2.00 tff(7191,plain,
% 1.74/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(7192,plain,
% 1.74/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(s(s(elem!1))))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[7191, 7190])).
% 1.74/2.00 tff(7193,plain,
% 1.74/2.00 (~r(s(s(elem!1)), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[7192, 45, 27, 7186, 7100])).
% 1.74/2.00 tff(7194,plain,
% 1.74/2.00 (b(s(s(elem!1)), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2018, 21, 154, 7193])).
% 1.74/2.00 tff(7195,plain,
% 1.74/2.00 (~b(s(s(elem!1)), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5109, 7194, 498, 577])).
% 1.74/2.00 tff(7196,plain,
% 1.74/2.00 (r(s(s(elem!1)), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1934, 7195, 1086])).
% 1.74/2.00 tff(7197,plain,
% 1.74/2.00 (~r(s(s(s(elem!1))), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4990, 7196, 324])).
% 1.74/2.00 tff(7198,plain,
% 1.74/2.00 (s(s(s(elem!1))) = elem!1),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[742, 7197, 7180])).
% 1.74/2.00 tff(7199,plain,
% 1.74/2.00 (s(s(s(s(elem!1)))) = s(elem!1)),
% 1.74/2.00 inference(monotonicity,[status(thm)],[7198])).
% 1.74/2.00 tff(7200,plain,
% 1.74/2.00 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.74/2.00 inference(symmetry,[status(thm)],[7199])).
% 1.74/2.00 tff(7201,plain,
% 1.74/2.00 (r(s(elem!1), z) <=> r(s(s(s(s(elem!1)))), z)),
% 1.74/2.00 inference(monotonicity,[status(thm)],[7200])).
% 1.74/2.00 tff(7202,plain,
% 1.74/2.00 (r(s(s(s(s(elem!1)))), z) <=> r(s(elem!1), z)),
% 1.74/2.00 inference(symmetry,[status(thm)],[7201])).
% 1.74/2.00 tff(7203,plain,
% 1.74/2.00 (r(s(elem!1), z)),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[7182, 7202])).
% 1.74/2.00 tff(7204,plain,
% 1.74/2.00 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(elem!1), s(z))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[7199])).
% 1.74/2.00 tff(7205,plain,
% 1.74/2.00 (b(s(elem!1), s(z))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[7184, 7204])).
% 1.74/2.00 tff(7206,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(7207,plain,
% 1.74/2.00 (((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z))))) <=> ((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(7208,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z))))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[7207])).
% 1.74/2.00 tff(7209,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.74/2.01 inference(transitivity,[status(thm)],[7208, 7206])).
% 1.74/2.01 tff(7210,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(7211,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[7210, 7209])).
% 1.74/2.01 tff(7212,plain,
% 1.74/2.01 (~b(s(s(elem!1)), s(s(z)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[7211, 128, 498, 577, 2006, 2993])).
% 1.74/2.01 tff(7213,plain,
% 1.74/2.01 (r(s(s(elem!1)), s(s(z)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[4339, 21, 1, 7212])).
% 1.74/2.01 tff(7214,plain,
% 1.74/2.01 (~b(s(s(z)), elem!1)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[1555, 128, 498, 577, 2993])).
% 1.74/2.01 tff(7215,plain,
% 1.74/2.01 (r(s(s(z)), elem!1)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[370, 7214, 484])).
% 1.74/2.01 tff(7216,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5045, 45, 2349, 7215, 7213])).
% 1.74/2.01 tff(7217,plain,((~b(s(s(z)), z)) | (~r(s(s(elem!1)), elem!1)) | (s(s(elem!1)) = s(s(z))) | (s(s(z)) = elem!1) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(7218,plain,
% 1.74/2.01 (~b(s(s(z)), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[7217, 7196, 1, 484, 498, 577, 7194])).
% 1.74/2.01 tff(7219,plain,
% 1.74/2.01 (r(s(s(z)), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[25, 7218])).
% 1.74/2.01 tff(7220,plain,
% 1.74/2.01 (~r(s(s(z)), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[1509, 7219, 272])).
% 1.74/2.01 tff(7221,plain,
% 1.74/2.01 (b(s(s(z)), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[86, 7220])).
% 1.74/2.01 tff(7222,plain,
% 1.74/2.01 (~r(s(z), s(s(z)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[1327, 7219, 272])).
% 1.74/2.01 tff(7223,plain,
% 1.74/2.01 (b(s(z), s(s(z)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[648, 7222])).
% 1.74/2.01 tff(7224,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(elem!1), s(s(z)))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(7225,plain,
% 1.74/2.01 (((~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z))))) <=> ((~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(elem!1), s(s(z)))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(7226,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(elem!1), s(s(z))))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[7225])).
% 1.74/2.01 tff(7227,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(elem!1), s(s(z)))))),
% 1.74/2.01 inference(transitivity,[status(thm)],[7226, 7224])).
% 1.74/2.01 tff(7228,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(7229,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(elem!1), s(s(z))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[7228, 7227])).
% 1.74/2.01 tff(7230,plain,
% 1.74/2.01 (~b(s(elem!1), s(s(z)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[7229, 128, 7223, 7221, 7205])).
% 1.74/2.01 tff(7231,plain,
% 1.74/2.01 (r(s(elem!1), s(s(z)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[473, 21, 759, 7230])).
% 1.74/2.01 tff(7232,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(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(elem!1), s(s(z)))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(7233,plain,
% 1.74/2.01 (((~r(s(s(z)), z)) | (~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(elem!1), s(s(z))))) <=> ((~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(elem!1), s(s(z)))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(7234,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(z)), z)) | (~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(elem!1), s(s(z))))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[7233])).
% 1.74/2.01 tff(7235,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(z)), z)) | (~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(elem!1), s(s(z)))))),
% 1.74/2.01 inference(transitivity,[status(thm)],[7234, 7232])).
% 1.74/2.01 tff(7236,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(z)), z)) | (~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(elem!1), s(s(z)))))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(7237,plain,
% 1.74/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(elem!1), s(s(z))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[7236, 7235])).
% 1.74/2.01 tff(7238,plain,
% 1.74/2.01 ((~r(s(elem!1), z)) | (~r(s(elem!1), s(s(z))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[7237, 45, 7219])).
% 1.74/2.01 tff(7239,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[7238, 7231, 7203])).
% 1.74/2.01 tff(7240,plain,((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (s(elem!1) = s(s(z))) | (~r(s(z), z)) | (s(s(elem!1)) = s(s(z))) | (s(s(z)) = elem!1) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(elem!1)) = elem!1) | (~r(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(7241,plain,
% 1.74/2.01 (s(s(z)) = elem!1),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[7240, 5016, 272, 1, 7171, 498, 7161, 324, 1086, 7142, 6292, 7135, 7144, 6811])).
% 1.74/2.01 tff(7242,plain,
% 1.74/2.01 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.74/2.01 inference(monotonicity,[status(thm)],[4610])).
% 1.74/2.01 tff(7243,plain,
% 1.74/2.01 ((s(s(s(elem!1))) = s(s(z))) <=> (elem!1 = s(s(s(elem!1))))),
% 1.74/2.01 inference(transitivity,[status(thm)],[7242, 705])).
% 1.74/2.01 tff(7244,plain,
% 1.74/2.01 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[7243])).
% 1.74/2.01 tff(7245,plain,
% 1.74/2.01 (~(elem!1 = s(s(s(elem!1))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[283, 7244])).
% 1.74/2.01 tff(7246,plain,
% 1.74/2.01 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.74/2.01 inference(transitivity,[status(thm)],[7243, 982])).
% 1.74/2.01 tff(7247,plain,
% 1.74/2.01 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[7246])).
% 1.74/2.01 tff(7248,plain,
% 1.74/2.01 (~(s(s(s(elem!1))) = elem!1)),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[283, 7247])).
% 1.74/2.01 tff(7249,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[6978, 7248, 7245, 1642, 876, 1086, 324, 385, 577, 498, 3452])).
% 1.74/2.01 tff(7250,plain,((~(s(s(z)) = elem!1)) | (elem!1 = s(z)) | (~b(s(z), s(s(elem!1)))) | (s(s(elem!1)) = elem!1) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(7251,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[7250, 7241, 7161, 7135, 1086, 324, 385, 5008, 498, 6811])).
% 1.74/2.01 tff(7252,plain,((s(z) = elem!1) | (s(s(elem!1)) = elem!1) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~b(z, elem!1)) | (~r(s(z), z)) | (s(s(elem!1)) = s(s(z))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(7253,plain,
% 1.74/2.01 (s(z) = elem!1),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[7252, 324, 1086, 385, 498, 272, 1, 5065])).
% 1.74/2.01 tff(7254,plain,
% 1.74/2.01 (b(z, s(z)) <=> b(z, elem!1)),
% 1.74/2.01 inference(monotonicity,[status(thm)],[7253])).
% 1.74/2.01 tff(7255,plain,
% 1.74/2.01 (b(z, elem!1) <=> b(z, s(z))),
% 1.74/2.01 inference(symmetry,[status(thm)],[7254])).
% 1.74/2.01 tff(7256,plain,
% 1.74/2.01 (b(z, s(z))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[498, 7255])).
% 1.74/2.01 tff(7257,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[7141, 7256])).
% 1.74/2.01 tff(7258,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, elem!1)) | (s(s(elem!1)) = elem!1) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (s(s(elem!1)) = s(s(z))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(7259,plain,
% 1.74/2.01 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[7258, 1086, 6809, 6039, 171, 4261, 4555])).
% 1.74/2.01 tff(7260,plain,
% 1.74/2.01 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[321, 7259, 2648])).
% 1.74/2.01 tff(7261,plain,
% 1.74/2.01 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(7262,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[7261])).
% 1.74/2.01 tff(7263,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 1.74/2.01 inference(transitivity,[status(thm)],[7262, 6784])).
% 1.74/2.01 tff(7264,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(7265,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[7264, 7263])).
% 1.74/2.01 tff(7266,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[7265, 128, 3378, 2106, 4152, 6811])).
% 1.74/2.01 tff(7267,plain,((~r(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(7268,plain,
% 1.74/2.01 (~r(s(z), s(s(elem!1)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[7267, 2106, 2025, 385, 272])).
% 1.74/2.01 tff(7269,plain,
% 1.74/2.01 (b(s(z), s(s(elem!1)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[117, 7268])).
% 1.74/2.01 tff(7270,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)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(7271,plain,
% 1.74/2.01 (((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(7272,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)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z)))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[7271])).
% 1.74/2.01 tff(7273,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)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.74/2.01 inference(transitivity,[status(thm)],[7272, 7270])).
% 1.74/2.01 tff(7274,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)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(7275,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)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z)))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[7274, 7273])).
% 1.74/2.01 tff(7276,plain,
% 1.74/2.01 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[7275, 45, 325, 385])).
% 1.74/2.01 tff(7277,plain,
% 1.74/2.01 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[889, 7276, 1679])).
% 1.74/2.01 tff(7278,plain,
% 1.74/2.01 (~r(s(z), s(s(s(elem!1))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[5249, 325, 272, 1063, 2106])).
% 1.74/2.01 tff(7279,plain,
% 1.74/2.01 (b(s(z), s(s(s(elem!1))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[339, 7278])).
% 1.74/2.01 tff(7280,plain,
% 1.74/2.01 (~r(s(z), s(s(elem!1)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[7267, 2106, 1679, 385, 272])).
% 1.74/2.01 tff(7281,plain,
% 1.74/2.01 (b(s(z), s(s(elem!1)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[117, 7280])).
% 1.74/2.01 tff(7282,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(7283,plain,
% 1.74/2.01 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(7284,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[7283])).
% 1.74/2.01 tff(7285,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.74/2.01 inference(transitivity,[status(thm)],[7284, 7282])).
% 1.74/2.01 tff(7286,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(7287,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[7286, 7285])).
% 1.74/2.01 tff(7288,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[7287, 128, 7281, 2106, 7279, 7277])).
% 1.74/2.01 tff(7289,plain,((~r(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (s(s(s(s(elem!1)))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(7290,plain,
% 1.74/2.01 (~r(s(s(elem!1)), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[7289, 2106, 385, 272, 2023])).
% 1.74/2.01 tff(7291,plain,
% 1.74/2.01 (b(s(s(elem!1)), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[292, 7290])).
% 1.74/2.01 tff(7292,plain,
% 1.74/2.01 (~b(z, s(s(elem!1)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[4168, 128, 30, 550, 876])).
% 1.74/2.01 tff(7293,plain,
% 1.74/2.01 (r(z, s(s(elem!1)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[160, 7292])).
% 1.74/2.01 tff(7294,plain,
% 1.74/2.01 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[4176, 128, 30, 876, 1841])).
% 1.74/2.01 tff(7295,plain,
% 1.74/2.01 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2212, 21, 1069, 7294])).
% 1.74/2.01 tff(7296,plain,
% 1.74/2.01 (~b(z, s(s(s(s(elem!1)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[4184, 128, 30, 550, 876, 1841])).
% 1.74/2.01 tff(7297,plain,
% 1.74/2.01 (r(z, s(s(s(s(elem!1)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2047, 21, 7296, 178])).
% 1.74/2.01 tff(7298,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[3222, 7297, 7295, 7293])).
% 1.74/2.01 tff(7299,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(7300,plain,
% 1.74/2.01 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[7299, 550, 7291, 1069, 7269])).
% 1.74/2.01 tff(7301,plain,
% 1.74/2.01 (r(s(s(s(s(elem!1)))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[1828, 7300])).
% 1.74/2.01 tff(7302,plain,
% 1.74/2.01 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[3951, 45, 7301, 385])).
% 1.74/2.01 tff(7303,plain,
% 1.74/2.01 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[1856, 7302, 2037])).
% 1.74/2.01 tff(7304,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(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(7305,plain,
% 1.74/2.01 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(7306,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(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[7305])).
% 1.74/2.01 tff(7307,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(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.74/2.01 inference(transitivity,[status(thm)],[7306, 7304])).
% 1.74/2.01 tff(7308,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(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(7309,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(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[7308, 7307])).
% 1.74/2.01 tff(7310,plain,
% 1.74/2.01 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[7309, 45, 7301, 385])).
% 1.74/2.01 tff(7311,plain,
% 1.74/2.01 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[1820, 7310, 2073])).
% 1.74/2.01 tff(7312,plain,
% 1.74/2.01 (~b(z, s(s(s(elem!1))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2309, 7311, 2106, 2023, 7303])).
% 1.74/2.01 tff(7313,plain,
% 1.74/2.01 (r(z, s(s(s(elem!1))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[858, 7312])).
% 1.74/2.01 tff(7314,plain,
% 1.74/2.01 (~r(s(z), s(s(s(elem!1))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[854, 7313, 272])).
% 1.74/2.01 tff(7315,plain,
% 1.74/2.01 (~r(s(s(s(s(elem!1)))), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[1745, 7301, 272])).
% 1.74/2.01 tff(7316,plain,
% 1.74/2.01 (b(s(s(s(s(elem!1)))), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2081, 7315])).
% 1.74/2.01 tff(7317,plain,
% 1.74/2.01 (~b(z, s(s(elem!1)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[4168, 128, 7291, 550, 7269])).
% 1.74/2.01 tff(7318,plain,
% 1.74/2.01 (r(z, s(s(elem!1)))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[160, 7317])).
% 1.74/2.02 tff(7319,plain,
% 1.74/2.02 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[4546, 7311, 7318, 7316])).
% 1.74/2.02 tff(7320,plain,
% 1.74/2.02 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[889, 7319, 2025])).
% 1.74/2.02 tff(7321,plain,
% 1.74/2.02 (~b(s(z), s(s(s(elem!1))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2114, 7320, 2106, 7291])).
% 1.74/2.02 tff(7322,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[339, 7321, 7314])).
% 1.74/2.02 tff(7323,plain,((~b(z, s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (s(s(elem!1)) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(7324,plain,
% 1.74/2.02 (~b(z, s(z))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[7323, 7260, 171, 6039, 1646])).
% 1.74/2.02 tff(7325,plain,
% 1.74/2.02 (r(z, s(z))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[415, 7324])).
% 1.74/2.02 tff(7326,plain,
% 1.74/2.02 (~r(z, s(s(s(elem!1))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[3611, 45, 7325, 6039])).
% 1.74/2.02 tff(7327,plain,
% 1.74/2.02 (b(z, s(s(s(elem!1))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[858, 7326])).
% 1.74/2.02 tff(7328,plain,
% 1.74/2.02 (~b(s(s(elem!1)), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[6639, 128, 7260, 7327, 6049])).
% 1.74/2.02 tff(7329,plain,
% 1.74/2.02 (r(s(s(elem!1)), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2018, 21, 154, 7328])).
% 1.74/2.02 tff(7330,plain,
% 1.74/2.02 (~r(s(s(elem!1)), s(z))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[7289, 7260, 6039, 171, 1664])).
% 1.74/2.02 tff(7331,plain,
% 1.74/2.02 (b(s(s(elem!1)), s(z))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[292, 7330])).
% 1.74/2.02 tff(7332,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(7333,plain,
% 1.74/2.02 (((~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(7334,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z))))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[7333])).
% 1.74/2.02 tff(7335,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.74/2.02 inference(transitivity,[status(thm)],[7334, 7332])).
% 1.74/2.02 tff(7336,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.74/2.02 inference(quant_inst,[status(thm)],[])).
% 1.74/2.02 tff(7337,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z))))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[7336, 7335])).
% 1.74/2.02 tff(7338,plain,
% 1.74/2.02 (~b(s(s(elem!1)), s(s(z)))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[7337, 128, 30, 7016, 7010])).
% 1.74/2.02 tff(7339,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(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(7340,plain,
% 1.74/2.02 (((~r(s(s(z)), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(7341,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)), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z))))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[7340])).
% 1.74/2.02 tff(7342,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)), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.74/2.02 inference(transitivity,[status(thm)],[7341, 7339])).
% 1.74/2.02 tff(7343,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)), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.74/2.02 inference(quant_inst,[status(thm)],[])).
% 1.74/2.02 tff(7344,plain,
% 1.74/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z))))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[7343, 7342])).
% 1.74/2.02 tff(7345,plain,
% 1.74/2.02 (~r(s(s(elem!1)), s(s(z)))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[7344, 45, 1519, 28])).
% 1.74/2.02 tff(7346,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[4339, 21, 1, 7345, 7338])).
% 1.74/2.02 tff(7347,plain,((~r(s(s(z)), z)) | (s(s(elem!1)) = s(s(z))) | (~b(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(7348,plain,
% 1.74/2.02 (~r(s(s(z)), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[7347, 4261, 7331, 7329, 171])).
% 1.74/2.02 tff(7349,plain,
% 1.74/2.02 (b(s(s(z)), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[25, 7348])).
% 1.74/2.02 tff(7350,plain,
% 1.74/2.02 (~r(s(z), s(s(elem!1)))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[7267, 7260, 4492, 6039, 171])).
% 1.74/2.02 tff(7351,plain,
% 1.74/2.02 (b(s(z), s(s(elem!1)))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[117, 7350])).
% 1.74/2.02 tff(7352,plain,
% 1.74/2.02 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[7165, 7325, 2649, 6039, 171])).
% 1.74/2.02 tff(7353,plain,
% 1.74/2.02 (b(s(s(s(s(elem!1)))), s(z))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1828, 7352])).
% 1.74/2.02 tff(7354,plain,
% 1.74/2.02 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2608, 7353, 7351, 7331])).
% 1.74/2.02 tff(7355,plain,
% 1.74/2.02 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1897, 7354, 1664])).
% 1.74/2.02 tff(7356,plain,
% 1.74/2.02 (~b(z, s(s(elem!1)))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[3460, 7327, 6049, 7260])).
% 1.74/2.02 tff(7357,plain,
% 1.74/2.02 (r(z, s(s(elem!1)))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[160, 7356])).
% 1.74/2.02 tff(7358,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(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(7359,plain,
% 1.74/2.02 (((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), z))) <=> ((~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(7360,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(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[7359])).
% 1.74/2.02 tff(7361,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(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.74/2.02 inference(transitivity,[status(thm)],[7360, 7358])).
% 1.74/2.02 tff(7362,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(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.74/2.02 inference(quant_inst,[status(thm)],[])).
% 1.74/2.02 tff(7363,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(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[7362, 7361])).
% 1.74/2.02 tff(7364,plain,
% 1.74/2.02 (~r(s(s(s(s(elem!1)))), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[7363, 45, 7325, 7357, 7355])).
% 1.74/2.02 tff(7365,plain,
% 1.74/2.02 (b(s(s(s(s(elem!1)))), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2081, 7364])).
% 1.74/2.02 tff(7366,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(7367,plain,
% 1.74/2.02 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(7368,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z))))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[7367])).
% 1.74/2.02 tff(7369,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.74/2.02 inference(transitivity,[status(thm)],[7368, 7366])).
% 1.74/2.02 tff(7370,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.74/2.02 inference(quant_inst,[status(thm)],[])).
% 1.74/2.02 tff(7371,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[7370, 7369])).
% 1.74/2.02 tff(7372,plain,
% 1.74/2.02 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[7371, 128, 7327, 6049, 7365, 7349])).
% 1.74/2.02 tff(7373,plain,
% 1.74/2.02 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[4309, 21, 239, 7372])).
% 1.74/2.02 tff(7374,plain,
% 1.74/2.02 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[4176, 128, 7331, 7351, 7353])).
% 1.74/2.02 tff(7375,plain,
% 1.74/2.02 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2212, 21, 1646, 7374])).
% 1.74/2.02 tff(7376,plain,
% 1.74/2.02 (~r(z, s(s(s(s(elem!1)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[3222, 7375, 7357])).
% 1.74/2.02 tff(7377,plain,
% 1.74/2.02 (b(z, s(s(s(s(elem!1)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2047, 21, 7376, 178])).
% 1.74/2.02 tff(7378,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(7379,plain,
% 1.74/2.02 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(7380,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[7379])).
% 1.74/2.02 tff(7381,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.74/2.02 inference(transitivity,[status(thm)],[7380, 7378])).
% 1.74/2.02 tff(7382,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.74/2.02 inference(quant_inst,[status(thm)],[])).
% 1.74/2.02 tff(7383,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[7382, 7381])).
% 1.74/2.02 tff(7384,plain,
% 1.74/2.02 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[7383, 128, 6049, 7365, 7377])).
% 1.74/2.02 tff(7385,plain,
% 1.74/2.02 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1856, 7384, 2649])).
% 1.74/2.02 tff(7386,plain,
% 1.74/2.02 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[3708, 45, 7375, 7385])).
% 1.74/2.02 tff(7387,plain,
% 1.74/2.02 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[889, 7386, 4492])).
% 1.74/2.02 tff(7388,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(7389,plain,
% 1.74/2.02 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(7390,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 1.86/2.02 inference(monotonicity,[status(thm)],[7389])).
% 1.86/2.02 tff(7391,plain,
% 1.86/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.86/2.02 inference(transitivity,[status(thm)],[7390, 7388])).
% 1.86/2.02 tff(7392,plain,
% 1.86/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.86/2.02 inference(quant_inst,[status(thm)],[])).
% 1.86/2.02 tff(7393,plain,
% 1.86/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z))))),
% 1.86/2.02 inference(modus_ponens,[status(thm)],[7392, 7391])).
% 1.86/2.02 tff(7394,plain,
% 1.86/2.02 (~b(s(s(s(elem!1))), s(s(z)))),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[7393, 128, 7387, 7327, 6049, 7349])).
% 1.86/2.02 tff(7395,plain,
% 1.86/2.02 (r(s(s(s(elem!1))), s(s(z)))),
% 1.86/2.02 inference(unit_resolution,[status(thm)],[4350, 21, 7394, 283])).
% 1.86/2.02 tff(7396,plain,
% 1.86/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.86/2.02 inference(rewrite,[status(thm)],[])).
% 1.86/2.02 tff(7397,plain,
% 1.86/2.02 (((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.86/2.02 inference(rewrite,[status(thm)],[])).
% 1.86/2.02 tff(7398,plain,
% 1.86/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.86/2.02 inference(monotonicity,[status(thm)],[7397])).
% 1.86/2.02 tff(7399,plain,
% 1.86/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.86/2.03 inference(transitivity,[status(thm)],[7398, 7396])).
% 1.86/2.03 tff(7400,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(7401,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[7400, 7399])).
% 1.86/2.03 tff(7402,plain,
% 1.86/2.03 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[7401, 128, 7353, 6049, 7365, 7377])).
% 1.86/2.03 tff(7403,plain,
% 1.86/2.03 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[1820, 7402, 2650])).
% 1.86/2.03 tff(7404,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(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(7405,plain,
% 1.86/2.03 (((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(7406,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(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[7405])).
% 1.86/2.03 tff(7407,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(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.86/2.03 inference(transitivity,[status(thm)],[7406, 7404])).
% 1.86/2.03 tff(7408,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(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(7409,plain,
% 1.86/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[7408, 7407])).
% 1.86/2.03 tff(7410,plain,
% 1.86/2.03 ($false),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[7409, 45, 7403, 7395, 7373])).
% 1.86/2.03 tff(7411,plain,((s(s(elem!1)) = elem!1) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 1.86/2.03 tff(7412,plain,
% 1.86/2.03 (s(s(elem!1)) = elem!1),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[7411, 164])).
% 1.86/2.03 tff(7413,plain,
% 1.86/2.03 (elem!1 = s(s(elem!1))),
% 1.86/2.03 inference(symmetry,[status(thm)],[7412])).
% 1.86/2.03 tff(7414,plain,
% 1.86/2.03 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[245, 7412])).
% 1.86/2.03 tff(7415,plain,
% 1.86/2.03 (b(s(z), s(s(elem!1))) <=> b(s(z), elem!1)),
% 1.86/2.03 inference(monotonicity,[status(thm)],[7412])).
% 1.86/2.03 tff(7416,plain,
% 1.86/2.03 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.86/2.03 inference(symmetry,[status(thm)],[5893])).
% 1.86/2.03 tff(7417,plain,
% 1.86/2.03 (b(s(s(s(elem!1))), elem!1) <=> b(s(elem!1), elem!1)),
% 1.86/2.03 inference(monotonicity,[status(thm)],[953])).
% 1.86/2.03 tff(7418,plain,
% 1.86/2.03 (b(s(elem!1), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 1.86/2.03 inference(symmetry,[status(thm)],[7417])).
% 1.86/2.03 tff(7419,plain,
% 1.86/2.03 (b(s(elem!1), elem!1) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.86/2.03 inference(transitivity,[status(thm)],[7418, 7416])).
% 1.86/2.03 tff(7420,plain,
% 1.86/2.03 ((~b(s(elem!1), elem!1)) <=> (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[7419])).
% 1.86/2.03 tff(7421,plain,
% 1.86/2.03 (b(s(elem!1), z) <=> b(s(s(s(elem!1))), z)),
% 1.86/2.03 inference(monotonicity,[status(thm)],[309])).
% 1.86/2.03 tff(7422,plain,
% 1.86/2.03 (b(s(s(s(elem!1))), z) <=> b(s(elem!1), z)),
% 1.86/2.03 inference(symmetry,[status(thm)],[7421])).
% 1.86/2.03 tff(7423,plain,
% 1.86/2.03 (b(s(elem!1), z)),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[6811, 7422])).
% 1.86/2.03 tff(7424,plain,
% 1.86/2.03 (~r(elem!1, z)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[1534, 1937, 199])).
% 1.86/2.03 tff(7425,plain,
% 1.86/2.03 (b(elem!1, z)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[574, 7424, 462])).
% 1.86/2.03 tff(7426,plain,
% 1.86/2.03 (((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(7427,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[7426])).
% 1.86/2.03 tff(7428,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)))),
% 1.86/2.03 inference(transitivity,[status(thm)],[7427, 5992])).
% 1.86/2.03 tff(7429,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(7430,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[7429, 7428])).
% 1.86/2.03 tff(7431,plain,
% 1.86/2.03 ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[7430, 128, 498, 7425])).
% 1.86/2.03 tff(7432,plain,
% 1.86/2.03 (~b(s(elem!1), elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[7431, 7423])).
% 1.86/2.03 tff(7433,plain,
% 1.86/2.03 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[7432, 7420])).
% 1.86/2.03 tff(7434,plain,
% 1.86/2.03 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[889, 7433, 4151])).
% 1.86/2.03 tff(7435,plain,
% 1.86/2.03 (s(s(s(elem!1))) = elem!1),
% 1.86/2.03 inference(transitivity,[status(thm)],[7434, 199])).
% 1.86/2.03 tff(7436,plain,
% 1.86/2.03 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), elem!1)),
% 1.86/2.03 inference(monotonicity,[status(thm)],[7435])).
% 1.86/2.03 tff(7437,plain,
% 1.86/2.03 (r(s(z), elem!1) <=> r(s(z), s(s(s(elem!1))))),
% 1.86/2.03 inference(symmetry,[status(thm)],[7436])).
% 1.86/2.03 tff(7438,plain,
% 1.86/2.03 (r(s(z), elem!1)),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[89, 1516])).
% 1.86/2.03 tff(7439,plain,
% 1.86/2.03 (r(s(z), s(s(s(elem!1))))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[7438, 7437])).
% 1.86/2.03 tff(7440,plain,
% 1.86/2.03 (s(s(elem!1)) = s(s(s(elem!1)))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[803, 7434])).
% 1.86/2.03 tff(7441,plain,
% 1.86/2.03 (~r(s(s(z)), s(z))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[1557, 7438, 272, 199])).
% 1.86/2.03 tff(7442,plain,
% 1.86/2.03 (b(s(s(z)), s(z))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[86, 7441])).
% 1.86/2.03 tff(7443,assumption,(~(elem!1 = s(s(z)))), introduced(assumption)).
% 1.86/2.03 tff(7444,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, s(s(z)))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(7445,plain,
% 1.86/2.03 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(7446,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, s(s(z))))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[7445])).
% 1.86/2.03 tff(7447,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, s(s(z)))))),
% 1.86/2.03 inference(transitivity,[status(thm)],[7446, 7444])).
% 1.86/2.03 tff(7448,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(7449,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, s(s(z))))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[7448, 7447])).
% 1.86/2.03 tff(7450,plain,
% 1.86/2.03 (~b(elem!1, s(s(z)))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[7449, 128, 498, 577, 2993])).
% 1.86/2.03 tff(7451,plain,
% 1.86/2.03 (r(elem!1, s(s(z)))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[493, 7450, 7443])).
% 1.86/2.03 tff(7452,plain,
% 1.86/2.03 (r(s(s(s(elem!1))), s(s(z))) <=> r(elem!1, s(s(z)))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[1091])).
% 1.86/2.03 tff(7453,plain,
% 1.86/2.03 (r(elem!1, s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 1.86/2.03 inference(symmetry,[status(thm)],[7452])).
% 1.86/2.03 tff(7454,assumption,(r(elem!1, s(s(z)))), introduced(assumption)).
% 1.86/2.03 tff(7455,plain,
% 1.86/2.03 (r(s(s(s(elem!1))), s(s(z)))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[7454, 7453])).
% 1.86/2.03 tff(7456,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(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(7457,plain,
% 1.86/2.03 (((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(7458,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(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z))))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[7457])).
% 1.86/2.03 tff(7459,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(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))),
% 1.86/2.03 inference(transitivity,[status(thm)],[7458, 7456])).
% 1.86/2.03 tff(7460,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(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(7461,plain,
% 1.86/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z))))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[7460, 7459])).
% 1.86/2.03 tff(7462,plain,
% 1.86/2.03 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[7461, 45, 323, 634])).
% 1.86/2.03 tff(7463,plain,
% 1.86/2.03 ($false),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[7462, 7455])).
% 1.86/2.03 tff(7464,plain,((~r(elem!1, s(s(z)))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.03 tff(7465,plain,
% 1.86/2.03 (~r(s(z), s(s(z)))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[7464, 7451, 307, 323])).
% 1.86/2.03 tff(7466,plain,
% 1.86/2.03 (b(s(z), s(s(z)))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[648, 7465])).
% 1.86/2.03 tff(7467,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(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), 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(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(7468,plain,
% 1.86/2.03 (((~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(7469,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(s(z), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), elem!1))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[7468])).
% 1.86/2.03 tff(7470,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(s(z), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.86/2.03 inference(transitivity,[status(thm)],[7469, 7467])).
% 1.86/2.03 tff(7471,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(s(z), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(7472,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(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), elem!1))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[7471, 7470])).
% 1.86/2.03 tff(7473,plain,
% 1.86/2.03 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[7472, 45, 272, 1340, 1094])).
% 1.86/2.03 tff(7474,plain,
% 1.86/2.03 ((s(s(s(s(s(s(z)))))) = s(z)) | b(s(s(s(s(s(s(z)))))), s(z))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[1148, 21, 7473])).
% 1.86/2.03 tff(7475,plain,
% 1.86/2.03 (b(s(s(s(s(s(s(z)))))), s(z))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[7474, 1112])).
% 1.86/2.03 tff(7476,assumption,(b(s(z), s(s(z)))), introduced(assumption)).
% 1.86/2.03 tff(7477,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)), s(s(s(s(s(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(X0, 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(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(7478,plain,
% 1.86/2.03 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(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(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(7479,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(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(X0, 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(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[7478])).
% 1.86/2.03 tff(7480,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(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(X0, 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(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.86/2.03 inference(transitivity,[status(thm)],[7479, 7477])).
% 1.86/2.03 tff(7481,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(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)))))))))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(7482,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[7481, 7480])).
% 1.86/2.03 tff(7483,plain,
% 1.86/2.03 ($false),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[7482, 128, 7476, 273, 7475, 1427])).
% 1.86/2.03 tff(7484,plain,((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~r(s(z), z)) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.03 tff(7485,plain,
% 1.86/2.03 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[7484, 7466, 273, 272, 1340, 7215])).
% 1.86/2.03 tff(7486,plain,
% 1.86/2.03 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[1055, 7485, 2956])).
% 1.86/2.03 tff(7487,plain,
% 1.86/2.03 (~r(s(s(s(s(z)))), elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[1356, 7215, 272, 1340])).
% 1.86/2.03 tff(7488,plain,
% 1.86/2.03 (b(s(s(s(s(z)))), elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[632, 7487, 2953])).
% 1.86/2.03 tff(7489,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(7490,plain,
% 1.86/2.03 (((~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(7491,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[7490])).
% 1.86/2.03 tff(7492,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.86/2.03 inference(transitivity,[status(thm)],[7491, 7489])).
% 1.86/2.03 tff(7493,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(7494,plain,
% 1.86/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[7493, 7492])).
% 1.86/2.04 tff(7495,plain,
% 1.86/2.04 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[7494, 128, 498, 577, 7488, 7486])).
% 1.86/2.04 tff(7496,plain,
% 1.86/2.04 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1215, 21, 1212, 7495])).
% 1.86/2.04 tff(7497,plain,
% 1.86/2.04 (~b(s(s(s(s(s(s(z)))))), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1016, 128, 498, 577, 7486])).
% 1.86/2.04 tff(7498,plain,
% 1.86/2.04 (r(s(s(s(s(s(s(z)))))), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1022, 21, 1019, 7497])).
% 1.86/2.04 tff(7499,plain,
% 1.86/2.04 (~b(s(s(s(s(z)))), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[583, 128, 498, 577, 7488])).
% 1.86/2.04 tff(7500,plain,
% 1.86/2.04 (r(s(s(s(s(z)))), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[589, 21, 586, 7499])).
% 1.86/2.04 tff(7501,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(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(7502,plain,
% 1.86/2.04 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(7503,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(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[7502])).
% 1.86/2.04 tff(7504,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(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.86/2.04 inference(transitivity,[status(thm)],[7503, 7501])).
% 1.86/2.04 tff(7505,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(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(7506,plain,
% 1.86/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[7505, 7504])).
% 1.86/2.04 tff(7507,plain,
% 1.86/2.04 ($false),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[7506, 45, 7500, 7498, 7496])).
% 1.86/2.04 tff(7508,plain,((~b(s(s(z)), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (s(s(s(s(s(s(z)))))) = elem!1) | (~b(s(s(z)), s(z))) | (~r(s(z), z)) | (~r(s(z), elem!1)) | (s(s(s(s(z)))) = elem!1) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (s(s(z)) = elem!1) | (elem!1 = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.04 tff(7509,plain,
% 1.86/2.04 (~b(s(s(z)), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[7508, 7425, 498, 246, 7442, 272, 7438, 243, 7440, 7439, 959, 991])).
% 1.86/2.04 tff(7510,plain,
% 1.86/2.04 (r(s(s(z)), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[25, 7509])).
% 1.86/2.04 tff(7511,plain,
% 1.86/2.04 (~r(s(z), s(s(z)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1327, 7510, 272])).
% 1.86/2.04 tff(7512,plain,
% 1.86/2.04 (b(s(z), s(s(z)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[648, 7511])).
% 1.86/2.04 tff(7513,plain,
% 1.86/2.04 (~b(s(s(s(s(z)))), elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[627, 591, 498, 577])).
% 1.86/2.04 tff(7514,plain,
% 1.86/2.04 (r(s(s(s(s(z)))), elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[632, 7513, 243])).
% 1.86/2.04 tff(7515,plain,
% 1.86/2.04 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1249, 7514, 307, 199])).
% 1.86/2.04 tff(7516,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(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(7517,plain,
% 1.86/2.04 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(7518,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(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(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(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[7517])).
% 1.86/2.04 tff(7519,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(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(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(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.86/2.04 inference(transitivity,[status(thm)],[7518, 7516])).
% 1.86/2.04 tff(7520,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(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(7521,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(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[7520, 7519])).
% 1.86/2.04 tff(7522,plain,
% 1.86/2.04 (~r(s(s(s(s(z)))), s(z))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[7521, 45, 323, 1186])).
% 1.86/2.04 tff(7523,plain,
% 1.86/2.04 (b(s(s(s(s(z)))), s(z))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[782, 21, 779, 7522])).
% 1.86/2.04 tff(7524,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(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(7525,plain,
% 1.86/2.04 (((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(7526,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(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[7525])).
% 1.86/2.04 tff(7527,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(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.86/2.04 inference(transitivity,[status(thm)],[7526, 7524])).
% 1.86/2.04 tff(7528,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(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(7529,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(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[7528, 7527])).
% 1.86/2.04 tff(7530,plain,
% 1.86/2.04 (~r(s(z), s(s(s(s(z)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[7529, 45, 323, 1186])).
% 1.86/2.04 tff(7531,plain,
% 1.86/2.04 (b(s(z), s(s(s(s(z)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[684, 21, 681, 7530])).
% 1.86/2.04 tff(7532,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(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(7533,plain,
% 1.86/2.04 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(7534,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(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(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(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[7533])).
% 1.86/2.04 tff(7535,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(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(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(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 1.86/2.04 inference(transitivity,[status(thm)],[7534, 7532])).
% 1.86/2.04 tff(7536,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(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(7537,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(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[7536, 7535])).
% 1.86/2.04 tff(7538,plain,
% 1.86/2.04 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[7537, 45, 323, 1197])).
% 1.86/2.04 tff(7539,plain,
% 1.86/2.04 ((s(s(s(s(s(s(z)))))) = s(z)) | b(s(s(s(s(s(s(z)))))), s(z))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1148, 21, 7538])).
% 1.86/2.04 tff(7540,plain,
% 1.86/2.04 (b(s(s(s(s(s(s(z)))))), s(z))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[7539, 1112])).
% 1.86/2.04 tff(7541,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z)))))), s(s(s(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(X0, 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(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(7542,plain,
% 1.86/2.04 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(7543,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[7542])).
% 1.86/2.04 tff(7544,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.86/2.04 inference(transitivity,[status(thm)],[7543, 7541])).
% 1.86/2.04 tff(7545,plain,
% 1.86/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(7546,plain,
% 1.86/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[7545, 7544])).
% 1.86/2.04 tff(7547,plain,
% 1.86/2.04 ($false),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[7546, 128, 7540, 7531, 1216, 7523])).
% 1.86/2.04 tff(7548,plain,((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.04 tff(7549,plain,
% 1.86/2.04 (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[7548, 7515, 323])).
% 1.86/2.04 tff(7550,plain,
% 1.86/2.04 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1098, 7549, 307])).
% 1.86/2.04 tff(7551,plain,
% 1.86/2.04 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1055, 7550, 246])).
% 1.86/2.04 tff(7552,plain,
% 1.86/2.04 (~b(s(s(s(s(s(s(z)))))), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1016, 128, 498, 577, 7551])).
% 1.86/2.04 tff(7553,plain,
% 1.86/2.04 (r(s(s(s(s(s(s(z)))))), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1022, 21, 1019, 7552])).
% 1.86/2.04 tff(7554,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), 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(X0, 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)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(7555,plain,
% 1.86/2.04 (((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(7556,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~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(X0, 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)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[7555])).
% 1.86/2.04 tff(7557,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~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(X0, 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)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.86/2.04 inference(transitivity,[status(thm)],[7556, 7554])).
% 1.86/2.04 tff(7558,plain,
% 1.86/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(7559,plain,
% 1.86/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[7558, 7557])).
% 1.86/2.04 tff(7560,plain,
% 1.86/2.04 (~b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[7559, 128, 498, 577, 591, 7551])).
% 1.86/2.04 tff(7561,plain,
% 1.86/2.04 (r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1176, 21, 1123, 7560])).
% 1.86/2.04 tff(7562,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(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)))))))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(7563,plain,
% 1.86/2.04 (((~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)))))))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(7564,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(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))))))))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[7563])).
% 1.86/2.04 tff(7565,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(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)))))))))),
% 1.86/2.04 inference(transitivity,[status(thm)],[7564, 7562])).
% 1.86/2.04 tff(7566,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(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)))))))))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(7567,plain,
% 1.86/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[7566, 7565])).
% 1.86/2.04 tff(7568,plain,
% 1.86/2.04 ($false),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[7567, 45, 28, 7561, 7553])).
% 1.86/2.04 tff(7569,plain,((~b(s(s(z)), elem!1)) | (~r(s(s(z)), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.04 tff(7570,plain,
% 1.86/2.04 (~b(s(s(z)), elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[7569, 7510, 498, 7425, 7440, 7439, 199])).
% 1.86/2.04 tff(7571,plain,
% 1.86/2.04 (r(s(s(z)), elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[370, 7570, 959])).
% 1.86/2.04 tff(7572,plain,
% 1.86/2.04 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[7484, 7571, 7442, 272, 7438, 7512])).
% 1.86/2.04 tff(7573,plain,
% 1.86/2.04 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1055, 7572, 246])).
% 1.86/2.04 tff(7574,plain,
% 1.86/2.04 (~b(s(s(s(s(s(s(z)))))), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1016, 128, 498, 7425, 7573])).
% 1.86/2.04 tff(7575,plain,
% 1.86/2.04 (r(s(s(s(s(s(s(z)))))), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1022, 21, 1019, 7574])).
% 1.86/2.04 tff(7576,plain,
% 1.86/2.04 (~r(s(s(s(s(z)))), elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1356, 7571, 272, 7438])).
% 1.86/2.04 tff(7577,plain,
% 1.86/2.04 (b(s(s(s(s(z)))), elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[632, 7576, 243])).
% 1.86/2.04 tff(7578,plain,
% 1.86/2.04 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[7494, 128, 498, 7425, 7577, 7573])).
% 1.86/2.04 tff(7579,plain,
% 1.86/2.04 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1215, 21, 1212, 7578])).
% 1.86/2.04 tff(7580,plain,
% 1.86/2.04 (~b(s(s(s(s(z)))), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[583, 128, 498, 7425, 7577])).
% 1.86/2.04 tff(7581,plain,
% 1.86/2.04 (r(s(s(s(s(z)))), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[589, 21, 586, 7580])).
% 1.86/2.04 tff(7582,plain,
% 1.86/2.04 ($false),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[7506, 45, 7581, 7579, 7575])).
% 1.86/2.04 tff(7583,plain,((~r(s(z), s(s(elem!1)))) | (~b(z, elem!1)) | (~r(s(z), z)) | (~(s(s(elem!1)) = elem!1)) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.04 tff(7584,plain,
% 1.86/2.04 (~r(s(z), s(s(elem!1)))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[7583, 6809, 171, 7412, 6039])).
% 1.86/2.05 tff(7585,plain,
% 1.86/2.05 (b(s(z), s(s(elem!1)))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[117, 7584])).
% 1.86/2.05 tff(7586,plain,
% 1.86/2.05 (b(s(z), elem!1)),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[7585, 7415])).
% 1.86/2.05 tff(7587,plain,
% 1.86/2.05 ((s(s(elem!1)) = z) <=> (elem!1 = z)),
% 1.86/2.05 inference(monotonicity,[status(thm)],[7412])).
% 1.86/2.05 tff(7588,plain,
% 1.86/2.05 ((s(s(elem!1)) = z) <=> (z = elem!1)),
% 1.86/2.05 inference(transitivity,[status(thm)],[7587, 247])).
% 1.86/2.05 tff(7589,plain,
% 1.86/2.05 ((s(s(elem!1)) = z) <=> (elem!1 = z)),
% 1.86/2.05 inference(transitivity,[status(thm)],[7588, 459])).
% 1.86/2.05 tff(7590,plain,
% 1.86/2.05 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = z))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[7589])).
% 1.86/2.05 tff(7591,plain,
% 1.86/2.05 (~(elem!1 = z)),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[154, 7590])).
% 1.86/2.05 tff(7592,plain,
% 1.86/2.05 (r(s(s(s(s(elem!1)))), s(z)) <=> r(elem!1, s(z))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[955])).
% 1.86/2.05 tff(7593,plain,
% 1.86/2.05 (r(elem!1, s(z)) <=> r(s(s(s(s(elem!1)))), s(z))),
% 1.86/2.05 inference(symmetry,[status(thm)],[7592])).
% 1.86/2.05 tff(7594,plain,
% 1.86/2.05 (r(s(s(s(s(elem!1)))), s(z))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[306, 7593])).
% 1.86/2.05 tff(7595,plain,
% 1.86/2.05 (~r(s(z), s(s(elem!1)))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[7583, 498, 272, 199, 385])).
% 1.86/2.05 tff(7596,plain,
% 1.86/2.05 (b(s(z), s(s(elem!1)))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[117, 7595])).
% 1.86/2.05 tff(7597,plain,
% 1.86/2.05 (b(s(z), elem!1)),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[7596, 860])).
% 1.86/2.05 tff(7598,plain,
% 1.86/2.05 (~r(s(s(elem!1)), z)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1962, 293, 272])).
% 1.86/2.05 tff(7599,plain,
% 1.86/2.05 (~r(elem!1, z)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1534, 7598, 199])).
% 1.86/2.05 tff(7600,plain,
% 1.86/2.05 (b(elem!1, z)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[574, 7599, 462])).
% 1.86/2.05 tff(7601,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(7602,plain,
% 1.86/2.05 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z)))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(7603,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(z)))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[7602])).
% 1.86/2.05 tff(7604,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 1.86/2.05 inference(transitivity,[status(thm)],[7603, 7601])).
% 1.86/2.05 tff(7605,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 1.86/2.05 inference(quant_inst,[status(thm)],[])).
% 1.86/2.05 tff(7606,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(z)))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[7605, 7604])).
% 1.86/2.05 tff(7607,plain,
% 1.86/2.05 (~b(z, s(z))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[7606, 128, 498, 7600, 7597])).
% 1.86/2.05 tff(7608,plain,
% 1.86/2.05 (r(z, s(z))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[415, 7607])).
% 1.86/2.05 tff(7609,plain,
% 1.86/2.05 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[7165, 7608, 7594, 385, 272])).
% 1.86/2.05 tff(7610,plain,
% 1.86/2.05 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1050, 7600, 498, 272, 7597])).
% 1.86/2.05 tff(7611,plain,
% 1.86/2.05 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1055, 7610, 246])).
% 1.86/2.05 tff(7612,assumption,(r(s(s(s(s(s(s(z)))))), s(z))), introduced(assumption)).
% 1.86/2.05 tff(7613,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(elem!1, s(z))) | (~r(s(s(s(s(s(s(z)))))), 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(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(7614,plain,
% 1.86/2.05 (((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(z)))))), elem!1))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(7615,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(elem!1, s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(elem!1, 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(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), elem!1))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[7614])).
% 1.86/2.05 tff(7616,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(elem!1, s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(elem!1, 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(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.86/2.05 inference(transitivity,[status(thm)],[7615, 7613])).
% 1.86/2.05 tff(7617,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(elem!1, s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(z)))))), elem!1)))),
% 1.86/2.05 inference(quant_inst,[status(thm)],[])).
% 1.86/2.05 tff(7618,plain,
% 1.86/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), elem!1))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[7617, 7616])).
% 1.86/2.05 tff(7619,plain,
% 1.86/2.05 ($false),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[7618, 45, 313, 1094, 7612])).
% 1.86/2.05 tff(7620,plain,((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(z)))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.05 tff(7621,plain,
% 1.86/2.05 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[7620, 306, 7611])).
% 1.86/2.05 tff(7622,plain,
% 1.86/2.05 ((s(s(s(s(s(s(z)))))) = s(z)) | b(s(s(s(s(s(s(z)))))), s(z))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1148, 21, 7621])).
% 1.86/2.05 tff(7623,plain,
% 1.86/2.05 (b(s(s(s(s(s(s(z)))))), s(z))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[7622, 1112])).
% 1.86/2.05 tff(7624,plain,
% 1.86/2.05 (r(s(s(z)), elem!1)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[370, 7214, 959])).
% 1.86/2.05 tff(7625,plain,
% 1.86/2.05 (~r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1172, 45, 7624, 1094])).
% 1.86/2.05 tff(7626,plain,
% 1.86/2.05 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(elem!1), s(s(z)))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[953])).
% 1.86/2.05 tff(7627,plain,
% 1.86/2.05 (r(s(elem!1), s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 1.86/2.05 inference(symmetry,[status(thm)],[7626])).
% 1.86/2.05 tff(7628,plain,
% 1.86/2.05 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 1.86/2.05 inference(symmetry,[status(thm)],[688])).
% 1.86/2.05 tff(7629,plain,
% 1.86/2.05 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 1.86/2.05 inference(symmetry,[status(thm)],[954])).
% 1.86/2.05 tff(7630,plain,
% 1.86/2.05 (elem!1 = s(elem!1)),
% 1.86/2.05 inference(transitivity,[status(thm)],[202, 7629, 7628, 953])).
% 1.86/2.05 tff(7631,plain,
% 1.86/2.05 (r(elem!1, s(s(z))) <=> r(s(elem!1), s(s(z)))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[7630])).
% 1.86/2.05 tff(7632,plain,
% 1.86/2.05 (r(elem!1, s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 1.86/2.05 inference(transitivity,[status(thm)],[7631, 7627])).
% 1.86/2.05 tff(7633,plain,
% 1.86/2.05 (r(elem!1, s(s(z)))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[493, 7450, 991])).
% 1.86/2.05 tff(7634,plain,
% 1.86/2.05 (r(s(s(s(elem!1))), s(s(z)))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[7633, 7632])).
% 1.86/2.05 tff(7635,plain,
% 1.86/2.05 (~r(s(s(z)), s(z))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[6248, 7634, 385])).
% 1.86/2.05 tff(7636,plain,
% 1.86/2.05 (b(s(s(z)), s(z))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[86, 7635])).
% 1.86/2.05 tff(7637,assumption,(b(s(s(s(s(s(s(z)))))), s(z))), introduced(assumption)).
% 1.86/2.05 tff(7638,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(7639,plain,
% 1.86/2.05 (((~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(z), elem!1)) | (~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), elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(7640,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(z), elem!1)) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[7639])).
% 1.86/2.05 tff(7641,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(z), elem!1)) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.86/2.05 inference(transitivity,[status(thm)],[7640, 7638])).
% 1.86/2.05 tff(7642,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(z), elem!1)) | (~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)))))))))),
% 1.86/2.05 inference(quant_inst,[status(thm)],[])).
% 1.86/2.05 tff(7643,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[7642, 7641])).
% 1.86/2.05 tff(7644,plain,
% 1.86/2.05 ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[7643, 128, 577, 922, 2993, 7637])).
% 1.86/2.05 tff(7645,plain,
% 1.86/2.05 (~b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[7644, 7636])).
% 1.86/2.05 tff(7646,plain,
% 1.86/2.05 ($false),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1176, 21, 1123, 7645, 7625])).
% 1.86/2.05 tff(7647,plain,((~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~(s(s(elem!1)) = elem!1)) | (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.05 tff(7648,plain,
% 1.86/2.05 (~b(s(s(z)), z)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[7647, 7600, 7597, 7623, 385, 7611, 199, 7609, 498])).
% 1.86/2.05 tff(7649,plain,
% 1.86/2.05 (r(s(s(z)), z)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[25, 7648])).
% 1.86/2.05 tff(7650,plain,
% 1.86/2.05 (~r(s(z), s(s(z)))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1327, 7649, 272])).
% 1.86/2.05 tff(7651,plain,
% 1.86/2.05 (b(s(z), s(s(z)))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[648, 7650])).
% 1.86/2.05 tff(7652,plain,
% 1.86/2.05 (~r(s(s(z)), s(z))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1509, 7649, 272])).
% 1.86/2.05 tff(7653,plain,
% 1.86/2.05 (b(s(s(z)), s(z))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[86, 7652])).
% 1.86/2.05 tff(7654,plain,
% 1.86/2.05 (((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(7655,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[7654])).
% 1.86/2.05 tff(7656,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.86/2.05 inference(transitivity,[status(thm)],[7655, 1139])).
% 1.86/2.05 tff(7657,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 1.86/2.05 inference(quant_inst,[status(thm)],[])).
% 1.86/2.05 tff(7658,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[7657, 7656])).
% 1.86/2.05 tff(7659,plain,
% 1.86/2.05 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[7658, 128, 7651, 7653, 7623])).
% 1.86/2.05 tff(7660,plain,
% 1.86/2.05 ((s(s(s(s(s(s(z)))))) = s(s(z))) | r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1134, 21, 7659])).
% 1.86/2.05 tff(7661,plain,
% 1.86/2.05 (r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[7660, 1124])).
% 1.86/2.05 tff(7662,assumption,(r(s(s(s(s(s(s(z)))))), s(s(z)))), introduced(assumption)).
% 1.86/2.05 tff(7663,plain,
% 1.86/2.05 ($false),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1130, 45, 1103, 1094, 7662])).
% 1.86/2.05 tff(7664,plain,((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.05 tff(7665,plain,
% 1.86/2.05 (~r(s(s(z)), elem!1)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[7664, 7611, 7661])).
% 1.86/2.05 tff(7666,plain,
% 1.86/2.05 (b(s(s(z)), elem!1)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[370, 7665, 959])).
% 1.86/2.05 tff(7667,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(7668,plain,
% 1.86/2.05 (((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, 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, z)) | (~b(z, elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(7669,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[7668])).
% 1.86/2.05 tff(7670,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 1.86/2.05 inference(transitivity,[status(thm)],[7669, 7667])).
% 1.86/2.05 tff(7671,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))))),
% 1.86/2.05 inference(quant_inst,[status(thm)],[])).
% 1.86/2.05 tff(7672,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[7671, 7670])).
% 1.86/2.05 tff(7673,plain,
% 1.86/2.05 ($false),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[7672, 128, 498, 7600, 7597, 7666, 7651])).
% 1.86/2.05 tff(7674,plain,(b(s(s(elem!1)), s(z)) | (~b(z, elem!1)) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.05 tff(7675,plain,
% 1.86/2.05 (b(s(s(elem!1)), s(z))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[7674, 6809, 171, 6039, 7412])).
% 1.86/2.05 tff(7676,plain,
% 1.86/2.05 ((s(s(elem!1)) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[7412])).
% 1.86/2.05 tff(7677,plain,
% 1.86/2.05 ((s(s(elem!1)) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 1.86/2.05 inference(transitivity,[status(thm)],[7676, 225])).
% 1.86/2.05 tff(7678,plain,
% 1.86/2.05 ((s(s(z)) = elem!1) <=> (s(s(elem!1)) = s(s(z)))),
% 1.86/2.05 inference(symmetry,[status(thm)],[7677])).
% 1.86/2.05 tff(7679,plain,
% 1.86/2.05 (s(s(s(elem!1))) = s(elem!1)),
% 1.86/2.05 inference(monotonicity,[status(thm)],[7412])).
% 1.86/2.05 tff(7680,plain,
% 1.86/2.05 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[7679])).
% 1.86/2.05 tff(7681,plain,
% 1.86/2.05 (s(s(s(s(elem!1)))) = elem!1),
% 1.86/2.05 inference(transitivity,[status(thm)],[7680, 7412])).
% 1.86/2.05 tff(7682,plain,
% 1.86/2.05 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[7681])).
% 1.86/2.05 tff(7683,plain,
% 1.86/2.05 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 1.86/2.05 inference(transitivity,[status(thm)],[7682, 225])).
% 1.86/2.05 tff(7684,plain,
% 1.86/2.05 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(elem!1)) = s(s(z)))),
% 1.86/2.05 inference(transitivity,[status(thm)],[7683, 7678])).
% 1.86/2.05 tff(7685,plain,
% 1.86/2.05 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(elem!1)) = s(s(z))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[7684])).
% 1.86/2.05 tff(7686,plain,
% 1.86/2.05 (~(s(s(elem!1)) = s(s(z)))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[239, 7685])).
% 1.86/2.05 tff(7687,plain,
% 1.86/2.05 (b(s(elem!1), z) <=> b(s(s(s(elem!1))), z)),
% 1.86/2.05 inference(monotonicity,[status(thm)],[354])).
% 1.86/2.05 tff(7688,plain,
% 1.86/2.05 (b(s(s(s(elem!1))), z) <=> b(s(elem!1), z)),
% 1.86/2.05 inference(symmetry,[status(thm)],[7687])).
% 1.86/2.05 tff(7689,plain,
% 1.86/2.05 (b(s(elem!1), z)),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[6811, 7688])).
% 1.86/2.05 tff(7690,plain,
% 1.86/2.05 ((z = s(elem!1)) <=> (s(elem!1) = z)),
% 1.86/2.05 inference(commutativity,[status(thm)],[])).
% 1.86/2.05 tff(7691,plain,
% 1.86/2.05 ((s(elem!1) = z) <=> (z = s(elem!1))),
% 1.86/2.05 inference(symmetry,[status(thm)],[7690])).
% 1.86/2.05 tff(7692,plain,
% 1.86/2.05 ((~(s(elem!1) = z)) <=> (~(z = s(elem!1)))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[7691])).
% 1.86/2.05 tff(7693,plain,
% 1.86/2.05 (~(z = s(elem!1))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[109, 7692])).
% 1.86/2.05 tff(7694,plain,
% 1.86/2.05 (r(s(elem!1), s(z))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[385, 258])).
% 1.86/2.05 tff(7695,plain,
% 1.86/2.05 (b(s(s(elem!1)), s(z))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[7674, 498, 272, 385, 199])).
% 1.86/2.05 tff(7696,plain,
% 1.86/2.05 (b(elem!1, s(z))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[7695, 270])).
% 1.86/2.05 tff(7697,plain,
% 1.86/2.05 (~b(z, s(z))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1156, 128, 498, 7696, 7597])).
% 1.86/2.05 tff(7698,plain,
% 1.86/2.05 (r(z, s(z))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[415, 7697])).
% 1.86/2.05 tff(7699,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(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(elem!1))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(7700,plain,
% 1.86/2.05 (((~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(elem!1)))) <=> ((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(elem!1))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(7701,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(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(elem!1)))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[7700])).
% 1.86/2.05 tff(7702,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(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(elem!1))))),
% 1.86/2.05 inference(transitivity,[status(thm)],[7701, 7699])).
% 1.86/2.05 tff(7703,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(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(elem!1))))),
% 1.86/2.05 inference(quant_inst,[status(thm)],[])).
% 1.86/2.05 tff(7704,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(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(elem!1)))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[7703, 7702])).
% 1.86/2.06 tff(7705,plain,
% 1.86/2.06 (~r(z, s(elem!1))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[7704, 45, 7698, 7694])).
% 1.86/2.06 tff(7706,plain,
% 1.86/2.06 (((~![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)))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(7707,plain,
% 1.86/2.06 ((~![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)))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(7708,plain,
% 1.86/2.06 ((~![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))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[7707, 7706])).
% 1.86/2.06 tff(7709,plain,
% 1.86/2.06 ((z = s(elem!1)) | b(z, s(elem!1))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[7708, 21, 7705])).
% 1.86/2.06 tff(7710,plain,
% 1.86/2.06 (b(z, s(elem!1))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[7709, 7693])).
% 1.86/2.06 tff(7711,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(7712,plain,
% 1.86/2.06 (((~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1)))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(7713,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1)))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[7712])).
% 1.86/2.06 tff(7714,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))))),
% 1.86/2.06 inference(transitivity,[status(thm)],[7713, 7711])).
% 1.86/2.06 tff(7715,plain,
% 1.86/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(7716,plain,
% 1.86/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1)))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[7715, 7714])).
% 1.86/2.06 tff(7717,plain,
% 1.86/2.06 (~b(s(s(z)), s(elem!1))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[7716, 128, 2993, 7710, 7689])).
% 1.86/2.06 tff(7718,plain,
% 1.86/2.06 ((s(s(z)) = s(elem!1)) | r(s(s(z)), s(elem!1))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[351, 21, 7717])).
% 1.86/2.06 tff(7719,plain,
% 1.86/2.06 (r(s(s(z)), s(elem!1))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[7718, 285])).
% 1.86/2.06 tff(7720,plain,
% 1.86/2.06 (~r(z, s(s(s(elem!1))))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[7705, 531])).
% 1.86/2.06 tff(7721,plain,
% 1.86/2.06 (b(z, s(s(s(elem!1))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[858, 7720])).
% 1.86/2.06 tff(7722,plain,
% 1.86/2.06 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[3460, 7721, 6811, 5953])).
% 1.86/2.06 tff(7723,plain,
% 1.86/2.06 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(elem!1), s(s(z)))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[226])).
% 1.86/2.06 tff(7724,plain,
% 1.86/2.06 (r(s(elem!1), s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 1.86/2.06 inference(symmetry,[status(thm)],[7723])).
% 1.86/2.06 tff(7725,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z)))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(7726,plain,
% 1.86/2.06 (((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(z))))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z)))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(7727,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z))))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[7726])).
% 1.86/2.06 tff(7728,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z)))))),
% 1.86/2.06 inference(transitivity,[status(thm)],[7727, 7725])).
% 1.86/2.06 tff(7729,plain,
% 1.86/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(z)))))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(7730,plain,
% 1.86/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z))))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[7729, 7728])).
% 1.86/2.06 tff(7731,plain,
% 1.86/2.06 (~b(s(elem!1), s(s(z)))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[7730, 128, 2993, 7710, 7689])).
% 1.86/2.06 tff(7732,plain,
% 1.86/2.06 (r(s(elem!1), s(s(z)))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[473, 21, 284, 7731])).
% 1.86/2.06 tff(7733,plain,
% 1.86/2.06 (r(s(s(s(elem!1))), s(s(z)))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[7732, 7724])).
% 1.86/2.06 tff(7734,plain,
% 1.86/2.06 (~r(s(s(z)), s(z))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[6248, 7733, 385])).
% 1.86/2.06 tff(7735,plain,
% 1.86/2.06 (b(s(s(z)), s(z))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[86, 7734])).
% 1.86/2.06 tff(7736,plain,
% 1.86/2.06 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[1291, 7735, 272, 498, 7597, 7696, 199])).
% 1.86/2.06 tff(7737,plain,
% 1.86/2.06 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[321, 7736, 7722])).
% 1.86/2.06 tff(7738,plain,
% 1.86/2.06 (r(elem!1, s(elem!1))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[7737, 358])).
% 1.86/2.06 tff(7739,plain,
% 1.86/2.06 (~r(elem!1, s(s(z)))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[481, 45, 7738, 7719])).
% 1.86/2.06 tff(7740,plain,
% 1.86/2.06 (~b(elem!1, s(s(z)))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[997, 128, 7696, 7597, 7735])).
% 1.86/2.06 tff(7741,plain,
% 1.86/2.06 ($false),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[493, 7740, 7739, 653])).
% 1.86/2.06 tff(7742,plain,((~b(s(s(z)), z)) | (~(s(s(elem!1)) = elem!1)) | (~r(s(z), z)) | (~b(z, elem!1)) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.06 tff(7743,plain,
% 1.86/2.06 (~b(s(s(z)), z)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[7742, 7412, 171, 6809, 6039])).
% 1.86/2.06 tff(7744,plain,
% 1.86/2.06 (r(s(s(z)), z)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[25, 7743])).
% 1.86/2.06 tff(7745,plain,
% 1.86/2.06 (~r(s(s(elem!1)), z)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[7347, 7744, 7686, 7675, 171])).
% 1.86/2.06 tff(7746,plain,
% 1.86/2.06 (~r(elem!1, z)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[1534, 7745, 7412])).
% 1.86/2.06 tff(7747,plain,
% 1.86/2.06 (b(elem!1, z)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[574, 7746, 7591])).
% 1.86/2.06 tff(7748,plain,
% 1.86/2.06 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[1050, 7747, 6809, 171, 7586])).
% 1.86/2.06 tff(7749,plain,
% 1.86/2.06 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[1055, 7748, 7414])).
% 1.86/2.06 tff(7750,plain,
% 1.86/2.06 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[7683])).
% 1.86/2.06 tff(7751,plain,
% 1.86/2.06 (~(s(s(z)) = elem!1)),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[239, 7750])).
% 1.86/2.06 tff(7752,plain,
% 1.86/2.06 (b(s(s(elem!1)), s(z)) <=> b(elem!1, s(z))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[7412])).
% 1.86/2.06 tff(7753,plain,
% 1.86/2.06 (b(elem!1, s(z))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[7675, 7752])).
% 1.86/2.06 tff(7754,plain,
% 1.86/2.06 (~b(z, s(z))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[1156, 128, 6809, 7753, 7586])).
% 1.86/2.06 tff(7755,plain,
% 1.86/2.06 (r(z, s(z))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[415, 7754])).
% 1.86/2.06 tff(7756,plain,
% 1.86/2.06 (~b(s(s(z)), elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[5679, 7747, 6809, 171, 7753, 7755, 7586])).
% 1.86/2.06 tff(7757,plain,
% 1.86/2.06 (r(s(s(z)), elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[370, 7756, 7751])).
% 1.86/2.06 tff(7758,plain,
% 1.86/2.06 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[7664, 7757, 7749])).
% 1.86/2.06 tff(7759,plain,
% 1.86/2.06 ((s(s(s(s(s(s(z)))))) = s(s(z))) | b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[1134, 21, 7758])).
% 1.86/2.06 tff(7760,plain,
% 1.86/2.06 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[7759, 1124])).
% 1.86/2.06 tff(7761,plain,
% 1.86/2.06 (~(s(s(s(s(z)))) = elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[242, 7412])).
% 1.86/2.06 tff(7762,plain,
% 1.86/2.06 (~b(s(s(s(s(z)))), elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[950, 7753, 6809, 7586, 171])).
% 1.86/2.06 tff(7763,plain,
% 1.86/2.06 (r(s(s(s(s(z)))), elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[632, 7762, 7761])).
% 1.86/2.06 tff(7764,plain,
% 1.86/2.06 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2986, 45, 7763, 7749])).
% 1.86/2.06 tff(7765,plain,
% 1.86/2.06 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[1215, 21, 1212, 7764])).
% 1.86/2.06 tff(7766,plain,
% 1.86/2.06 (~r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[1172, 45, 7757, 7749])).
% 1.86/2.06 tff(7767,plain,
% 1.86/2.06 (b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[1176, 21, 1123, 7766])).
% 1.86/2.06 tff(7768,plain,
% 1.86/2.06 (s(elem!1) = s(s(s(elem!1)))),
% 1.86/2.06 inference(symmetry,[status(thm)],[7679])).
% 1.86/2.06 tff(7769,plain,
% 1.86/2.06 (r(s(elem!1), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 1.86/2.06 inference(monotonicity,[status(thm)],[7768])).
% 1.86/2.06 tff(7770,plain,
% 1.86/2.06 (r(s(s(s(elem!1))), elem!1) <=> r(s(elem!1), elem!1)),
% 1.86/2.06 inference(symmetry,[status(thm)],[7769])).
% 1.86/2.06 tff(7771,plain,
% 1.86/2.06 (r(z, s(elem!1)) <=> r(z, s(s(s(elem!1))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[7768])).
% 1.86/2.06 tff(7772,plain,
% 1.86/2.06 ((~r(z, s(elem!1))) <=> (~r(z, s(s(s(elem!1)))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[7771])).
% 1.86/2.06 tff(7773,plain,
% 1.86/2.06 (r(s(s(s(elem!1))), s(z)) <=> r(s(elem!1), s(z))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[7679])).
% 1.86/2.06 tff(7774,plain,
% 1.86/2.06 (r(s(elem!1), s(z))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[6039, 7773])).
% 1.86/2.06 tff(7775,plain,
% 1.86/2.06 (~r(z, s(elem!1))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[7704, 45, 7755, 7774])).
% 1.86/2.06 tff(7776,plain,
% 1.86/2.06 (~r(z, s(s(s(elem!1))))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[7775, 7772])).
% 1.86/2.06 tff(7777,plain,
% 1.86/2.06 (b(z, s(s(s(elem!1))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[858, 7776])).
% 1.86/2.06 tff(7778,plain,
% 1.86/2.06 (~b(s(s(s(elem!1))), elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[7179, 7747, 6809, 7777])).
% 1.86/2.06 tff(7779,plain,
% 1.86/2.06 (~r(s(s(z)), s(z))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[1509, 7744, 171])).
% 1.86/2.06 tff(7780,plain,
% 1.86/2.06 (b(s(s(z)), s(z))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[86, 7779])).
% 1.86/2.06 tff(7781,plain,
% 1.86/2.06 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[1291, 7780, 171, 6809, 7586, 7753, 7412])).
% 1.86/2.06 tff(7782,plain,
% 1.86/2.06 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[693, 7781])).
% 1.86/2.06 tff(7783,plain,
% 1.86/2.06 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[700, 7782])).
% 1.86/2.06 tff(7784,plain,
% 1.86/2.06 (~(s(s(s(elem!1))) = elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[714, 7783, 7412])).
% 1.86/2.06 tff(7785,plain,
% 1.86/2.06 (r(s(s(s(elem!1))), elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[742, 7784, 7778])).
% 1.86/2.06 tff(7786,plain,
% 1.86/2.06 (r(s(elem!1), elem!1)),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[7785, 7770])).
% 1.86/2.06 tff(7787,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(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)) | (~r(s(elem!1), s(s(z)))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(7788,plain,
% 1.86/2.06 (((~r(s(s(z)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), z)) | (~r(s(elem!1), s(s(z))))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)) | (~r(s(elem!1), s(s(z)))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(7789,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(z)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), z)) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)) | (~r(s(elem!1), s(s(z))))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[7788])).
% 1.86/2.06 tff(7790,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(z)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), z)) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)) | (~r(s(elem!1), s(s(z)))))),
% 1.86/2.06 inference(transitivity,[status(thm)],[7789, 7787])).
% 1.86/2.06 tff(7791,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(z)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), z)) | (~r(s(elem!1), s(s(z)))))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(7792,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(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)) | (~r(s(elem!1), s(s(z))))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[7791, 7790])).
% 1.86/2.06 tff(7793,plain,
% 1.86/2.06 (~r(s(elem!1), s(s(z)))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[7792, 45, 7757, 7744, 7786])).
% 1.86/2.06 tff(7794,plain,
% 1.86/2.06 ((s(s(s(elem!1))) = s(s(z))) <=> (s(elem!1) = s(s(z)))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[7679])).
% 1.86/2.06 tff(7795,plain,
% 1.86/2.06 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(elem!1) = s(s(z))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[7794])).
% 1.86/2.06 tff(7796,plain,
% 1.86/2.06 (~(s(elem!1) = s(s(z)))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[283, 7795])).
% 1.86/2.06 tff(7797,plain,
% 1.86/2.06 (b(s(elem!1), s(s(z)))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[473, 21, 7796, 7793])).
% 1.86/2.06 tff(7798,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(z)))) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(7799,plain,
% 1.86/2.06 (((~b(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)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1)))) <=> ((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(7800,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1)))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[7799])).
% 1.86/2.06 tff(7801,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.86/2.06 inference(transitivity,[status(thm)],[7800, 7798])).
% 1.86/2.06 tff(7802,plain,
% 1.86/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(7803,plain,
% 1.86/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1)))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[7802, 7801])).
% 1.86/2.06 tff(7804,plain,
% 1.86/2.06 ((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1)))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[7803, 128, 7797, 7767, 7765])).
% 1.86/2.06 tff(7805,plain,
% 1.86/2.06 (~b(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[7804, 7760])).
% 1.86/2.06 tff(7806,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(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~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), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(7807,plain,
% 1.86/2.06 (((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(7808,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(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~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), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(elem!1)))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[7807])).
% 1.86/2.06 tff(7809,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(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~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), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.86/2.06 inference(transitivity,[status(thm)],[7808, 7806])).
% 1.86/2.06 tff(7810,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(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(7811,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(elem!1), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(elem!1)))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[7810, 7809])).
% 1.86/2.06 tff(7812,plain,
% 1.86/2.06 (~r(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[7811, 45, 7749, 7786])).
% 1.86/2.06 tff(7813,plain,
% 1.86/2.06 (((~![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)))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(7814,plain,
% 1.86/2.06 ((~![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)))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(7815,plain,
% 1.86/2.06 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(elem!1)) | b(s(s(s(s(s(s(z)))))), s(elem!1)) | r(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[7814, 7813])).
% 1.86/2.06 tff(7816,plain,
% 1.86/2.06 ((s(s(s(s(s(s(z)))))) = s(elem!1)) | b(s(s(s(s(s(s(z)))))), s(elem!1))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[7815, 21, 7812])).
% 1.86/2.06 tff(7817,plain,
% 1.86/2.06 (s(s(s(s(s(s(z)))))) = s(elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[7816, 7805])).
% 1.86/2.06 tff(7818,plain,
% 1.86/2.06 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(elem!1))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[7817])).
% 1.86/2.06 tff(7819,plain,
% 1.86/2.06 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 1.86/2.06 inference(transitivity,[status(thm)],[208, 7818, 201, 7413])).
% 1.86/2.06 tff(7820,plain,
% 1.86/2.06 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(elem!1)))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[7819])).
% 1.86/2.06 tff(7821,plain,
% 1.86/2.06 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(z))))))),
% 1.86/2.06 inference(symmetry,[status(thm)],[7820])).
% 1.86/2.06 tff(7822,plain,
% 1.86/2.06 (s(elem!1) = s(s(s(s(z))))),
% 1.86/2.06 inference(transitivity,[status(thm)],[106, 7821, 163])).
% 1.86/2.06 tff(7823,plain,
% 1.86/2.06 (~(s(elem!1) = s(s(s(s(z)))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[761, 7796, 7412])).
% 1.86/2.06 tff(7824,plain,
% 1.86/2.06 ($false),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[7823, 7822])).
% 1.86/2.06 tff(7825,plain,(b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 1.86/2.06 tff(7826,plain,
% 1.86/2.06 ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[3603, 7825])).
% 1.86/2.06 tff(7827,plain,
% 1.86/2.06 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[7826, 161, 30])).
% 1.86/2.06 tff(7828,plain,
% 1.86/2.06 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[1073, 7827])).
% 1.86/2.06 tff(7829,plain,
% 1.86/2.06 (s(s(elem!1)) = elem!1),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[1089, 7828])).
% 1.86/2.06 tff(7830,plain,
% 1.86/2.06 (r(s(s(elem!1)), z) <=> r(elem!1, z)),
% 1.86/2.06 inference(monotonicity,[status(thm)],[7829])).
% 1.86/2.06 tff(7831,plain,
% 1.86/2.06 ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[3544, 7825])).
% 1.86/2.06 tff(7832,plain,
% 1.86/2.06 (~b(s(s(elem!1)), z)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[7831, 161, 30])).
% 1.86/2.06 tff(7833,assumption,(~b(s(s(elem!1)), z)), introduced(assumption)).
% 1.86/2.06 tff(7834,plain,
% 1.86/2.06 ($false),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2018, 21, 154, 7833, 1532])).
% 1.86/2.06 tff(7835,plain,(b(s(s(elem!1)), z) | r(s(s(elem!1)), z)), inference(lemma,lemma(discharge,[]))).
% 1.86/2.06 tff(7836,plain,
% 1.86/2.06 (r(s(s(elem!1)), z)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[7835, 7832])).
% 1.86/2.06 tff(7837,plain,
% 1.86/2.06 (r(elem!1, z)),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[7836, 7830])).
% 1.86/2.06 tff(7838,plain,
% 1.86/2.06 (elem!1 = s(s(elem!1))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[377, 7829])).
% 1.86/2.06 tff(7839,plain,
% 1.86/2.06 (b(z, elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[457, 7838, 161])).
% 1.86/2.06 tff(7840,plain,
% 1.86/2.06 (b(s(s(elem!1)), s(z)) <=> b(elem!1, s(z))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[7829])).
% 1.86/2.06 tff(7841,plain,
% 1.86/2.06 (b(elem!1, s(z))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[30, 7840])).
% 1.86/2.06 tff(7842,plain,
% 1.86/2.06 ((s(s(elem!1)) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[7829])).
% 1.86/2.06 tff(7843,plain,
% 1.86/2.06 ((s(s(elem!1)) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 1.86/2.06 inference(transitivity,[status(thm)],[7842, 225])).
% 1.86/2.06 tff(7844,plain,
% 1.86/2.06 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[7843])).
% 1.86/2.06 tff(7845,plain,
% 1.86/2.06 (~(s(s(z)) = elem!1)),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[1, 7844])).
% 1.86/2.06 tff(7846,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(X0, 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))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(7847,plain,
% 1.86/2.06 (((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(7848,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), 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(X0, 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)))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[7847])).
% 1.86/2.06 tff(7849,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), 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(X0, 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))))),
% 1.86/2.07 inference(transitivity,[status(thm)],[7848, 7846])).
% 1.86/2.07 tff(7850,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(7851,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[7850, 7849])).
% 1.86/2.07 tff(7852,plain,
% 1.86/2.07 (~b(s(s(z)), z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[7851, 128, 498, 297, 3527, 273])).
% 1.86/2.07 tff(7853,plain,
% 1.86/2.07 (r(s(s(z)), z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[25, 7852])).
% 1.86/2.07 tff(7854,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(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)))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(7855,plain,
% 1.86/2.07 (((~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)))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(7856,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(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))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[7855])).
% 1.86/2.07 tff(7857,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(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)))),
% 1.86/2.07 inference(transitivity,[status(thm)],[7856, 7854])).
% 1.86/2.07 tff(7858,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(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(7859,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(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[7858, 7857])).
% 1.86/2.07 tff(7860,plain,
% 1.86/2.07 (~r(s(s(z)), elem!1)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[7859, 45, 1004, 7853])).
% 1.86/2.07 tff(7861,plain,
% 1.86/2.07 (b(s(s(z)), elem!1)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[370, 7860, 484])).
% 1.86/2.07 tff(7862,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(7863,plain,
% 1.86/2.07 (((~b(z, elem!1)) | (~b(s(s(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(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(7864,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, 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)), s(z))) | (~b(s(s(z)), elem!1))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[7863])).
% 1.86/2.07 tff(7865,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, 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)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.86/2.07 inference(transitivity,[status(thm)],[7864, 7862])).
% 1.86/2.07 tff(7866,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(7867,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[7866, 7865])).
% 1.86/2.07 tff(7868,plain,
% 1.86/2.07 ($false),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[7867, 128, 498, 297, 3527, 7861, 273])).
% 1.86/2.07 tff(7869,plain,((~b(s(s(z)), s(z))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (s(s(z)) = elem!1) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.07 tff(7870,plain,
% 1.86/2.07 ((~b(s(s(z)), s(z))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (s(s(z)) = elem!1) | (~r(elem!1, z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[7869, 7825])).
% 1.86/2.07 tff(7871,plain,
% 1.86/2.07 ($false),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[7870, 7845, 7841, 87, 7839, 7837])).
% 1.86/2.07 tff(7872,plain,((s(s(elem!1)) = s(s(z))) | (~b(s(s(elem!1)), s(z))) | (~r(s(s(z)), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.07 tff(7873,plain,
% 1.86/2.07 (s(s(elem!1)) = s(s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[7872, 30, 28, 27])).
% 1.86/2.07 tff(7874,plain,
% 1.86/2.07 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[7873])).
% 1.86/2.07 tff(7875,plain,
% 1.86/2.07 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.86/2.07 inference(symmetry,[status(thm)],[7874])).
% 1.86/2.07 tff(7876,plain,
% 1.86/2.07 (r(s(s(z)), s(s(s(z)))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[7875])).
% 1.86/2.07 tff(7877,plain,
% 1.86/2.07 (r(s(s(z)), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(z))))),
% 1.86/2.07 inference(symmetry,[status(thm)],[7876])).
% 1.86/2.07 tff(7878,plain,
% 1.86/2.07 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[7873])).
% 1.86/2.07 tff(7879,plain,
% 1.86/2.07 (z = elem!1),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[4260, 7873])).
% 1.86/2.07 tff(7880,plain,
% 1.86/2.07 ((s(s(s(s(s(s(z)))))) = z) <=> (s(s(s(s(s(s(z)))))) = elem!1)),
% 1.86/2.07 inference(monotonicity,[status(thm)],[7879])).
% 1.86/2.07 tff(7881,plain,
% 1.86/2.07 ((~(s(s(s(s(s(s(z)))))) = z)) <=> (~(s(s(s(s(s(s(z)))))) = elem!1))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[7880])).
% 1.86/2.07 tff(7882,plain,
% 1.86/2.07 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[1019, 7881])).
% 1.86/2.07 tff(7883,plain,
% 1.86/2.07 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1055, 7882, 29])).
% 1.86/2.07 tff(7884,plain,
% 1.86/2.07 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[4252])).
% 1.86/2.07 tff(7885,plain,
% 1.86/2.07 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.86/2.07 inference(symmetry,[status(thm)],[7884])).
% 1.86/2.07 tff(7886,plain,
% 1.86/2.07 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[7884])).
% 1.86/2.07 tff(7887,plain,
% 1.86/2.07 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[7886])).
% 1.86/2.07 tff(7888,plain,
% 1.86/2.07 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z))))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[7887])).
% 1.86/2.07 tff(7889,plain,
% 1.86/2.07 (s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(elem!1))))))),
% 1.86/2.07 inference(symmetry,[status(thm)],[7888])).
% 1.86/2.07 tff(7890,plain,
% 1.86/2.07 ((s(s(s(s(s(s(z)))))) = s(s(s(z)))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[7889, 7885])).
% 1.86/2.07 tff(7891,plain,
% 1.86/2.07 ((s(s(s(s(s(s(z)))))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1)))))))),
% 1.86/2.07 inference(transitivity,[status(thm)],[7890, 3226])).
% 1.86/2.07 tff(7892,plain,
% 1.86/2.07 ((s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(z)))))) = s(s(s(z))))),
% 1.86/2.07 inference(symmetry,[status(thm)],[7891])).
% 1.86/2.07 tff(7893,plain,
% 1.86/2.07 ((~(s(s(s(elem!1))) = s(s(s(s(s(s(elem!1)))))))) <=> (~(s(s(s(s(s(s(z)))))) = s(s(s(z)))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[7892])).
% 1.86/2.07 tff(7894,plain,
% 1.86/2.07 ((s(elem!1) = s(s(s(s(elem!1))))) <=> (s(z) = s(s(s(s(elem!1)))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[4254])).
% 1.86/2.07 tff(7895,plain,
% 1.86/2.07 ((s(elem!1) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(z))),
% 1.86/2.07 inference(transitivity,[status(thm)],[7894, 2245])).
% 1.86/2.07 tff(7896,plain,
% 1.86/2.07 ((s(s(s(s(elem!1)))) = s(z)) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 1.86/2.07 inference(symmetry,[status(thm)],[7895])).
% 1.86/2.07 tff(7897,plain,
% 1.86/2.07 ((~(s(s(s(s(elem!1)))) = s(z))) <=> (~(s(elem!1) = s(s(s(s(elem!1))))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[7896])).
% 1.86/2.07 tff(7898,plain,
% 1.86/2.07 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[1723, 7897])).
% 1.86/2.07 tff(7899,plain,
% 1.86/2.07 (~(s(s(s(elem!1))) = s(s(s(s(s(s(elem!1)))))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[3236, 7898])).
% 1.86/2.07 tff(7900,plain,
% 1.86/2.07 (~(s(s(s(s(s(s(z)))))) = s(s(s(z))))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[7899, 7893])).
% 1.86/2.07 tff(7901,plain,
% 1.86/2.07 (r(s(s(s(s(s(s(z)))))), s(s(s(z)))) <=> r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[7885])).
% 1.86/2.07 tff(7902,plain,
% 1.86/2.07 (r(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.86/2.07 inference(symmetry,[status(thm)],[7901])).
% 1.86/2.07 tff(7903,plain,
% 1.86/2.07 ((~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[7902])).
% 1.86/2.07 tff(7904,plain,
% 1.86/2.07 (s(s(z)) = s(s(elem!1))),
% 1.86/2.07 inference(symmetry,[status(thm)],[4252])).
% 1.86/2.07 tff(7905,plain,
% 1.86/2.07 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[7904])).
% 1.86/2.07 tff(7906,plain,
% 1.86/2.07 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[7905])).
% 1.86/2.07 tff(7907,plain,
% 1.86/2.07 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[239, 7906])).
% 1.86/2.07 tff(7908,assumption,(~r(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 1.86/2.07 tff(7909,plain,
% 1.86/2.07 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[321, 1678, 7908])).
% 1.86/2.07 tff(7910,plain,
% 1.86/2.07 (~b(z, s(s(elem!1)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[3600, 27, 3527, 30, 1063])).
% 1.86/2.07 tff(7911,plain,
% 1.86/2.07 (r(z, s(s(elem!1)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[160, 7910])).
% 1.86/2.07 tff(7912,plain,
% 1.86/2.07 (~r(s(z), s(s(elem!1)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[97, 27, 7911])).
% 1.86/2.07 tff(7913,plain,
% 1.86/2.07 (b(s(z), s(s(elem!1)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[117, 7912])).
% 1.86/2.07 tff(7914,plain,
% 1.86/2.07 (~b(s(s(s(elem!1))), s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2726, 7913, 30, 2106])).
% 1.86/2.07 tff(7915,plain,
% 1.86/2.07 (r(s(s(s(elem!1))), s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[195, 7914, 191])).
% 1.86/2.07 tff(7916,plain,
% 1.86/2.07 (~r(s(s(s(elem!1))), z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[3935, 45, 27, 7915])).
% 1.86/2.07 tff(7917,plain,
% 1.86/2.07 (b(s(s(s(elem!1))), z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[547, 21, 382, 7916])).
% 1.86/2.07 tff(7918,plain,
% 1.86/2.07 (~r(z, s(s(s(elem!1))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[3611, 45, 27, 7915])).
% 1.86/2.07 tff(7919,plain,
% 1.86/2.07 (b(z, s(s(s(elem!1))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[436, 21, 7918, 384])).
% 1.86/2.07 tff(7920,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(7921,plain,
% 1.86/2.07 (((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(7922,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1)))))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[7921])).
% 1.86/2.07 tff(7923,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))),
% 1.86/2.07 inference(transitivity,[status(thm)],[7922, 7920])).
% 1.86/2.07 tff(7924,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(7925,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1)))))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[7924, 7923])).
% 1.86/2.07 tff(7926,plain,
% 1.86/2.07 ($false),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[7925, 128, 3527, 549, 7919, 7917])).
% 1.86/2.07 tff(7927,plain,((~r(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.07 tff(7928,plain,
% 1.86/2.07 (~r(z, s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[7927, 7909, 549, 30, 3527, 1063])).
% 1.86/2.07 tff(7929,plain,
% 1.86/2.07 (b(z, s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[415, 7928])).
% 1.86/2.07 tff(7930,plain,
% 1.86/2.07 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 1.86/2.07 inference(symmetry,[status(thm)],[799])).
% 1.86/2.07 tff(7931,plain,
% 1.86/2.07 ((~(s(s(elem!1)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[7930])).
% 1.86/2.07 tff(7932,plain,
% 1.86/2.07 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[1678, 7931])).
% 1.86/2.07 tff(7933,plain,
% 1.86/2.07 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2114, 7909, 30, 549])).
% 1.86/2.07 tff(7934,plain,
% 1.86/2.07 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[889, 7933, 7932])).
% 1.86/2.07 tff(7935,plain,
% 1.86/2.07 (~b(z, s(s(elem!1)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[3535, 7929, 3527, 30])).
% 1.86/2.07 tff(7936,plain,
% 1.86/2.07 (r(z, s(s(elem!1)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[160, 7935])).
% 1.86/2.07 tff(7937,plain,
% 1.86/2.07 (~r(z, s(s(s(elem!1))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[4402, 45, 7936, 7934])).
% 1.86/2.07 tff(7938,plain,
% 1.86/2.07 (~r(s(s(s(elem!1))), z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[4395, 45, 7936, 7934])).
% 1.86/2.07 tff(7939,plain,
% 1.86/2.07 ($false),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[561, 7938, 7937, 549, 7929])).
% 1.86/2.07 tff(7940,plain,((s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | r(s(s(elem!1)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.07 tff(7941,plain,
% 1.86/2.07 ((s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[7940, 7825])).
% 1.86/2.07 tff(7942,plain,
% 1.86/2.07 (~b(s(z), s(s(s(elem!1))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[7941, 7908, 30, 7907])).
% 1.86/2.07 tff(7943,plain,
% 1.86/2.07 (r(s(z), s(s(s(elem!1))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[339, 7942])).
% 1.86/2.07 tff(7944,plain,
% 1.86/2.07 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[7886])).
% 1.86/2.07 tff(7945,plain,
% 1.86/2.07 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.86/2.07 inference(transitivity,[status(thm)],[7905, 3209])).
% 1.86/2.07 tff(7946,plain,
% 1.86/2.07 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[7945])).
% 1.86/2.07 tff(7947,plain,
% 1.86/2.07 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[239, 7946])).
% 1.86/2.07 tff(7948,assumption,(~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))), introduced(assumption)).
% 1.86/2.07 tff(7949,plain,
% 1.86/2.07 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1820, 2073, 7948])).
% 1.86/2.07 tff(7950,plain,
% 1.86/2.07 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[321, 2024, 7908])).
% 1.86/2.07 tff(7951,plain,
% 1.86/2.07 (~b(z, s(s(elem!1)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[3603, 30, 1063, 3527])).
% 1.86/2.07 tff(7952,plain,
% 1.86/2.07 (r(z, s(s(elem!1)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[160, 7951])).
% 1.86/2.07 tff(7953,plain,
% 1.86/2.07 (~b(s(z), s(s(elem!1)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2726, 30, 2106, 2718])).
% 1.86/2.07 tff(7954,plain,
% 1.86/2.07 (r(s(z), s(s(elem!1)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[117, 7953])).
% 1.86/2.07 tff(7955,plain,
% 1.86/2.07 ($false),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[97, 7954, 7952, 27])).
% 1.86/2.07 tff(7956,plain,((~b(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.07 tff(7957,plain,
% 1.86/2.07 (~b(s(s(elem!1)), s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[7956, 2718, 2106, 27, 1063, 3527])).
% 1.86/2.07 tff(7958,plain,
% 1.86/2.07 (r(s(s(elem!1)), s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[292, 7957])).
% 1.86/2.07 tff(7959,plain,
% 1.86/2.07 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2176, 7958, 27, 1063])).
% 1.86/2.07 tff(7960,plain,
% 1.86/2.07 (b(s(s(s(s(elem!1)))), s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1828, 7959])).
% 1.86/2.07 tff(7961,plain,
% 1.86/2.07 (~r(z, s(s(elem!1)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[405, 7958, 27])).
% 1.86/2.07 tff(7962,plain,
% 1.86/2.07 (b(z, s(s(elem!1)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[160, 7961])).
% 1.86/2.07 tff(7963,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(7964,plain,
% 1.86/2.07 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z)))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(7965,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[7964])).
% 1.86/2.07 tff(7966,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.86/2.07 inference(transitivity,[status(thm)],[7965, 7963])).
% 1.86/2.07 tff(7967,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(7968,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[7967, 7966])).
% 1.86/2.07 tff(7969,plain,
% 1.86/2.07 (~b(s(s(s(s(elem!1)))), z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[7968, 128, 7962, 3527, 2106, 1842, 7960])).
% 1.86/2.07 tff(7970,plain,
% 1.86/2.07 (r(s(s(s(s(elem!1)))), z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2081, 7969])).
% 1.86/2.07 tff(7971,plain,
% 1.86/2.07 (~b(s(s(elem!1)), s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[7927, 549, 3527, 27, 2106, 1063])).
% 1.86/2.07 tff(7972,plain,
% 1.86/2.07 (r(s(s(elem!1)), s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[292, 7971])).
% 1.86/2.07 tff(7973,plain,
% 1.86/2.07 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2176, 7972, 27, 1063])).
% 1.86/2.07 tff(7974,plain,
% 1.86/2.07 (b(s(s(s(s(elem!1)))), s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1828, 7973])).
% 1.86/2.07 tff(7975,plain,
% 1.86/2.07 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1851, 7974, 1842, 549])).
% 1.86/2.07 tff(7976,plain,
% 1.86/2.07 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1856, 7975, 1680])).
% 1.86/2.07 tff(7977,plain,
% 1.86/2.07 (~r(s(s(s(elem!1))), s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[4126, 7976, 27, 1842, 549, 7974])).
% 1.86/2.07 tff(7978,plain,
% 1.86/2.07 (b(s(s(s(elem!1))), s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[196, 7977])).
% 1.86/2.07 tff(7979,plain,
% 1.86/2.07 ($false),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[4479, 128, 549, 1842, 7978, 7974])).
% 1.86/2.07 tff(7980,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(z))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.07 tff(7981,plain,
% 1.86/2.07 (~b(s(z), s(s(s(elem!1))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[7980, 1842, 27, 1063, 3527, 2106])).
% 1.86/2.07 tff(7982,plain,
% 1.86/2.07 (r(s(z), s(s(s(elem!1))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[339, 7981])).
% 1.86/2.07 tff(7983,plain,
% 1.86/2.07 (~r(s(s(elem!1)), z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2170, 45, 7958, 27])).
% 1.86/2.07 tff(7984,plain,
% 1.86/2.07 (b(s(s(elem!1)), z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2018, 21, 154, 7983])).
% 1.86/2.07 tff(7985,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(s(elem!1)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(s(elem!1)))) | (~b(s(z), z)))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(7986,plain,
% 1.86/2.07 (((~b(s(s(elem!1)), z)) | (~b(s(z), 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(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(7987,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(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(X0, 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), s(s(elem!1)))) | (~b(s(z), z))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[7986])).
% 1.86/2.07 tff(7988,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(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(X0, 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), s(s(elem!1)))) | (~b(s(z), z)))),
% 1.86/2.07 inference(transitivity,[status(thm)],[7987, 7985])).
% 1.86/2.07 tff(7989,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(7990,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), s(s(elem!1)))) | (~b(s(z), z))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[7989, 7988])).
% 1.86/2.07 tff(7991,plain,
% 1.86/2.07 (~b(s(z), s(s(elem!1)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[7990, 128, 7962, 3527, 7984])).
% 1.86/2.07 tff(7992,plain,
% 1.86/2.07 (r(s(z), s(s(elem!1)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[117, 7991])).
% 1.86/2.07 tff(7993,plain,
% 1.86/2.07 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1802, 7992, 7982])).
% 1.86/2.07 tff(7994,plain,
% 1.86/2.08 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[889, 7993, 1679])).
% 1.86/2.08 tff(7995,plain,
% 1.86/2.08 ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[5617, 128, 7962, 2106, 2718])).
% 1.86/2.08 tff(7996,plain,
% 1.86/2.08 (~b(s(s(s(elem!1))), z)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[7995, 7994])).
% 1.86/2.08 tff(7997,plain,
% 1.86/2.08 (r(s(s(s(elem!1))), z)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[547, 21, 382, 7996])).
% 1.86/2.08 tff(7998,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(7999,plain,
% 1.86/2.08 (((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(8000,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[7999])).
% 1.86/2.08 tff(8001,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.86/2.08 inference(transitivity,[status(thm)],[8000, 7998])).
% 1.86/2.08 tff(8002,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.86/2.08 inference(quant_inst,[status(thm)],[])).
% 1.86/2.08 tff(8003,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[8002, 8001])).
% 1.86/2.08 tff(8004,plain,
% 1.86/2.08 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[8003, 128, 7962, 3527, 7994, 2718, 7960])).
% 1.86/2.08 tff(8005,plain,
% 1.86/2.08 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[1856, 8004, 1680])).
% 1.86/2.08 tff(8006,plain,
% 1.86/2.08 ($false),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[1874, 8005, 7997, 7970])).
% 1.86/2.08 tff(8007,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(z))) | (s(s(s(s(elem!1)))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.08 tff(8008,plain,
% 1.86/2.08 (~b(s(s(s(elem!1))), s(z))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[8007, 7950, 3527, 7949, 27, 2023])).
% 1.86/2.08 tff(8009,plain,
% 1.86/2.08 (r(s(s(s(elem!1))), s(z))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[196, 8008])).
% 1.86/2.08 tff(8010,plain,
% 1.86/2.08 (~r(z, s(s(s(elem!1))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3611, 45, 27, 8009])).
% 1.86/2.08 tff(8011,plain,
% 1.86/2.08 (b(z, s(s(s(elem!1))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[858, 8010])).
% 1.86/2.08 tff(8012,plain,
% 1.86/2.08 (~r(s(s(s(elem!1))), z)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3935, 45, 27, 8009])).
% 1.86/2.08 tff(8013,plain,
% 1.86/2.08 (b(s(s(s(elem!1))), z)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[547, 21, 382, 8012])).
% 1.86/2.08 tff(8014,plain,
% 1.86/2.08 (~b(z, s(s(elem!1)))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3460, 8013, 7950, 8011])).
% 1.86/2.08 tff(8015,plain,
% 1.86/2.08 (r(z, s(s(elem!1)))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[160, 8014])).
% 1.86/2.08 tff(8016,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(8017,plain,
% 1.86/2.08 (((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(8018,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1))))))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[8017])).
% 1.86/2.08 tff(8019,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.86/2.08 inference(transitivity,[status(thm)],[8018, 8016])).
% 1.86/2.08 tff(8020,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.86/2.08 inference(quant_inst,[status(thm)],[])).
% 1.86/2.08 tff(8021,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1))))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[8020, 8019])).
% 1.86/2.08 tff(8022,plain,
% 1.86/2.08 (~b(z, s(s(s(s(elem!1)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[8021, 128, 7949, 8011, 8013])).
% 1.86/2.08 tff(8023,plain,
% 1.86/2.08 (r(z, s(s(s(s(elem!1)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[2047, 21, 8022, 178])).
% 1.86/2.08 tff(8024,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(8025,plain,
% 1.86/2.08 (((~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(8026,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1)))))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[8025])).
% 1.86/2.08 tff(8027,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))),
% 1.86/2.08 inference(transitivity,[status(thm)],[8026, 8024])).
% 1.86/2.08 tff(8028,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.86/2.08 inference(quant_inst,[status(thm)],[])).
% 1.86/2.08 tff(8029,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1)))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[8028, 8027])).
% 1.86/2.08 tff(8030,plain,
% 1.86/2.08 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[8029, 128, 7950, 7949, 8011, 8013])).
% 1.86/2.08 tff(8031,plain,
% 1.86/2.08 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[2212, 21, 1069, 8030])).
% 1.86/2.08 tff(8032,plain,
% 1.86/2.08 ($false),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3222, 8031, 8023, 8015])).
% 1.86/2.08 tff(8033,plain,((s(s(elem!1)) = s(s(s(s(elem!1))))) | (~r(z, s(z))) | (~b(s(z), z)) | r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.08 tff(8034,plain,
% 1.86/2.08 ((s(s(elem!1)) = s(s(s(s(elem!1))))) | (~r(z, s(z))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[8033, 7825])).
% 1.86/2.08 tff(8035,plain,
% 1.86/2.08 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[8034, 7908, 7947, 27])).
% 1.86/2.08 tff(8036,plain,
% 1.86/2.08 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[8035, 7944])).
% 1.86/2.08 tff(8037,plain,
% 1.86/2.08 (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[7548, 8036, 7943])).
% 1.86/2.08 tff(8038,plain,
% 1.86/2.08 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[8037, 7903])).
% 1.86/2.08 tff(8039,plain,
% 1.86/2.08 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 1.86/2.08 inference(monotonicity,[status(thm)],[7885])).
% 1.86/2.08 tff(8040,plain,
% 1.86/2.08 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), elem!1)),
% 1.86/2.08 inference(symmetry,[status(thm)],[8039])).
% 1.86/2.08 tff(8041,plain,
% 1.86/2.08 (z = elem!1),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[4260, 4252])).
% 1.86/2.08 tff(8042,plain,
% 1.86/2.08 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 1.86/2.08 inference(monotonicity,[status(thm)],[8041])).
% 1.86/2.08 tff(8043,plain,
% 1.86/2.08 ((s(s(s(elem!1))) = z) <=> (elem!1 = s(s(s(elem!1))))),
% 1.86/2.08 inference(transitivity,[status(thm)],[8042, 705])).
% 1.86/2.08 tff(8044,plain,
% 1.86/2.08 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 1.86/2.08 inference(transitivity,[status(thm)],[8043, 982])).
% 1.86/2.08 tff(8045,plain,
% 1.86/2.08 ((~(s(s(s(elem!1))) = z)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[8044])).
% 1.86/2.08 tff(8046,plain,
% 1.86/2.08 (~(s(s(s(elem!1))) = elem!1)),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[382, 8045])).
% 1.86/2.08 tff(8047,plain,
% 1.86/2.08 (r(s(s(s(z))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 1.86/2.08 inference(monotonicity,[status(thm)],[7885])).
% 1.86/2.08 tff(8048,plain,
% 1.86/2.08 ((~r(s(s(s(z))), elem!1)) <=> (~r(s(s(s(elem!1))), elem!1))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[8047])).
% 1.86/2.08 tff(8049,plain,
% 1.86/2.08 (r(s(s(s(z))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[7885])).
% 1.86/2.08 tff(8050,plain,
% 1.86/2.08 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(z))), s(z))),
% 1.86/2.08 inference(symmetry,[status(thm)],[8049])).
% 1.86/2.08 tff(8051,plain,
% 1.86/2.08 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[7904])).
% 1.86/2.08 tff(8052,plain,
% 1.86/2.08 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 1.86/2.08 inference(transitivity,[status(thm)],[8051, 799])).
% 1.86/2.08 tff(8053,plain,
% 1.86/2.08 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[8052])).
% 1.86/2.08 tff(8054,plain,
% 1.86/2.08 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[283, 8053])).
% 1.86/2.08 tff(8055,plain,
% 1.86/2.08 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[321, 7908, 8054])).
% 1.86/2.08 tff(8056,plain,
% 1.86/2.08 ((~b(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[7956, 7825])).
% 1.86/2.08 tff(8057,plain,
% 1.86/2.08 (~b(s(s(s(elem!1))), s(z))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[8056, 8055, 30, 7907, 27])).
% 1.86/2.08 tff(8058,plain,
% 1.86/2.08 (r(s(s(s(elem!1))), s(z))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[196, 8057])).
% 1.86/2.08 tff(8059,plain,
% 1.86/2.08 (r(s(s(s(z))), s(z))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[8058, 8050])).
% 1.86/2.08 tff(8060,plain,
% 1.86/2.08 (r(z, s(z)) <=> r(elem!1, s(z))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[8041])).
% 1.86/2.08 tff(8061,plain,
% 1.86/2.08 (r(elem!1, s(z))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[27, 8060])).
% 1.86/2.08 tff(8062,plain,
% 1.86/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(8063,plain,
% 1.86/2.08 (((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(8064,plain,
% 1.86/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[8063])).
% 1.86/2.08 tff(8065,plain,
% 1.86/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))),
% 1.86/2.08 inference(transitivity,[status(thm)],[8064, 8062])).
% 1.86/2.08 tff(8066,plain,
% 1.86/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)))),
% 1.86/2.08 inference(quant_inst,[status(thm)],[])).
% 1.86/2.08 tff(8067,plain,
% 1.86/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[8066, 8065])).
% 1.86/2.08 tff(8068,plain,
% 1.86/2.08 ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[8067, 45, 8061])).
% 1.86/2.08 tff(8069,plain,
% 1.86/2.08 (~r(s(s(s(z))), elem!1)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[8068, 8059])).
% 1.86/2.08 tff(8070,plain,
% 1.86/2.08 (~r(s(s(s(elem!1))), elem!1)),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[8069, 8048])).
% 1.86/2.08 tff(8071,plain,
% 1.86/2.08 (b(s(s(s(elem!1))), elem!1)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[742, 8070, 8046])).
% 1.86/2.08 tff(8072,plain,
% 1.86/2.08 (b(s(s(s(z))), elem!1)),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[8071, 8040])).
% 1.86/2.08 tff(8073,plain,
% 1.86/2.08 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[7885])).
% 1.86/2.08 tff(8074,plain,
% 1.86/2.08 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(z))))),
% 1.86/2.08 inference(symmetry,[status(thm)],[8073])).
% 1.86/2.08 tff(8075,plain,
% 1.86/2.08 ((~(s(s(s(elem!1))) = z)) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[8043])).
% 1.86/2.08 tff(8076,plain,
% 1.86/2.08 (~(elem!1 = s(s(s(elem!1))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[382, 8075])).
% 1.86/2.08 tff(8077,plain,
% 1.86/2.08 (~r(elem!1, s(s(s(elem!1))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[4073, 7943, 8041, 8061])).
% 1.86/2.08 tff(8078,plain,
% 1.86/2.08 (b(elem!1, s(s(s(elem!1))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[2466, 8077, 8076])).
% 1.86/2.08 tff(8079,plain,
% 1.86/2.08 (b(elem!1, s(s(s(z))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[8078, 8074])).
% 1.86/2.08 tff(8080,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(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(s(z)))))), s(s(s(z))))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(8081,plain,
% 1.86/2.08 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(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(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~b(s(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(s(z)))))), s(s(s(z))))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(8082,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(s(z)))))), elem!1)) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(z)))))), s(s(s(z)))))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[8081])).
% 1.86/2.08 tff(8083,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(s(z)))))), elem!1)) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(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(s(z)))))), s(s(s(z))))))),
% 1.86/2.08 inference(transitivity,[status(thm)],[8082, 8080])).
% 1.86/2.08 tff(8084,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.86/2.08 inference(quant_inst,[status(thm)],[])).
% 1.86/2.08 tff(8085,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(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(s(z)))))), s(s(s(z)))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[8084, 8083])).
% 1.86/2.08 tff(8086,plain,
% 1.86/2.08 ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[8085, 128, 1010])).
% 1.86/2.08 tff(8087,plain,
% 1.86/2.08 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[8086, 8079, 8072])).
% 1.86/2.08 tff(8088,plain,
% 1.86/2.08 (((~![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)))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(8089,plain,
% 1.86/2.08 ((~![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)))))),
% 1.86/2.08 inference(quant_inst,[status(thm)],[])).
% 1.86/2.08 tff(8090,plain,
% 1.86/2.08 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(z)))))), s(s(s(z)))) | r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[8089, 8088])).
% 1.86/2.08 tff(8091,plain,
% 1.86/2.08 ((s(s(s(s(s(s(z)))))) = s(s(s(z)))) | r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[8090, 21, 8087])).
% 1.86/2.08 tff(8092,plain,
% 1.86/2.08 ($false),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[8091, 8038, 7900])).
% 1.86/2.08 tff(8093,plain,(r(s(s(elem!1)), s(s(s(elem!1)))) | (~(s(s(elem!1)) = s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.08 tff(8094,plain,
% 1.86/2.08 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[8093, 7873, 7883, 30, 27])).
% 1.86/2.08 tff(8095,plain,
% 1.86/2.08 (r(s(s(z)), s(s(s(elem!1))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[8094, 7878])).
% 1.86/2.08 tff(8096,plain,
% 1.86/2.08 (r(s(s(z)), s(s(s(z))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[8095, 7877])).
% 1.86/2.08 tff(8097,plain,
% 1.86/2.08 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[7875])).
% 1.86/2.08 tff(8098,plain,
% 1.86/2.08 (r(elem!1, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(z))))),
% 1.86/2.08 inference(symmetry,[status(thm)],[8097])).
% 1.86/2.08 tff(8099,plain,
% 1.86/2.08 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 1.86/2.08 inference(monotonicity,[status(thm)],[7879])).
% 1.86/2.08 tff(8100,plain,
% 1.86/2.08 ((s(s(s(elem!1))) = z) <=> (elem!1 = s(s(s(elem!1))))),
% 1.86/2.08 inference(transitivity,[status(thm)],[8099, 705])).
% 1.86/2.08 tff(8101,plain,
% 1.86/2.08 ((~(s(s(s(elem!1))) = z)) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[8100])).
% 1.86/2.08 tff(8102,plain,
% 1.86/2.08 (~(elem!1 = s(s(s(elem!1))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[382, 8101])).
% 1.86/2.08 tff(8103,plain,
% 1.86/2.08 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[7875])).
% 1.86/2.08 tff(8104,plain,
% 1.86/2.08 ((~b(elem!1, s(s(s(z))))) <=> (~b(elem!1, s(s(s(elem!1)))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[8103])).
% 1.86/2.08 tff(8105,plain,
% 1.86/2.08 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 1.86/2.08 inference(monotonicity,[status(thm)],[7875])).
% 1.86/2.08 tff(8106,plain,
% 1.86/2.08 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), elem!1)),
% 1.86/2.08 inference(symmetry,[status(thm)],[8105])).
% 1.86/2.08 tff(8107,plain,
% 1.86/2.08 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 1.86/2.08 inference(transitivity,[status(thm)],[8100, 982])).
% 1.86/2.08 tff(8108,plain,
% 1.86/2.08 ((~(s(s(s(elem!1))) = z)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[8107])).
% 1.86/2.08 tff(8109,plain,
% 1.86/2.08 (~(s(s(s(elem!1))) = elem!1)),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[382, 8108])).
% 1.86/2.08 tff(8110,plain,
% 1.86/2.08 (r(s(s(elem!1)), elem!1) <=> r(s(s(z)), elem!1)),
% 1.86/2.08 inference(monotonicity,[status(thm)],[7873])).
% 1.86/2.08 tff(8111,plain,
% 1.86/2.08 (r(s(s(z)), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 1.86/2.08 inference(symmetry,[status(thm)],[8110])).
% 1.86/2.08 tff(8112,plain,
% 1.86/2.08 (r(s(s(z)), z) <=> r(s(s(z)), elem!1)),
% 1.86/2.08 inference(monotonicity,[status(thm)],[7879])).
% 1.86/2.08 tff(8113,plain,
% 1.86/2.08 (r(s(s(z)), z) <=> r(s(s(elem!1)), elem!1)),
% 1.86/2.08 inference(transitivity,[status(thm)],[8112, 8111])).
% 1.86/2.08 tff(8114,plain,
% 1.86/2.08 (r(s(s(elem!1)), elem!1)),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[28, 8113])).
% 1.86/2.08 tff(8115,plain,
% 1.86/2.08 (~r(s(s(s(elem!1))), elem!1)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[4990, 8094, 8114])).
% 1.86/2.08 tff(8116,plain,
% 1.86/2.08 (b(s(s(s(elem!1))), elem!1)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[742, 8115, 8109])).
% 1.86/2.08 tff(8117,plain,
% 1.86/2.08 (b(s(s(s(z))), elem!1)),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[8116, 8106])).
% 1.86/2.08 tff(8118,plain,
% 1.86/2.08 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[7885])).
% 1.86/2.08 tff(8119,plain,
% 1.86/2.08 ((~b(s(s(s(z))), s(z))) <=> (~b(s(s(s(elem!1))), s(z)))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[8118])).
% 1.86/2.08 tff(8120,assumption,(b(elem!1, s(s(s(z))))), introduced(assumption)).
% 1.86/2.08 tff(8121,assumption,(b(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.86/2.08 tff(8122,plain,
% 1.86/2.08 (b(s(z), z) <=> b(s(z), elem!1)),
% 1.86/2.08 inference(monotonicity,[status(thm)],[8041])).
% 1.86/2.08 tff(8123,plain,
% 1.86/2.08 (b(s(z), elem!1)),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[7825, 8122])).
% 1.86/2.08 tff(8124,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(8125,plain,
% 1.86/2.08 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(8126,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[8125])).
% 1.86/2.09 tff(8127,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.86/2.09 inference(transitivity,[status(thm)],[8126, 8124])).
% 1.86/2.09 tff(8128,plain,
% 1.86/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 1.86/2.09 inference(quant_inst,[status(thm)],[])).
% 1.86/2.09 tff(8129,plain,
% 1.86/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[8128, 8127])).
% 1.86/2.09 tff(8130,plain,
% 1.86/2.09 ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[8129, 128, 8123, 8121])).
% 1.86/2.09 tff(8131,plain,
% 1.86/2.09 (~b(s(s(s(z))), s(z))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[8130, 8120])).
% 1.86/2.09 tff(8132,plain,
% 1.86/2.09 (~b(s(s(s(elem!1))), s(z))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[8131, 8119])).
% 1.86/2.09 tff(8133,plain,
% 1.86/2.09 (r(s(s(s(elem!1))), s(z))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[196, 8132])).
% 1.86/2.09 tff(8134,plain,
% 1.86/2.09 (r(s(s(s(z))), s(z))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[8133, 8050])).
% 1.86/2.09 tff(8135,plain,
% 1.86/2.09 ((s(s(s(z))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1)))))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[7885, 7889])).
% 1.86/2.09 tff(8136,plain,
% 1.86/2.09 ((s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(z))) = s(s(s(s(s(s(z)))))))),
% 1.86/2.09 inference(symmetry,[status(thm)],[8135])).
% 1.86/2.09 tff(8137,plain,
% 1.86/2.09 ((~(s(s(s(elem!1))) = s(s(s(s(s(s(elem!1)))))))) <=> (~(s(s(s(z))) = s(s(s(s(s(s(z))))))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[8136])).
% 1.86/2.09 tff(8138,plain,
% 1.86/2.09 (~(s(s(s(z))) = s(s(s(s(s(s(z)))))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[7899, 8137])).
% 1.86/2.09 tff(8139,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(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(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(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(z))), s(s(s(s(s(s(z)))))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(8140,plain,
% 1.86/2.09 (((~b(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(s(z)))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(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(z))), s(s(s(s(s(s(z)))))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(8141,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(s(z)))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(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(z))), s(s(s(s(s(s(z))))))))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[8140])).
% 1.86/2.09 tff(8142,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(s(z)))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(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(z))), s(s(s(s(s(s(z)))))))))),
% 1.86/2.09 inference(transitivity,[status(thm)],[8141, 8139])).
% 1.86/2.09 tff(8143,plain,
% 1.86/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(s(z)))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.86/2.09 inference(quant_inst,[status(thm)],[])).
% 1.86/2.09 tff(8144,plain,
% 1.86/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(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(z))), s(s(s(s(s(s(z))))))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[8143, 8142])).
% 1.86/2.09 tff(8145,plain,
% 1.86/2.09 ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[8144, 128, 1010, 8121])).
% 1.86/2.09 tff(8146,plain,
% 1.86/2.09 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[8145, 8120])).
% 1.86/2.09 tff(8147,plain,
% 1.86/2.09 (((~![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))))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(8148,plain,
% 1.86/2.09 ((~![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))))))))),
% 1.86/2.09 inference(quant_inst,[status(thm)],[])).
% 1.86/2.09 tff(8149,plain,
% 1.86/2.09 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(s(z))))))) | b(s(s(s(z))), s(s(s(s(s(s(z))))))) | r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[8148, 8147])).
% 1.86/2.09 tff(8150,plain,
% 1.86/2.09 ((s(s(s(z))) = s(s(s(s(s(s(z))))))) | r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[8149, 21, 8146])).
% 1.86/2.09 tff(8151,plain,
% 1.86/2.09 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[8150, 8138])).
% 1.86/2.09 tff(8152,assumption,(s(s(s(s(s(s(z)))))) = s(z)), introduced(assumption)).
% 1.86/2.09 tff(8153,plain,
% 1.86/2.09 (s(z) = s(s(s(s(s(s(z))))))),
% 1.86/2.09 inference(symmetry,[status(thm)],[8152])).
% 1.86/2.09 tff(8154,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[1038, 8153])).
% 1.86/2.09 tff(8155,plain,(~(s(s(s(s(s(s(z)))))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(8156,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(8157,plain,
% 1.86/2.09 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(8158,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[8157])).
% 1.86/2.09 tff(8159,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.86/2.09 inference(transitivity,[status(thm)],[8158, 8156])).
% 1.86/2.09 tff(8160,plain,
% 1.86/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.86/2.09 inference(quant_inst,[status(thm)],[])).
% 1.86/2.09 tff(8161,plain,
% 1.86/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[8160, 8159])).
% 1.86/2.09 tff(8162,plain,
% 1.86/2.09 ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(elem!1, s(s(s(z)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[8161, 128, 8123, 1010, 8121])).
% 1.86/2.09 tff(8163,plain,
% 1.86/2.09 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[8162, 8120])).
% 1.86/2.09 tff(8164,plain,
% 1.86/2.09 (r(s(s(s(s(s(s(z)))))), s(z))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[1148, 21, 8163, 8155])).
% 1.86/2.09 tff(8165,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(s(s(z)))))), s(z))) | (~r(s(s(s(z))), 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(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(8166,plain,
% 1.86/2.09 (((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(8167,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(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), 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(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[8166])).
% 1.86/2.09 tff(8168,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(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), 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(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.86/2.09 inference(transitivity,[status(thm)],[8167, 8165])).
% 1.86/2.09 tff(8169,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(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.86/2.09 inference(quant_inst,[status(thm)],[])).
% 1.86/2.09 tff(8170,plain,
% 1.86/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[8169, 8168])).
% 1.86/2.09 tff(8171,plain,
% 1.86/2.09 ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[8170, 45, 8164])).
% 1.86/2.09 tff(8172,plain,
% 1.86/2.09 (~r(s(s(s(z))), s(z))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[8171, 8151])).
% 1.86/2.09 tff(8173,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[8172, 8134])).
% 1.86/2.09 tff(8174,plain,((~b(elem!1, s(s(s(z))))) | (~(s(s(elem!1)) = s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(8175,plain,
% 1.86/2.09 (~b(elem!1, s(s(s(z))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[8174, 7873, 7883, 8117])).
% 1.86/2.09 tff(8176,plain,
% 1.86/2.09 (~b(elem!1, s(s(s(elem!1))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[8175, 8104])).
% 1.86/2.09 tff(8177,plain,
% 1.86/2.09 (r(elem!1, s(s(s(elem!1))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2466, 8176, 8102])).
% 1.86/2.09 tff(8178,plain,
% 1.86/2.09 (r(elem!1, s(s(s(z))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[8177, 8098])).
% 1.86/2.09 tff(8179,plain,
% 1.86/2.09 (r(s(s(z)), elem!1)),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[28, 8112])).
% 1.86/2.09 tff(8180,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)), 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))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(8181,plain,
% 1.86/2.09 (((~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))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(8182,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(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)))))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[8181])).
% 1.86/2.09 tff(8183,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(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))))))),
% 1.86/2.09 inference(transitivity,[status(thm)],[8182, 8180])).
% 1.86/2.09 tff(8184,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(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)))),
% 1.86/2.09 inference(quant_inst,[status(thm)],[])).
% 1.86/2.09 tff(8185,plain,
% 1.86/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[8184, 8183])).
% 1.86/2.09 tff(8186,plain,
% 1.86/2.09 ((~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[8185, 45, 8179])).
% 1.86/2.09 tff(8187,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[8186, 8178, 8096])).
% 1.86/2.09 tff(8188,plain,((~b(s(s(elem!1)), s(z))) | (~r(z, s(z))) | r(s(s(s(s(s(s(z)))))), elem!1) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(8189,plain,
% 1.86/2.09 (~b(s(s(elem!1)), s(z))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[8188, 29, 27, 28])).
% 1.86/2.09 tff(8190,plain,
% 1.86/2.09 (r(s(s(elem!1)), s(z))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[292, 8189])).
% 1.86/2.09 tff(8191,plain,
% 1.86/2.09 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2176, 2023, 27, 325])).
% 1.86/2.09 tff(8192,plain,
% 1.86/2.09 (b(s(s(s(s(elem!1)))), s(z))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[1828, 8191])).
% 1.86/2.09 tff(8193,plain,
% 1.86/2.09 (~r(z, s(s(elem!1)))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[405, 325, 27])).
% 1.86/2.09 tff(8194,plain,
% 1.86/2.09 (b(z, s(s(elem!1)))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[160, 8193])).
% 1.86/2.09 tff(8195,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2170, 45, 325, 27, 1519])).
% 1.86/2.09 tff(8196,plain,((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(8197,plain,
% 1.86/2.09 (~r(s(s(elem!1)), z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[8196, 325, 27])).
% 1.86/2.09 tff(8198,plain,
% 1.86/2.09 (b(s(s(elem!1)), z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[7835, 8197])).
% 1.86/2.09 tff(8199,plain,
% 1.86/2.09 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[8034, 7908, 1069, 27])).
% 1.86/2.09 tff(8200,plain,
% 1.86/2.09 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[321, 7908, 2024])).
% 1.86/2.09 tff(8201,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[3460, 6275, 6276, 453, 2106])).
% 1.86/2.09 tff(8202,plain,((~r(s(s(s(elem!1))), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(8203,plain,
% 1.86/2.09 (~r(s(s(s(elem!1))), s(z))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[8202, 8200, 453, 27])).
% 1.86/2.09 tff(8204,plain,
% 1.86/2.09 (b(s(s(s(elem!1))), s(z))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[196, 8203])).
% 1.86/2.09 tff(8205,plain,
% 1.86/2.09 (~r(s(s(s(s(elem!1)))), z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[1780, 520, 1772])).
% 1.86/2.09 tff(8206,plain,
% 1.86/2.09 (b(s(s(s(s(elem!1)))), z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2081, 8205])).
% 1.86/2.09 tff(8207,plain,
% 1.86/2.09 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2092, 8206, 453, 2006])).
% 1.86/2.09 tff(8208,plain,
% 1.86/2.09 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[1897, 8207, 1063])).
% 1.86/2.09 tff(8209,plain,
% 1.86/2.09 (~b(s(z), s(s(elem!1)))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[7990, 128, 453, 7825, 2006])).
% 1.86/2.09 tff(8210,plain,
% 1.86/2.09 (r(s(z), s(s(elem!1)))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[117, 8209])).
% 1.86/2.09 tff(8211,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(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(8212,plain,
% 1.86/2.09 (((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(z), s(s(s(s(elem!1))))))) <=> ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(8213,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(elem!1)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[8212])).
% 1.86/2.09 tff(8214,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(elem!1)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.86/2.09 inference(transitivity,[status(thm)],[8213, 8211])).
% 1.86/2.09 tff(8215,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(elem!1)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.86/2.09 inference(quant_inst,[status(thm)],[])).
% 1.86/2.09 tff(8216,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(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[8215, 8214])).
% 1.86/2.09 tff(8217,plain,
% 1.86/2.09 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[8216, 45, 8210, 8208])).
% 1.86/2.09 tff(8218,plain,
% 1.86/2.09 ((s(z) = s(s(s(s(elem!1))))) | b(s(z), s(s(s(s(elem!1)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2258, 21, 8217])).
% 1.86/2.09 tff(8219,plain,
% 1.86/2.09 (b(s(z), s(s(s(s(elem!1)))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[8218, 2248])).
% 1.86/2.09 tff(8220,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(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), z)))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(8221,plain,
% 1.86/2.09 (((~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), z)))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(8222,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)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), z))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[8221])).
% 1.86/2.09 tff(8223,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)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), z)))),
% 1.86/2.10 inference(transitivity,[status(thm)],[8222, 8220])).
% 1.86/2.10 tff(8224,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)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.86/2.10 inference(quant_inst,[status(thm)],[])).
% 1.86/2.10 tff(8225,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(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), z))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[8224, 8223])).
% 1.86/2.10 tff(8226,plain,
% 1.86/2.10 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[8225, 45, 520, 28])).
% 1.86/2.10 tff(8227,plain,
% 1.86/2.10 (b(s(s(s(elem!1))), s(s(z)))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[4350, 21, 8226, 283])).
% 1.86/2.10 tff(8228,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(8229,plain,
% 1.86/2.10 (((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(8230,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[8229])).
% 1.86/2.10 tff(8231,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.86/2.10 inference(transitivity,[status(thm)],[8230, 8228])).
% 1.86/2.10 tff(8232,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.86/2.10 inference(quant_inst,[status(thm)],[])).
% 1.86/2.10 tff(8233,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[8232, 8231])).
% 1.86/2.10 tff(8234,plain,
% 1.86/2.10 ($false),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[8233, 128, 2718, 1841, 273, 8227, 8219])).
% 1.86/2.10 tff(8235,plain,((~r(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.10 tff(8236,plain,
% 1.86/2.10 (~r(s(s(s(elem!1))), z)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[8235, 8204, 1841, 87, 28, 2023, 453, 2006, 8199])).
% 1.86/2.10 tff(8237,plain,
% 1.86/2.10 (b(s(s(s(elem!1))), z)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[5301, 8236])).
% 1.86/2.10 tff(8238,plain,
% 1.86/2.10 ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[5617, 128, 453, 8200, 8204])).
% 1.86/2.10 tff(8239,plain,
% 1.86/2.10 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[8238, 8237])).
% 1.86/2.10 tff(8240,plain,
% 1.86/2.10 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[889, 8239, 2025])).
% 1.86/2.10 tff(8241,plain,
% 1.86/2.10 (~r(s(z), s(s(s(elem!1))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[1802, 8240, 8210])).
% 1.86/2.10 tff(8242,plain,
% 1.86/2.10 (b(s(z), s(s(s(elem!1))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[339, 8241])).
% 1.86/2.10 tff(8243,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(8244,plain,
% 1.86/2.10 (((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(8245,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[8244])).
% 1.86/2.10 tff(8246,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.86/2.10 inference(transitivity,[status(thm)],[8245, 8243])).
% 1.86/2.10 tff(8247,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.86/2.10 inference(quant_inst,[status(thm)],[])).
% 1.86/2.10 tff(8248,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1)))))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[8247, 8246])).
% 1.86/2.10 tff(8249,plain,
% 1.86/2.10 ($false),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[8248, 128, 453, 7825, 2006, 8242, 8237])).
% 1.86/2.10 tff(8250,plain,(r(s(s(elem!1)), s(s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), z)) | (~r(z, s(z))) | (s(s(elem!1)) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.10 tff(8251,plain,
% 1.86/2.10 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[8250, 8192, 8198, 8194, 28, 27, 1069])).
% 1.86/2.10 tff(8252,plain,
% 1.86/2.10 (~r(s(s(s(elem!1))), s(z))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[393, 8251, 325])).
% 1.86/2.10 tff(8253,plain,
% 1.86/2.10 (b(s(s(s(elem!1))), s(z))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[196, 8252])).
% 1.86/2.10 tff(8254,plain,
% 1.86/2.10 (~r(s(z), s(s(s(elem!1))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[333, 8251, 325])).
% 1.86/2.10 tff(8255,plain,
% 1.86/2.10 (b(s(z), s(s(s(elem!1))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[339, 8254])).
% 1.86/2.10 tff(8256,plain,
% 1.86/2.10 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[4305, 128, 8255, 8253, 8192, 87])).
% 1.86/2.10 tff(8257,plain,
% 1.86/2.10 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[4309, 21, 239, 8256])).
% 1.86/2.10 tff(8258,plain,
% 1.86/2.10 (~b(s(s(s(elem!1))), s(s(z)))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[4346, 128, 8255, 8253, 87])).
% 1.86/2.10 tff(8259,plain,
% 1.86/2.10 (r(s(s(s(elem!1))), s(s(z)))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[4350, 21, 8258, 283])).
% 1.86/2.10 tff(8260,plain,
% 1.86/2.10 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[3633, 128, 8255, 8253, 8192])).
% 1.86/2.10 tff(8261,plain,
% 1.86/2.10 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[1820, 8260, 2073])).
% 1.86/2.10 tff(8262,plain,
% 1.86/2.10 ($false),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[7409, 45, 8261, 8259, 8257])).
% 1.86/2.10 tff(8263,plain,((s(s(elem!1)) = s(s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.10 tff(8264,plain,
% 1.86/2.10 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[8263, 8190, 28, 27])).
% 1.86/2.10 tff(8265,plain,
% 1.86/2.10 (s(s(elem!1)) = elem!1),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[1089, 8264])).
% 1.86/2.10 tff(8266,plain,
% 1.86/2.10 (~(s(s(s(s(z)))) = elem!1)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[242, 8265])).
% 1.86/2.10 tff(8267,plain,
% 1.86/2.10 (~r(z, s(s(elem!1)))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[405, 8190, 27])).
% 1.86/2.10 tff(8268,plain,
% 1.86/2.10 (b(z, s(s(elem!1)))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[160, 8267])).
% 1.86/2.10 tff(8269,plain,
% 1.86/2.10 (elem!1 = s(s(elem!1))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[377, 8265])).
% 1.86/2.10 tff(8270,plain,
% 1.86/2.10 (b(z, elem!1)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[457, 8269, 8268])).
% 1.86/2.10 tff(8271,plain,
% 1.86/2.10 (b(s(s(elem!1)), z) <=> b(elem!1, z)),
% 1.86/2.10 inference(monotonicity,[status(thm)],[8265])).
% 1.86/2.10 tff(8272,plain,
% 1.86/2.10 (~r(s(s(elem!1)), z)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[8196, 8190, 27])).
% 1.86/2.10 tff(8273,plain,
% 1.86/2.10 (b(s(s(elem!1)), z)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[7835, 8272])).
% 1.86/2.10 tff(8274,plain,
% 1.86/2.10 (b(elem!1, z)),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[8273, 8271])).
% 1.86/2.10 tff(8275,plain,
% 1.86/2.10 (s(s(s(elem!1))) = s(elem!1)),
% 1.86/2.10 inference(monotonicity,[status(thm)],[8265])).
% 1.86/2.10 tff(8276,plain,
% 1.86/2.10 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[8275])).
% 1.86/2.10 tff(8277,plain,
% 1.86/2.10 (s(s(s(s(elem!1)))) = elem!1),
% 1.86/2.10 inference(transitivity,[status(thm)],[8276, 8265])).
% 1.86/2.10 tff(8278,plain,
% 1.86/2.10 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[8277])).
% 1.86/2.10 tff(8279,plain,
% 1.86/2.10 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 1.86/2.10 inference(transitivity,[status(thm)],[8278, 225])).
% 1.86/2.10 tff(8280,plain,
% 1.86/2.10 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[8279])).
% 1.86/2.10 tff(8281,plain,
% 1.86/2.10 (~(s(s(z)) = elem!1)),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[239, 8280])).
% 1.86/2.10 tff(8282,plain,
% 1.86/2.10 (r(s(z), s(s(elem!1))) <=> r(s(z), elem!1)),
% 1.86/2.10 inference(monotonicity,[status(thm)],[8265])).
% 1.86/2.10 tff(8283,plain,
% 1.86/2.10 (~b(s(z), s(s(elem!1)))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[7990, 128, 8268, 7825, 8273])).
% 1.86/2.10 tff(8284,plain,
% 1.86/2.10 (r(s(z), s(s(elem!1)))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[117, 8283])).
% 1.86/2.10 tff(8285,plain,
% 1.86/2.10 (r(s(z), elem!1)),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[8284, 8282])).
% 1.86/2.10 tff(8286,plain,
% 1.86/2.10 (~b(s(s(s(s(z)))), elem!1)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[627, 591, 577, 498])).
% 1.86/2.10 tff(8287,plain,
% 1.86/2.10 (r(s(s(s(s(z)))), elem!1)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[632, 8286, 2953])).
% 1.86/2.10 tff(8288,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(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))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(8289,plain,
% 1.86/2.10 (((~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))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(8290,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(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)))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[8289])).
% 1.86/2.10 tff(8291,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(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))))),
% 1.86/2.10 inference(transitivity,[status(thm)],[8290, 8288])).
% 1.86/2.10 tff(8292,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(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.86/2.10 inference(quant_inst,[status(thm)],[])).
% 1.86/2.10 tff(8293,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(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z)))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[8292, 8291])).
% 1.86/2.10 tff(8294,plain,
% 1.86/2.10 (~r(s(s(s(s(z)))), s(z))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[8293, 45, 1340, 8287])).
% 1.86/2.10 tff(8295,plain,
% 1.86/2.10 (b(s(s(s(s(z)))), s(z))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[782, 21, 779, 8294])).
% 1.86/2.10 tff(8296,plain,
% 1.86/2.10 (~r(s(z), s(s(s(s(z)))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[672, 45, 1340, 8287])).
% 1.86/2.10 tff(8297,plain,
% 1.86/2.10 (b(s(z), s(s(s(s(z)))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[684, 21, 681, 8296])).
% 1.86/2.10 tff(8298,plain,
% 1.86/2.10 (~r(s(s(z)), s(z))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[2946, 5128, 27])).
% 1.86/2.10 tff(8299,plain,
% 1.86/2.10 (b(s(s(z)), s(z))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[86, 8298])).
% 1.86/2.10 tff(8300,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(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(X0, 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(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(8301,plain,
% 1.86/2.10 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(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(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(8302,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(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(X0, 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(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[8301])).
% 1.86/2.10 tff(8303,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(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(X0, 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(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.86/2.10 inference(transitivity,[status(thm)],[8302, 8300])).
% 1.86/2.10 tff(8304,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.86/2.10 inference(quant_inst,[status(thm)],[])).
% 1.86/2.10 tff(8305,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[8304, 8303])).
% 1.86/2.10 tff(8306,plain,
% 1.86/2.10 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[8305, 128, 8299, 8297, 8295])).
% 1.86/2.10 tff(8307,plain,
% 1.86/2.10 ((s(s(s(s(z)))) = s(s(z))) | r(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[971, 21, 8306])).
% 1.86/2.10 tff(8308,plain,
% 1.86/2.10 (r(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[8307, 921])).
% 1.86/2.10 tff(8309,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(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(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(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(8310,plain,
% 1.86/2.10 (((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(8311,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(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[8310])).
% 1.86/2.10 tff(8312,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(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 1.86/2.10 inference(transitivity,[status(thm)],[8311, 8309])).
% 1.86/2.10 tff(8313,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(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.86/2.10 inference(quant_inst,[status(thm)],[])).
% 1.86/2.10 tff(8314,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(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[8313, 8312])).
% 1.86/2.10 tff(8315,plain,
% 1.86/2.10 (~r(s(s(s(s(z)))), z)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[8314, 45, 27, 5128, 8308])).
% 1.86/2.10 tff(8316,plain,
% 1.86/2.10 (b(s(s(s(s(z)))), z)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[589, 21, 586, 8315])).
% 1.86/2.10 tff(8317,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(8318,plain,
% 1.86/2.10 (((~b(elem!1, z)) | (~b(s(z), 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(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)))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(8319,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), 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(X0, 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(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[8318])).
% 1.86/2.10 tff(8320,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), 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(X0, 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(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.86/2.10 inference(transitivity,[status(thm)],[8319, 8317])).
% 1.86/2.10 tff(8321,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.86/2.10 inference(quant_inst,[status(thm)],[])).
% 1.86/2.10 tff(8322,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[8321, 8320])).
% 1.86/2.10 tff(8323,plain,
% 1.86/2.10 ($false),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[8322, 128, 498, 577, 3527, 8297, 8316])).
% 1.86/2.10 tff(8324,plain,((~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.86/2.10 tff(8325,plain,
% 1.86/2.10 ((~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (s(s(s(s(z)))) = elem!1)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[8324, 7825])).
% 1.86/2.10 tff(8326,plain,
% 1.86/2.10 (~b(s(s(z)), elem!1)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[8325, 8274, 27, 8285, 8270, 8266])).
% 1.86/2.11 tff(8327,plain,
% 1.86/2.11 (r(s(s(z)), elem!1)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[370, 8326, 8281])).
% 1.86/2.11 tff(8328,plain,
% 1.86/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(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)))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(8329,plain,
% 1.86/2.11 (((~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)))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(8330,plain,
% 1.86/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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))))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[8329])).
% 1.86/2.11 tff(8331,plain,
% 1.86/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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)))))),
% 1.86/2.11 inference(transitivity,[status(thm)],[8330, 8328])).
% 1.86/2.11 tff(8332,plain,
% 1.86/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))))),
% 1.86/2.11 inference(quant_inst,[status(thm)],[])).
% 1.86/2.11 tff(8333,plain,
% 1.86/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z))))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[8332, 8331])).
% 1.86/2.11 tff(8334,plain,
% 1.86/2.11 (~r(s(z), s(s(z)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[8333, 45, 8285, 8327])).
% 1.86/2.11 tff(8335,plain,
% 1.86/2.11 (b(s(z), s(s(z)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[648, 8334])).
% 1.86/2.11 tff(8336,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), s(s(z)))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(8337,plain,
% 1.86/2.11 (((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(8338,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), 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(X0, 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(z), s(s(z))))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[8337])).
% 1.86/2.11 tff(8339,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), 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(X0, 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(z), s(s(z)))))),
% 1.86/2.11 inference(transitivity,[status(thm)],[8338, 8336])).
% 1.86/2.11 tff(8340,plain,
% 1.86/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))),
% 1.86/2.11 inference(quant_inst,[status(thm)],[])).
% 1.86/2.11 tff(8341,plain,
% 1.86/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[8340, 8339])).
% 1.86/2.11 tff(8342,plain,
% 1.86/2.11 ($false),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[8341, 128, 498, 577, 3527, 7476, 2993])).
% 1.86/2.11 tff(8343,plain,((~b(s(s(z)), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.11 tff(8344,plain,
% 1.86/2.11 (~b(s(s(z)), z)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[8343, 498, 577, 3527, 7476])).
% 1.86/2.11 tff(8345,plain,
% 1.86/2.11 (r(s(s(z)), z)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[25, 8344])).
% 1.86/2.11 tff(8346,plain,
% 1.86/2.11 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[625, 45, 8345, 590])).
% 1.86/2.11 tff(8347,plain,
% 1.86/2.11 (b(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[610, 21, 607, 8346])).
% 1.86/2.11 tff(8348,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(8349,plain,
% 1.86/2.11 (((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z))))) <=> ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(8350,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[8349])).
% 1.86/2.11 tff(8351,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.86/2.11 inference(transitivity,[status(thm)],[8350, 8348])).
% 1.86/2.11 tff(8352,plain,
% 1.86/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))),
% 1.86/2.11 inference(quant_inst,[status(thm)],[])).
% 1.86/2.11 tff(8353,plain,
% 1.86/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[8352, 8351])).
% 1.86/2.11 tff(8354,plain,
% 1.86/2.11 (~b(s(z), s(s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[8353, 128, 577, 3527, 7476, 576, 8347])).
% 1.86/2.11 tff(8355,plain,
% 1.86/2.11 (r(s(z), s(s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[684, 21, 681, 8354])).
% 1.86/2.11 tff(8356,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(8357,plain,
% 1.86/2.11 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z))))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(8358,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[8357])).
% 1.86/2.11 tff(8359,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.86/2.11 inference(transitivity,[status(thm)],[8358, 8356])).
% 1.86/2.11 tff(8360,plain,
% 1.86/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))))),
% 1.86/2.11 inference(quant_inst,[status(thm)],[])).
% 1.86/2.11 tff(8361,plain,
% 1.86/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[8360, 8359])).
% 1.86/2.11 tff(8362,plain,
% 1.86/2.11 (~b(z, s(s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[8361, 128, 498, 577, 576])).
% 1.86/2.11 tff(8363,plain,
% 1.86/2.11 ((z = s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[2905, 21, 8362])).
% 1.86/2.11 tff(8364,plain,
% 1.86/2.11 (r(z, s(s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[8363, 2895])).
% 1.86/2.11 tff(8365,plain,
% 1.86/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(8366,plain,
% 1.86/2.11 (((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(8367,plain,
% 1.86/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[8366])).
% 1.86/2.11 tff(8368,plain,
% 1.86/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 1.86/2.11 inference(transitivity,[status(thm)],[8367, 8365])).
% 1.86/2.11 tff(8369,plain,
% 1.86/2.11 ((~![X0: $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))))),
% 1.86/2.11 inference(quant_inst,[status(thm)],[])).
% 1.86/2.11 tff(8370,plain,
% 1.86/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[8369, 8368])).
% 1.86/2.11 tff(8371,plain,
% 1.86/2.11 ($false),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[8370, 45, 27, 8364, 8355])).
% 1.86/2.11 tff(8372,plain,((~b(s(s(s(s(z)))), elem!1)) | (~r(z, s(z))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.11 tff(8373,plain,
% 1.86/2.11 ((~b(s(s(s(s(z)))), elem!1)) | (~r(z, s(z))) | (~b(elem!1, z)) | (~b(s(z), s(s(z)))) | (~b(z, elem!1))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[8372, 7825])).
% 1.86/2.11 tff(8374,plain,
% 1.86/2.11 (~b(s(s(s(s(z)))), elem!1)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[8373, 8335, 27, 8274, 8270])).
% 1.86/2.11 tff(8375,plain,
% 1.86/2.11 (r(s(s(s(s(z)))), elem!1)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[632, 8374, 8266])).
% 1.86/2.11 tff(8376,plain,
% 1.86/2.11 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[979, 45, 8327, 8375])).
% 1.86/2.11 tff(8377,plain,
% 1.86/2.11 (b(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[610, 21, 607, 8376])).
% 1.86/2.11 tff(8378,plain,
% 1.86/2.11 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[245, 8265])).
% 1.86/2.11 tff(8379,plain,
% 1.86/2.11 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[1055, 8378, 29])).
% 1.86/2.11 tff(8380,plain,
% 1.86/2.11 (~b(s(s(s(s(s(s(z)))))), z)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[1016, 128, 8270, 8274, 8379])).
% 1.86/2.11 tff(8381,plain,
% 1.86/2.11 (r(s(s(s(s(s(s(z)))))), z)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[1022, 21, 1019, 8380])).
% 1.86/2.11 tff(8382,plain,
% 1.86/2.11 (~r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[7567, 45, 28, 8381])).
% 1.86/2.11 tff(8383,plain,
% 1.86/2.11 (b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[1176, 21, 1123, 8382])).
% 1.86/2.11 tff(8384,plain,
% 1.86/2.11 (~r(s(s(s(s(z)))), s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[8293, 45, 8285, 8375])).
% 1.86/2.11 tff(8385,plain,
% 1.86/2.11 (b(s(s(s(s(z)))), s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[784, 8384])).
% 1.86/2.11 tff(8386,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(8387,plain,
% 1.86/2.11 (((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(8388,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(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(X0, 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(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[8387])).
% 1.86/2.11 tff(8389,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(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(X0, 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(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.86/2.11 inference(transitivity,[status(thm)],[8388, 8386])).
% 1.86/2.11 tff(8390,plain,
% 1.86/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.86/2.11 inference(quant_inst,[status(thm)],[])).
% 1.86/2.11 tff(8391,plain,
% 1.86/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[8390, 8389])).
% 1.86/2.11 tff(8392,plain,
% 1.86/2.11 ($false),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[8391, 128, 8335, 87, 8385, 8383, 8377])).
% 1.86/2.11 tff(8393,plain,(r(s(s(s(s(s(s(z)))))), elem!1) | (~r(s(s(z)), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.11 tff(8394,plain,
% 1.86/2.11 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[8393, 27, 28])).
% 1.86/2.11 tff(8395,plain,
% 1.86/2.11 (~b(s(s(elem!1)), s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[7872, 1, 28, 27])).
% 1.86/2.11 tff(8396,plain,
% 1.86/2.11 (r(s(s(elem!1)), s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[292, 8395])).
% 1.86/2.11 tff(8397,plain,
% 1.86/2.11 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[8263, 8396, 28, 27])).
% 1.86/2.11 tff(8398,plain,
% 1.86/2.11 (s(s(elem!1)) = elem!1),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[1089, 8397])).
% 1.86/2.11 tff(8399,plain,
% 1.86/2.11 ((s(s(elem!1)) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[8398])).
% 1.86/2.11 tff(8400,plain,
% 1.86/2.11 ((s(s(elem!1)) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 1.86/2.11 inference(transitivity,[status(thm)],[8399, 225])).
% 1.86/2.11 tff(8401,plain,
% 1.86/2.11 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[8400])).
% 1.86/2.11 tff(8402,plain,
% 1.86/2.11 (~(s(s(z)) = elem!1)),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[1, 8401])).
% 1.86/2.11 tff(8403,plain,
% 1.86/2.11 (~(s(s(s(s(z)))) = elem!1)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[242, 8398])).
% 1.86/2.11 tff(8404,plain,
% 1.86/2.11 (~r(z, s(s(elem!1)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[405, 8396, 27])).
% 1.86/2.11 tff(8405,plain,
% 1.86/2.11 (b(z, s(s(elem!1)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[160, 8404])).
% 1.86/2.11 tff(8406,plain,
% 1.86/2.11 (elem!1 = s(s(elem!1))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[377, 8398])).
% 1.86/2.11 tff(8407,plain,
% 1.86/2.11 (b(z, elem!1)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[457, 8406, 8405])).
% 1.86/2.11 tff(8408,plain,
% 1.86/2.11 (b(s(s(elem!1)), z) <=> b(elem!1, z)),
% 1.86/2.11 inference(monotonicity,[status(thm)],[8398])).
% 1.86/2.11 tff(8409,plain,
% 1.86/2.11 ((s(s(s(s(s(s(elem!1)))))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(s(elem!1)))))))),
% 1.86/2.11 inference(commutativity,[status(thm)],[])).
% 1.86/2.11 tff(8410,plain,
% 1.86/2.11 ((s(elem!1) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = s(elem!1))),
% 1.86/2.11 inference(symmetry,[status(thm)],[8409])).
% 1.86/2.11 tff(8411,plain,
% 1.86/2.11 ((~(s(elem!1) = s(s(s(s(s(s(elem!1)))))))) <=> (~(s(s(s(s(s(s(elem!1)))))) = s(elem!1)))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[8410])).
% 1.86/2.11 tff(8412,plain,
% 1.86/2.11 (~r(s(s(elem!1)), s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[8196, 1519, 27])).
% 1.86/2.11 tff(8413,plain,
% 1.86/2.11 (b(s(s(elem!1)), s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[292, 8412])).
% 1.86/2.11 tff(8414,plain,
% 1.86/2.11 (s(s(elem!1)) = s(s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[7872, 8413, 28, 27])).
% 1.86/2.11 tff(8415,plain,
% 1.86/2.11 (z = elem!1),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[4260, 8414])).
% 1.86/2.11 tff(8416,plain,
% 1.86/2.11 (~(s(elem!1) = s(s(s(s(s(s(elem!1)))))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3337, 8415])).
% 1.86/2.11 tff(8417,plain,
% 1.86/2.11 (~(s(s(s(s(s(s(elem!1)))))) = s(elem!1))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[8416, 8411])).
% 1.86/2.11 tff(8418,plain,
% 1.86/2.11 (s(z) = s(elem!1)),
% 1.86/2.11 inference(monotonicity,[status(thm)],[8415])).
% 1.86/2.11 tff(8419,plain,
% 1.86/2.11 (s(elem!1) = s(z)),
% 1.86/2.11 inference(symmetry,[status(thm)],[8418])).
% 1.86/2.11 tff(8420,plain,
% 1.86/2.11 (s(s(z)) = s(s(elem!1))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[8418])).
% 1.86/2.11 tff(8421,plain,
% 1.86/2.11 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[8420])).
% 1.86/2.11 tff(8422,plain,
% 1.86/2.11 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[8421])).
% 1.86/2.11 tff(8423,plain,
% 1.86/2.11 (s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[8422])).
% 1.86/2.11 tff(8424,plain,
% 1.86/2.11 (s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(elem!1))))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[8423])).
% 1.86/2.11 tff(8425,plain,
% 1.86/2.11 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z))))))),
% 1.86/2.11 inference(symmetry,[status(thm)],[8424])).
% 1.86/2.11 tff(8426,plain,
% 1.86/2.11 (r(s(s(s(s(s(s(elem!1)))))), s(elem!1)) <=> r(s(s(s(s(s(s(z)))))), s(z))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[8425, 8419])).
% 1.86/2.11 tff(8427,plain,
% 1.86/2.11 (r(s(s(s(s(s(s(z)))))), s(z)) <=> r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 1.86/2.11 inference(symmetry,[status(thm)],[8426])).
% 1.86/2.11 tff(8428,plain,
% 1.86/2.11 ((~r(s(s(s(s(s(s(z)))))), s(z))) <=> (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1)))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[8427])).
% 1.86/2.11 tff(8429,plain,
% 1.86/2.11 (r(z, s(z)) <=> r(elem!1, s(z))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[8415])).
% 1.86/2.11 tff(8430,plain,
% 1.86/2.11 (r(elem!1, s(z))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[27, 8429])).
% 1.86/2.11 tff(8431,plain,
% 1.86/2.11 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[7620, 8430, 8394])).
% 1.86/2.11 tff(8432,plain,
% 1.86/2.11 (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[8431, 8428])).
% 1.86/2.11 tff(8433,plain,
% 1.86/2.11 (s(s(elem!1)) = s(s(z))),
% 1.86/2.11 inference(symmetry,[status(thm)],[8420])).
% 1.86/2.11 tff(8434,plain,
% 1.86/2.11 ((s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) <=> (s(s(s(s(s(s(z)))))) = s(s(z)))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[8425, 8433])).
% 1.86/2.11 tff(8435,plain,
% 1.86/2.11 ((s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) <=> (s(s(z)) = s(s(s(s(s(s(z)))))))),
% 1.86/2.11 inference(transitivity,[status(thm)],[8434, 1113])).
% 1.86/2.11 tff(8436,plain,
% 1.86/2.11 ((s(s(z)) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 1.86/2.11 inference(symmetry,[status(thm)],[8435])).
% 1.86/2.11 tff(8437,plain,
% 1.86/2.11 ((~(s(s(z)) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[8436])).
% 1.86/2.11 tff(8438,plain,
% 1.86/2.11 (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[1123, 8437])).
% 1.86/2.11 tff(8439,plain,
% 1.86/2.11 (r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3926, 8415, 8394])).
% 1.86/2.11 tff(8440,plain,
% 1.86/2.11 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 1.86/2.11 inference(monotonicity,[status(thm)],[8415])).
% 1.86/2.11 tff(8441,plain,
% 1.86/2.11 (r(s(s(elem!1)), elem!1)),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[1519, 8440])).
% 1.86/2.11 tff(8442,plain,
% 1.86/2.11 (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3899, 45, 8441, 8439])).
% 1.86/2.11 tff(8443,plain,
% 1.86/2.11 ((s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3269, 21, 8442])).
% 1.86/2.11 tff(8444,plain,
% 1.86/2.11 (b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[8443, 8438])).
% 1.86/2.11 tff(8445,plain,
% 1.86/2.11 ((s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(z)) = s(s(s(s(s(s(z)))))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[8433, 8425])).
% 1.86/2.11 tff(8446,plain,
% 1.86/2.11 ((s(s(z)) = s(s(s(s(s(s(z))))))) <=> (s(s(elem!1)) = s(s(s(s(s(s(elem!1)))))))),
% 1.86/2.11 inference(symmetry,[status(thm)],[8445])).
% 1.86/2.11 tff(8447,plain,
% 1.86/2.11 ((~(s(s(z)) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[8446])).
% 1.86/2.11 tff(8448,plain,
% 1.86/2.11 (~(s(s(elem!1)) = s(s(s(s(s(s(elem!1)))))))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[1123, 8447])).
% 1.86/2.11 tff(8449,plain,
% 1.86/2.11 (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3909, 45, 8441, 8439])).
% 1.86/2.11 tff(8450,plain,
% 1.86/2.11 ((s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) | b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3287, 21, 8449])).
% 1.86/2.11 tff(8451,plain,
% 1.86/2.11 (b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[8450, 8448])).
% 1.86/2.11 tff(8452,plain,
% 1.86/2.11 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[8420])).
% 1.86/2.11 tff(8453,plain,
% 1.86/2.11 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[8452])).
% 1.86/2.11 tff(8454,plain,
% 1.86/2.11 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[239, 8453])).
% 1.86/2.11 tff(8455,plain,
% 1.86/2.11 ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3600, 7825])).
% 1.86/2.11 tff(8456,plain,
% 1.86/2.11 (~b(z, s(s(elem!1)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[8455, 8454, 27, 8413])).
% 1.86/2.11 tff(8457,plain,
% 1.86/2.11 (r(z, s(s(elem!1)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[160, 8456])).
% 1.86/2.11 tff(8458,plain,
% 1.86/2.11 (~r(s(z), s(s(elem!1)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[97, 8457, 27])).
% 1.86/2.11 tff(8459,plain,
% 1.86/2.11 (b(s(z), s(s(elem!1)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[117, 8458])).
% 1.86/2.11 tff(8460,plain,
% 1.86/2.11 (b(s(elem!1), s(s(elem!1)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[2709, 8459, 8415])).
% 1.86/2.11 tff(8461,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(8462,plain,
% 1.86/2.12 (((~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1)))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(8463,plain,
% 1.86/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1)))))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[8462])).
% 1.86/2.12 tff(8464,plain,
% 1.86/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 1.86/2.12 inference(transitivity,[status(thm)],[8463, 8461])).
% 1.86/2.12 tff(8465,plain,
% 1.86/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(8466,plain,
% 1.86/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1)))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[8465, 8464])).
% 1.86/2.12 tff(8467,plain,
% 1.86/2.12 (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[8466, 128, 8460, 8451, 8444])).
% 1.86/2.12 tff(8468,plain,
% 1.86/2.12 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(elem!1)) | b(s(s(s(s(s(s(elem!1)))))), s(elem!1)) | r(s(s(s(s(s(s(elem!1)))))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(elem!1)) | b(s(s(s(s(s(s(elem!1)))))), s(elem!1)) | r(s(s(s(s(s(s(elem!1)))))), s(elem!1)))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(8469,plain,
% 1.86/2.12 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(elem!1)) | b(s(s(s(s(s(s(elem!1)))))), s(elem!1)) | r(s(s(s(s(s(s(elem!1)))))), s(elem!1)))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(8470,plain,
% 1.86/2.12 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(elem!1)) | b(s(s(s(s(s(s(elem!1)))))), s(elem!1)) | r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[8469, 8468])).
% 1.86/2.12 tff(8471,plain,
% 1.86/2.12 ((s(s(s(s(s(s(elem!1)))))) = s(elem!1)) | r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[8470, 21, 8467])).
% 1.86/2.12 tff(8472,plain,
% 1.86/2.12 ($false),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[8471, 8432, 8417])).
% 1.86/2.12 tff(8473,plain,((~r(s(s(elem!1)), z)) | (~r(z, s(z))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.12 tff(8474,plain,
% 1.86/2.12 (~r(s(s(elem!1)), z)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[8473, 27, 28])).
% 1.86/2.12 tff(8475,plain,
% 1.86/2.12 (b(s(s(elem!1)), z)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[7835, 8474])).
% 1.86/2.12 tff(8476,plain,
% 1.86/2.12 (b(elem!1, z)),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[8475, 8408])).
% 1.86/2.12 tff(8477,plain,
% 1.86/2.12 ((s(s(elem!1)) = s(z)) <=> (elem!1 = s(z))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[8398])).
% 1.86/2.12 tff(8478,plain,
% 1.86/2.12 ((s(s(elem!1)) = s(z)) <=> (s(z) = elem!1)),
% 1.86/2.12 inference(transitivity,[status(thm)],[8477, 253])).
% 1.86/2.12 tff(8479,plain,
% 1.86/2.12 ((~(s(s(elem!1)) = s(z))) <=> (~(s(z) = elem!1))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[8478])).
% 1.86/2.12 tff(8480,plain,
% 1.86/2.12 (~(s(z) = elem!1)),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[111, 8479])).
% 1.86/2.12 tff(8481,plain,
% 1.86/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(8482,plain,
% 1.86/2.12 (((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(8483,plain,
% 1.86/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z))))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[8482])).
% 1.86/2.12 tff(8484,plain,
% 1.86/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)))),
% 1.86/2.12 inference(transitivity,[status(thm)],[8483, 8481])).
% 1.86/2.12 tff(8485,plain,
% 1.86/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(8486,plain,
% 1.86/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[8485, 8484])).
% 1.86/2.12 tff(8487,plain,
% 1.86/2.12 (~b(s(z), elem!1)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[8486, 128, 8407, 8476, 7825])).
% 1.86/2.12 tff(8488,plain,
% 1.86/2.12 (r(s(z), elem!1)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[665, 8487, 8480])).
% 1.86/2.12 tff(8489,plain,
% 1.86/2.12 (~b(s(s(z)), elem!1)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[8325, 8488, 27, 8476, 8407, 8403])).
% 1.86/2.12 tff(8490,plain,
% 1.86/2.12 (r(s(s(z)), elem!1)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[370, 8489, 8402])).
% 1.86/2.12 tff(8491,plain,
% 1.86/2.12 (~r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[1172, 45, 8490, 8394])).
% 1.86/2.12 tff(8492,plain,
% 1.86/2.12 (b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[1176, 21, 1123, 8491])).
% 1.86/2.12 tff(8493,plain,
% 1.86/2.12 (r(s(s(elem!1)), s(z)) <=> r(elem!1, s(z))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[8398])).
% 1.86/2.12 tff(8494,plain,
% 1.86/2.12 (r(elem!1, s(z))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[8396, 8493])).
% 1.86/2.12 tff(8495,plain,
% 1.86/2.12 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[7620, 8494, 8394])).
% 1.86/2.12 tff(8496,plain,
% 1.86/2.12 (b(s(s(s(s(s(s(z)))))), s(z))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[1148, 21, 8495, 8155])).
% 1.86/2.12 tff(8497,plain,
% 1.86/2.12 (~r(s(z), s(s(z)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[8333, 45, 8488, 8490])).
% 1.86/2.12 tff(8498,plain,
% 1.86/2.12 (b(s(z), s(s(z)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[648, 8497])).
% 1.86/2.12 tff(8499,plain,
% 1.86/2.12 ($false),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[7482, 128, 8498, 87, 8496, 8492])).
% 1.86/2.12 tff(8500,plain,((s(s(elem!1)) = s(s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.12 tff(8501,plain,
% 1.86/2.12 (s(s(elem!1)) = s(s(z))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[8500, 27, 26])).
% 1.86/2.12 tff(8502,plain,
% 1.86/2.12 (b(s(s(elem!1)), z) <=> b(s(s(z)), z)),
% 1.86/2.12 inference(monotonicity,[status(thm)],[8501])).
% 1.86/2.12 tff(8503,plain,
% 1.86/2.12 (b(s(s(z)), z) <=> b(s(s(elem!1)), z)),
% 1.86/2.12 inference(symmetry,[status(thm)],[8502])).
% 1.86/2.12 tff(8504,plain,
% 1.86/2.12 ((~b(s(s(z)), z)) <=> (~b(s(s(elem!1)), z))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[8503])).
% 1.86/2.12 tff(8505,plain,
% 1.86/2.12 (~b(s(s(elem!1)), z)),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[2, 8504])).
% 1.86/2.12 tff(8506,plain,
% 1.86/2.12 (~r(s(s(elem!1)), z)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[8473, 27, 26])).
% 1.86/2.12 tff(8507,plain,
% 1.86/2.12 (b(s(s(elem!1)), z)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[7835, 8506])).
% 1.86/2.12 tff(8508,plain,
% 1.86/2.12 ($false),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[8507, 8505])).
% 1.86/2.12 tff(8509,plain,((~r(z, s(z))) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 1.86/2.12 tff(8510,plain,
% 1.86/2.12 (~r(z, s(z))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[8509, 2])).
% 1.86/2.12 tff(8511,plain,
% 1.86/2.12 (b(z, s(z))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[415, 8510])).
% 1.86/2.12 tff(8512,plain,
% 1.86/2.12 (b(s(s(elem!1)), s(s(z)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[4339, 21, 1, 7345])).
% 1.86/2.12 tff(8513,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(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(z)), s(s(elem!1)))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(8514,plain,
% 1.86/2.12 (((~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(8515,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(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1))))))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[8514])).
% 1.86/2.12 tff(8516,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(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.86/2.12 inference(transitivity,[status(thm)],[8515, 8513])).
% 1.86/2.12 tff(8517,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(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(8518,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(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1))))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[8517, 8516])).
% 1.86/2.12 tff(8519,plain,
% 1.86/2.12 (~r(s(s(z)), s(s(elem!1)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[8518, 45, 1519, 28])).
% 1.86/2.12 tff(8520,plain,
% 1.86/2.12 ((s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[138, 21, 8519])).
% 1.86/2.12 tff(8521,plain,
% 1.86/2.12 (b(s(s(z)), s(s(elem!1)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[8520, 34])).
% 1.86/2.12 tff(8522,assumption,(b(s(s(elem!1)), s(s(z)))), introduced(assumption)).
% 1.86/2.12 tff(8523,assumption,(b(s(s(z)), s(s(elem!1)))), introduced(assumption)).
% 1.86/2.12 tff(8524,plain,
% 1.86/2.12 ((s(s(elem!1)) = s(s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(z)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[4148, 7825])).
% 1.86/2.12 tff(8525,plain,
% 1.86/2.12 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[8524, 2511, 550, 30])).
% 1.86/2.12 tff(8526,plain,
% 1.86/2.12 (r(s(s(s(s(elem!1)))), s(z))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[1828, 8525])).
% 1.86/2.12 tff(8527,plain,
% 1.86/2.12 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[6248, 385, 35])).
% 1.86/2.12 tff(8528,plain,
% 1.86/2.12 (b(s(s(s(elem!1))), s(s(z)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[4350, 21, 8527, 283])).
% 1.86/2.12 tff(8529,plain,
% 1.86/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(8530,plain,
% 1.86/2.12 (((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(8531,plain,
% 1.86/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[8530])).
% 1.86/2.12 tff(8532,plain,
% 1.86/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.86/2.12 inference(transitivity,[status(thm)],[8531, 8529])).
% 1.86/2.12 tff(8533,plain,
% 1.86/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(8534,plain,
% 1.86/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[8533, 8532])).
% 1.86/2.12 tff(8535,plain,
% 1.86/2.12 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.96/2.12 inference(unit_resolution,[status(thm)],[8534, 128, 8528, 8522, 8523])).
% 1.96/2.12 tff(8536,plain,
% 1.96/2.12 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.96/2.12 inference(unit_resolution,[status(thm)],[889, 8535, 1691])).
% 1.96/2.12 tff(8537,plain,
% 1.96/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.96/2.12 inference(rewrite,[status(thm)],[])).
% 1.96/2.12 tff(8538,plain,
% 1.96/2.12 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(elem!1)))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.96/2.12 inference(rewrite,[status(thm)],[])).
% 1.96/2.12 tff(8539,plain,
% 1.96/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 1.96/2.12 inference(monotonicity,[status(thm)],[8538])).
% 1.96/2.12 tff(8540,plain,
% 1.96/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.96/2.12 inference(transitivity,[status(thm)],[8539, 8537])).
% 1.96/2.12 tff(8541,plain,
% 1.96/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.96/2.12 inference(quant_inst,[status(thm)],[])).
% 1.96/2.12 tff(8542,plain,
% 1.96/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 1.96/2.12 inference(modus_ponens,[status(thm)],[8541, 8540])).
% 1.96/2.12 tff(8543,plain,
% 1.96/2.12 (~r(s(s(z)), s(s(s(elem!1))))),
% 1.96/2.12 inference(unit_resolution,[status(thm)],[8542, 45, 385, 35])).
% 1.96/2.12 tff(8544,plain,
% 1.96/2.12 ((s(s(z)) = s(s(s(elem!1)))) | b(s(s(z)), s(s(s(elem!1))))),
% 1.96/2.12 inference(unit_resolution,[status(thm)],[4283, 21, 8543])).
% 1.96/2.12 tff(8545,plain,
% 1.96/2.12 (b(s(s(z)), s(s(s(elem!1))))),
% 1.96/2.12 inference(unit_resolution,[status(thm)],[8544, 4271])).
% 1.96/2.12 tff(8546,plain,
% 1.96/2.12 (~r(z, s(s(s(elem!1))))),
% 1.96/2.12 inference(unit_resolution,[status(thm)],[4402, 45, 88, 8536])).
% 1.96/2.12 tff(8547,plain,
% 1.96/2.12 (b(z, s(s(s(elem!1))))),
% 1.96/2.12 inference(unit_resolution,[status(thm)],[858, 8546])).
% 1.96/2.12 tff(8548,plain,
% 1.96/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.96/2.12 inference(rewrite,[status(thm)],[])).
% 1.96/2.12 tff(8549,plain,
% 1.96/2.12 (((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.96/2.12 inference(rewrite,[status(thm)],[])).
% 1.96/2.12 tff(8550,plain,
% 1.96/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))))),
% 1.96/2.12 inference(monotonicity,[status(thm)],[8549])).
% 1.96/2.12 tff(8551,plain,
% 1.96/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.96/2.12 inference(transitivity,[status(thm)],[8550, 8548])).
% 1.96/2.12 tff(8552,plain,
% 1.96/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))))),
% 1.96/2.12 inference(quant_inst,[status(thm)],[])).
% 1.96/2.12 tff(8553,plain,
% 1.96/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))),
% 1.96/2.12 inference(modus_ponens,[status(thm)],[8552, 8551])).
% 1.96/2.12 tff(8554,plain,
% 1.96/2.12 ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z))))),
% 1.96/2.12 inference(unit_resolution,[status(thm)],[8553, 128, 30, 550, 8528, 8523])).
% 1.96/2.12 tff(8555,plain,
% 1.96/2.12 (~b(z, s(s(z)))),
% 1.96/2.12 inference(unit_resolution,[status(thm)],[8554, 8547])).
% 1.96/2.12 tff(8556,plain,
% 1.96/2.12 (r(z, s(s(z)))),
% 1.96/2.12 inference(unit_resolution,[status(thm)],[516, 8555])).
% 1.96/2.12 tff(8557,assumption,(b(s(s(z)), s(s(s(elem!1))))), introduced(assumption)).
% 1.96/2.12 tff(8558,plain,
% 1.96/2.12 (b(s(s(s(elem!1))), z)),
% 1.96/2.12 inference(unit_resolution,[status(thm)],[5301, 4535])).
% 1.96/2.12 tff(8559,plain,
% 1.96/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.96/2.12 inference(rewrite,[status(thm)],[])).
% 1.96/2.12 tff(8560,plain,
% 1.96/2.12 (((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.96/2.12 inference(rewrite,[status(thm)],[])).
% 1.96/2.12 tff(8561,plain,
% 1.96/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z))))))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[8560])).
% 1.96/2.13 tff(8562,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.96/2.13 inference(transitivity,[status(thm)],[8561, 8559])).
% 1.96/2.13 tff(8563,plain,
% 1.96/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.96/2.13 inference(quant_inst,[status(thm)],[])).
% 1.96/2.13 tff(8564,plain,
% 1.96/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[8563, 8562])).
% 1.96/2.13 tff(8565,plain,
% 1.96/2.13 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[8564, 128, 1842, 4538, 8558, 8557])).
% 1.96/2.13 tff(8566,plain,
% 1.96/2.13 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[4309, 21, 239, 8565])).
% 1.96/2.13 tff(8567,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(8568,plain,
% 1.96/2.13 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1))))))) <=> ((~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(8569,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1))))))))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[8568])).
% 1.96/2.13 tff(8570,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.96/2.13 inference(transitivity,[status(thm)],[8569, 8567])).
% 1.96/2.13 tff(8571,plain,
% 1.96/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.96/2.13 inference(quant_inst,[status(thm)],[])).
% 1.96/2.13 tff(8572,plain,
% 1.96/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1))))))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[8571, 8570])).
% 1.96/2.13 tff(8573,plain,
% 1.96/2.13 (~b(z, s(s(s(s(elem!1)))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[8572, 128, 550, 1842, 4538, 8558])).
% 1.96/2.13 tff(8574,plain,
% 1.96/2.13 (r(z, s(s(s(s(elem!1)))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[2047, 21, 8573, 178])).
% 1.96/2.13 tff(8575,plain,
% 1.96/2.13 (~b(s(s(s(s(elem!1)))), z)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[4546, 1842, 88, 1794])).
% 1.96/2.13 tff(8576,plain,
% 1.96/2.13 (r(s(s(s(s(elem!1)))), z)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[2081, 8575])).
% 1.96/2.13 tff(8577,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(elem!1)))), z)) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(8578,plain,
% 1.96/2.13 (((~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z))) <=> ((~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(8579,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(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[8578])).
% 1.96/2.13 tff(8580,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(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.96/2.13 inference(transitivity,[status(thm)],[8579, 8577])).
% 1.96/2.13 tff(8581,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(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.96/2.13 inference(quant_inst,[status(thm)],[])).
% 1.96/2.13 tff(8582,plain,
% 1.96/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[8581, 8580])).
% 1.96/2.13 tff(8583,plain,
% 1.96/2.13 ($false),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[8582, 45, 8576, 8574, 519, 8566])).
% 1.96/2.13 tff(8584,plain,((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.13 tff(8585,plain,
% 1.96/2.13 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[8584, 8556, 8545, 550, 88, 8536])).
% 1.96/2.13 tff(8586,plain,
% 1.96/2.13 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[1820, 8585, 712])).
% 1.96/2.13 tff(8587,plain,
% 1.96/2.13 (~r(s(s(s(elem!1))), z)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[4395, 45, 88, 8536])).
% 1.96/2.13 tff(8588,plain,
% 1.96/2.13 (~b(s(z), s(s(s(elem!1))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[561, 8587, 550, 8546])).
% 1.96/2.13 tff(8589,plain,
% 1.96/2.13 (r(s(z), s(s(s(elem!1))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[339, 8588])).
% 1.96/2.13 tff(8590,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(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(8591,plain,
% 1.96/2.13 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z)))) <=> ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(8592,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(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[8591])).
% 1.96/2.13 tff(8593,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(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.96/2.13 inference(transitivity,[status(thm)],[8592, 8590])).
% 1.96/2.13 tff(8594,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(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.96/2.13 inference(quant_inst,[status(thm)],[])).
% 1.96/2.13 tff(8595,plain,
% 1.96/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[8594, 8593])).
% 1.96/2.13 tff(8596,plain,
% 1.96/2.13 ($false),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[8595, 45, 1737, 8589, 8586])).
% 1.96/2.13 tff(8597,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(z, s(z))) | (~r(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.13 tff(8598,plain,
% 1.96/2.13 (~r(s(s(s(elem!1))), s(z))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[8597, 8526, 2392, 550, 88, 30, 8523, 1679, 8522, 35])).
% 1.96/2.13 tff(8599,plain,
% 1.96/2.13 (b(s(s(s(elem!1))), s(z))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[196, 8598])).
% 1.96/2.13 tff(8600,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(8601,plain,
% 1.96/2.13 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(8602,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(z))) | (~b(z, s(s(s(elem!1)))))))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[8601])).
% 1.96/2.13 tff(8603,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))))),
% 1.96/2.13 inference(transitivity,[status(thm)],[8602, 8600])).
% 1.96/2.13 tff(8604,plain,
% 1.96/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))),
% 1.96/2.13 inference(quant_inst,[status(thm)],[])).
% 1.96/2.13 tff(8605,plain,
% 1.96/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(z))) | (~b(z, s(s(s(elem!1)))))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[8604, 8603])).
% 1.96/2.13 tff(8606,plain,
% 1.96/2.13 (~b(z, s(s(s(elem!1))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[8605, 128, 550, 7825, 8599])).
% 1.96/2.13 tff(8607,plain,
% 1.96/2.13 (r(z, s(s(s(elem!1))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[858, 8606])).
% 1.96/2.13 tff(8608,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(8609,plain,
% 1.96/2.13 (((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(8610,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[8609])).
% 1.96/2.13 tff(8611,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.96/2.13 inference(transitivity,[status(thm)],[8610, 8608])).
% 1.96/2.13 tff(8612,plain,
% 1.96/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.96/2.13 inference(quant_inst,[status(thm)],[])).
% 1.96/2.13 tff(8613,plain,
% 1.96/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[8612, 8611])).
% 1.96/2.13 tff(8614,plain,
% 1.96/2.13 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[8613, 128, 30, 550, 7825, 8599])).
% 1.96/2.13 tff(8615,plain,
% 1.96/2.13 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[889, 8614, 1679])).
% 1.96/2.13 tff(8616,plain,
% 1.96/2.13 ($false),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[4402, 45, 88, 8615, 8607])).
% 1.96/2.13 tff(8617,plain,((s(s(s(s(elem!1)))) = s(s(elem!1))) | (~r(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.13 tff(8618,plain,
% 1.96/2.13 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[8617, 35, 30, 550, 8523, 8522, 88])).
% 1.96/2.13 tff(8619,plain,
% 1.96/2.13 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[1073, 8618])).
% 1.96/2.13 tff(8620,plain,
% 1.96/2.13 (s(s(elem!1)) = elem!1),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[1089, 8619])).
% 1.96/2.13 tff(8621,plain,
% 1.96/2.13 (r(s(z), s(s(elem!1))) <=> r(s(z), elem!1)),
% 1.96/2.13 inference(monotonicity,[status(thm)],[8620])).
% 1.96/2.13 tff(8622,plain,
% 1.96/2.13 (r(s(z), elem!1) <=> r(s(z), s(s(elem!1)))),
% 1.96/2.13 inference(symmetry,[status(thm)],[8621])).
% 1.96/2.13 tff(8623,plain,
% 1.96/2.13 ((s(s(elem!1)) = s(z)) <=> (elem!1 = s(z))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[8620])).
% 1.96/2.13 tff(8624,plain,
% 1.96/2.13 ((s(s(elem!1)) = s(z)) <=> (s(z) = elem!1)),
% 1.96/2.13 inference(transitivity,[status(thm)],[8623, 253])).
% 1.96/2.13 tff(8625,plain,
% 1.96/2.13 ((~(s(s(elem!1)) = s(z))) <=> (~(s(z) = elem!1))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[8624])).
% 1.96/2.13 tff(8626,plain,
% 1.96/2.13 (~(s(z) = elem!1)),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[111, 8625])).
% 1.96/2.13 tff(8627,plain,
% 1.96/2.13 (b(s(s(z)), s(s(elem!1))) <=> b(s(s(z)), elem!1)),
% 1.96/2.13 inference(monotonicity,[status(thm)],[8620])).
% 1.96/2.13 tff(8628,plain,
% 1.96/2.13 (b(s(s(z)), elem!1)),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[8523, 8627])).
% 1.96/2.13 tff(8629,plain,
% 1.96/2.13 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[245, 8620])).
% 1.96/2.13 tff(8630,plain,
% 1.96/2.13 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[1055, 8629, 29])).
% 1.96/2.13 tff(8631,plain,
% 1.96/2.13 (b(s(s(elem!1)), s(z)) <=> b(elem!1, s(z))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[8620])).
% 1.96/2.13 tff(8632,plain,
% 1.96/2.13 (b(elem!1, s(z))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[30, 8631])).
% 1.96/2.13 tff(8633,plain,
% 1.96/2.13 (~b(s(z), elem!1)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[2976, 8632, 35, 8630, 8628])).
% 1.96/2.13 tff(8634,plain,
% 1.96/2.13 (r(s(z), elem!1)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[665, 8633, 8626])).
% 1.96/2.13 tff(8635,plain,
% 1.96/2.13 (r(s(z), s(s(elem!1)))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[8634, 8622])).
% 1.96/2.13 tff(8636,plain,
% 1.96/2.13 (s(s(s(elem!1))) = s(elem!1)),
% 1.96/2.13 inference(monotonicity,[status(thm)],[8620])).
% 1.96/2.13 tff(8637,plain,
% 1.96/2.13 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[8636])).
% 1.96/2.13 tff(8638,plain,
% 1.96/2.13 (s(s(s(s(elem!1)))) = elem!1),
% 1.96/2.13 inference(transitivity,[status(thm)],[8637, 8620])).
% 1.96/2.13 tff(8639,plain,
% 1.96/2.13 (b(s(s(s(s(elem!1)))), s(z)) <=> b(elem!1, s(z))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[8638])).
% 1.96/2.13 tff(8640,plain,
% 1.96/2.13 (b(elem!1, s(z)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 1.96/2.13 inference(symmetry,[status(thm)],[8639])).
% 1.96/2.13 tff(8641,plain,
% 1.96/2.13 (b(s(s(s(s(elem!1)))), s(z))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[8632, 8640])).
% 1.96/2.13 tff(8642,plain,
% 1.96/2.13 (r(s(s(elem!1)), s(s(z))) <=> r(elem!1, s(s(z)))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[8620])).
% 1.96/2.13 tff(8643,plain,
% 1.96/2.13 ((~r(s(s(elem!1)), s(s(z)))) <=> (~r(elem!1, s(s(z))))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[8642])).
% 1.96/2.13 tff(8644,assumption,(~r(s(s(elem!1)), s(s(z)))), introduced(assumption)).
% 1.96/2.13 tff(8645,plain,
% 1.96/2.13 (~r(elem!1, s(s(z)))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[8644, 8643])).
% 1.96/2.13 tff(8646,plain,
% 1.96/2.13 (r(z, s(s(elem!1))) <=> r(z, elem!1)),
% 1.96/2.13 inference(monotonicity,[status(thm)],[8620])).
% 1.96/2.13 tff(8647,plain,
% 1.96/2.13 (r(z, elem!1)),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[88, 8646])).
% 1.96/2.13 tff(8648,plain,
% 1.96/2.13 (r(s(s(z)), s(s(elem!1))) <=> r(s(s(z)), elem!1)),
% 1.96/2.13 inference(monotonicity,[status(thm)],[8620])).
% 1.96/2.13 tff(8649,plain,
% 1.96/2.13 ((~r(s(s(z)), s(s(elem!1)))) <=> (~r(s(s(z)), elem!1))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[8648])).
% 1.96/2.13 tff(8650,assumption,(~r(s(s(z)), s(s(elem!1)))), introduced(assumption)).
% 1.96/2.13 tff(8651,plain,
% 1.96/2.13 (~r(s(s(z)), elem!1)),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[8650, 8649])).
% 1.96/2.13 tff(8652,plain,
% 1.96/2.13 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[700, 696])).
% 1.96/2.13 tff(8653,plain,
% 1.96/2.13 (s(s(elem!1)) = s(s(s(elem!1)))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[693, 8652])).
% 1.96/2.13 tff(8654,plain,
% 1.96/2.13 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 1.96/2.13 inference(symmetry,[status(thm)],[696])).
% 1.96/2.13 tff(8655,plain,
% 1.96/2.13 (s(s(s(elem!1))) = elem!1),
% 1.96/2.13 inference(transitivity,[status(thm)],[8654, 954, 199])).
% 1.96/2.13 tff(8656,plain,
% 1.96/2.13 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), elem!1)),
% 1.96/2.13 inference(monotonicity,[status(thm)],[8655])).
% 1.96/2.13 tff(8657,plain,
% 1.96/2.13 (r(s(z), elem!1) <=> r(s(z), s(s(s(elem!1))))),
% 1.96/2.13 inference(symmetry,[status(thm)],[8656])).
% 1.96/2.13 tff(8658,plain,
% 1.96/2.13 (r(s(z), s(s(s(elem!1))))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[1340, 8657])).
% 1.96/2.13 tff(8659,plain,
% 1.96/2.13 (r(z, s(s(s(elem!1)))) <=> r(z, elem!1)),
% 1.96/2.13 inference(monotonicity,[status(thm)],[8655])).
% 1.96/2.13 tff(8660,plain,
% 1.96/2.13 (r(z, elem!1) <=> r(z, s(s(s(elem!1))))),
% 1.96/2.13 inference(symmetry,[status(thm)],[8659])).
% 1.96/2.13 tff(8661,plain,
% 1.96/2.13 (r(z, s(s(s(elem!1))))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[1416, 8660])).
% 1.96/2.13 tff(8662,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(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(8663,plain,
% 1.96/2.13 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(8664,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(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[8663])).
% 1.96/2.14 tff(8665,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(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.96/2.14 inference(transitivity,[status(thm)],[8664, 8662])).
% 1.96/2.14 tff(8666,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(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)))),
% 1.96/2.14 inference(quant_inst,[status(thm)],[])).
% 1.96/2.14 tff(8667,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(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[8666, 8665])).
% 1.96/2.14 tff(8668,plain,
% 1.96/2.14 ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[8667, 45, 424])).
% 1.96/2.14 tff(8669,plain,
% 1.96/2.14 (~r(s(s(s(s(z)))), z)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[8668, 1186])).
% 1.96/2.14 tff(8670,plain,
% 1.96/2.14 (b(s(s(s(s(z)))), z)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[589, 21, 586, 8669])).
% 1.96/2.14 tff(8671,plain,
% 1.96/2.14 ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[7521, 45, 323])).
% 1.96/2.14 tff(8672,plain,
% 1.96/2.14 (~r(s(s(s(s(z)))), s(z))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[8671, 1186])).
% 1.96/2.14 tff(8673,plain,
% 1.96/2.14 (b(s(s(s(s(z)))), s(z))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[782, 21, 779, 8672])).
% 1.96/2.14 tff(8674,plain,
% 1.96/2.14 ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[7529, 45, 323])).
% 1.96/2.14 tff(8675,plain,
% 1.96/2.14 (~r(s(z), s(s(s(s(z)))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[8674, 1186])).
% 1.96/2.14 tff(8676,plain,
% 1.96/2.14 (b(s(z), s(s(s(s(z)))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[684, 21, 681, 8675])).
% 1.96/2.14 tff(8677,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(8678,plain,
% 1.96/2.14 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(8679,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[8678])).
% 1.96/2.14 tff(8680,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.96/2.14 inference(transitivity,[status(thm)],[8679, 8677])).
% 1.96/2.14 tff(8681,plain,
% 1.96/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.96/2.14 inference(quant_inst,[status(thm)],[])).
% 1.96/2.14 tff(8682,plain,
% 1.96/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[8681, 8680])).
% 1.96/2.14 tff(8683,plain,
% 1.96/2.14 ($false),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[8682, 128, 550, 8676, 8673, 8670])).
% 1.96/2.14 tff(8684,plain,((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.14 tff(8685,plain,
% 1.96/2.14 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[8684, 8661, 550, 8658])).
% 1.96/2.14 tff(8686,plain,
% 1.96/2.14 (r(s(s(z)), s(s(s(elem!1)))) <=> r(s(s(z)), elem!1)),
% 1.96/2.14 inference(monotonicity,[status(thm)],[8655])).
% 1.96/2.14 tff(8687,plain,
% 1.96/2.14 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(s(s(elem!1))))),
% 1.96/2.14 inference(symmetry,[status(thm)],[8686])).
% 1.96/2.14 tff(8688,plain,
% 1.96/2.14 ((~r(s(s(z)), elem!1)) <=> (~r(s(s(z)), s(s(s(elem!1)))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[8687])).
% 1.96/2.14 tff(8689,plain,
% 1.96/2.14 (~r(s(s(z)), s(s(s(elem!1))))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[496, 8688])).
% 1.96/2.14 tff(8690,plain,
% 1.96/2.14 (s(elem!1) = elem!1),
% 1.96/2.14 inference(transitivity,[status(thm)],[309, 8654, 954, 199])).
% 1.96/2.14 tff(8691,plain,
% 1.96/2.14 (r(s(elem!1), s(s(z))) <=> r(elem!1, s(s(z)))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[8690])).
% 1.96/2.14 tff(8692,plain,
% 1.96/2.14 (r(elem!1, s(s(z))) <=> r(s(elem!1), s(s(z)))),
% 1.96/2.14 inference(symmetry,[status(thm)],[8691])).
% 1.96/2.14 tff(8693,plain,
% 1.96/2.14 (r(elem!1, s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 1.96/2.14 inference(transitivity,[status(thm)],[8692, 7627])).
% 1.96/2.14 tff(8694,plain,
% 1.96/2.14 ((~r(elem!1, s(s(z)))) <=> (~r(s(s(s(elem!1))), s(s(z))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[8693])).
% 1.96/2.14 tff(8695,plain,
% 1.96/2.14 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[483, 8694])).
% 1.96/2.14 tff(8696,plain,
% 1.96/2.14 (b(s(s(s(elem!1))), s(s(z))) <=> b(elem!1, s(s(z)))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[1091])).
% 1.96/2.14 tff(8697,plain,
% 1.96/2.14 (b(elem!1, s(s(z))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 1.96/2.14 inference(symmetry,[status(thm)],[8696])).
% 1.96/2.14 tff(8698,plain,
% 1.96/2.14 (s(s(s(s(elem!1)))) = elem!1),
% 1.96/2.14 inference(transitivity,[status(thm)],[1060, 308, 1090])).
% 1.96/2.14 tff(8699,plain,
% 1.96/2.14 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[8698])).
% 1.96/2.14 tff(8700,plain,
% 1.96/2.14 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 1.96/2.14 inference(transitivity,[status(thm)],[8699, 225])).
% 1.96/2.14 tff(8701,plain,
% 1.96/2.14 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 1.96/2.14 inference(transitivity,[status(thm)],[8700, 650])).
% 1.96/2.14 tff(8702,plain,
% 1.96/2.14 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(elem!1 = s(s(z))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[8701])).
% 1.96/2.14 tff(8703,plain,
% 1.96/2.14 (~(elem!1 = s(s(z)))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[239, 8702])).
% 1.96/2.14 tff(8704,plain,
% 1.96/2.14 ((~r(s(s(s(elem!1))), s(s(z)))) <=> (~r(elem!1, s(s(z))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[7452])).
% 1.96/2.14 tff(8705,assumption,(~r(s(s(s(elem!1))), s(s(z)))), introduced(assumption)).
% 1.96/2.14 tff(8706,plain,
% 1.96/2.14 (~r(elem!1, s(s(z)))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[8705, 8704])).
% 1.96/2.14 tff(8707,plain,
% 1.96/2.14 (b(elem!1, s(s(z)))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[493, 8706, 8703])).
% 1.96/2.14 tff(8708,plain,
% 1.96/2.14 (b(s(s(s(elem!1))), s(s(z)))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[8707, 8697])).
% 1.96/2.14 tff(8709,plain,
% 1.96/2.14 (b(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.96/2.14 inference(monotonicity,[status(thm)],[1091])).
% 1.96/2.14 tff(8710,plain,
% 1.96/2.14 (b(s(s(s(s(s(s(z)))))), elem!1) <=> b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 1.96/2.14 inference(symmetry,[status(thm)],[8709])).
% 1.96/2.14 tff(8711,plain,
% 1.96/2.14 (b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[1010, 8710])).
% 1.96/2.14 tff(8712,plain,
% 1.96/2.14 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(elem!1))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[1101])).
% 1.96/2.14 tff(8713,plain,
% 1.96/2.14 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[8700])).
% 1.96/2.14 tff(8714,plain,
% 1.96/2.14 (~(s(s(z)) = elem!1)),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[239, 8713])).
% 1.96/2.14 tff(8715,plain,
% 1.96/2.14 (r(s(s(z)), s(s(s(elem!1)))) <=> r(s(s(z)), elem!1)),
% 1.96/2.14 inference(symmetry,[status(thm)],[1102])).
% 1.96/2.14 tff(8716,plain,
% 1.96/2.14 ((~r(s(s(z)), s(s(s(elem!1))))) <=> (~r(s(s(z)), elem!1))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[8715])).
% 1.96/2.14 tff(8717,plain,
% 1.96/2.14 (~r(s(s(z)), elem!1)),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[1105, 8716])).
% 1.96/2.14 tff(8718,plain,
% 1.96/2.14 (b(s(s(z)), elem!1)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[370, 8717, 8714])).
% 1.96/2.14 tff(8719,plain,
% 1.96/2.14 (b(s(s(z)), s(s(s(elem!1))))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[8718, 8712])).
% 1.96/2.14 tff(8720,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(8721,plain,
% 1.96/2.14 (((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(8722,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[8721])).
% 1.96/2.14 tff(8723,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 1.96/2.14 inference(transitivity,[status(thm)],[8722, 8720])).
% 1.96/2.14 tff(8724,plain,
% 1.96/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.96/2.14 inference(quant_inst,[status(thm)],[])).
% 1.96/2.14 tff(8725,plain,
% 1.96/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[8724, 8723])).
% 1.96/2.14 tff(8726,plain,
% 1.96/2.14 ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[8725, 128, 8719])).
% 1.96/2.14 tff(8727,plain,
% 1.96/2.14 (~b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[8726, 8711, 8708])).
% 1.96/2.14 tff(8728,plain,
% 1.96/2.14 (r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[1176, 21, 1123, 8727])).
% 1.96/2.14 tff(8729,plain,
% 1.96/2.14 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), elem!1)),
% 1.96/2.14 inference(monotonicity,[status(thm)],[1091])).
% 1.96/2.14 tff(8730,plain,
% 1.96/2.14 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.96/2.14 inference(symmetry,[status(thm)],[8729])).
% 1.96/2.14 tff(8731,plain,
% 1.96/2.14 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[576, 8730])).
% 1.96/2.14 tff(8732,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(8733,plain,
% 1.96/2.14 (((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), 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(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(8734,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[8733])).
% 1.96/2.14 tff(8735,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.96/2.14 inference(transitivity,[status(thm)],[8734, 8732])).
% 1.96/2.14 tff(8736,plain,
% 1.96/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.96/2.14 inference(quant_inst,[status(thm)],[])).
% 1.96/2.14 tff(8737,plain,
% 1.96/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[8736, 8735])).
% 1.96/2.14 tff(8738,plain,
% 1.96/2.14 ((~b(s(s(s(elem!1))), 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(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[8737, 128, 8719])).
% 1.96/2.14 tff(8739,plain,
% 1.96/2.14 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[8738, 8731, 8711, 8708])).
% 1.96/2.14 tff(8740,plain,
% 1.96/2.14 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[1215, 21, 1212, 8739])).
% 1.96/2.14 tff(8741,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(8742,plain,
% 1.96/2.14 (((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(8743,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[8742])).
% 1.96/2.14 tff(8744,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.96/2.14 inference(transitivity,[status(thm)],[8743, 8741])).
% 1.96/2.14 tff(8745,plain,
% 1.96/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.96/2.14 inference(quant_inst,[status(thm)],[])).
% 1.96/2.14 tff(8746,plain,
% 1.96/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[8745, 8744])).
% 1.96/2.14 tff(8747,plain,
% 1.96/2.14 ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[8746, 128, 8719])).
% 1.96/2.14 tff(8748,plain,
% 1.96/2.14 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[8747, 8731, 8708])).
% 1.96/2.14 tff(8749,plain,
% 1.96/2.14 (r(s(s(z)), s(s(s(s(z)))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[610, 21, 607, 8748])).
% 1.96/2.14 tff(8750,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(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(8751,plain,
% 1.96/2.14 (((~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(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(8752,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(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(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[8751])).
% 1.96/2.14 tff(8753,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(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(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.96/2.14 inference(transitivity,[status(thm)],[8752, 8750])).
% 1.96/2.14 tff(8754,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(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)))))))))),
% 1.96/2.14 inference(quant_inst,[status(thm)],[])).
% 1.96/2.14 tff(8755,plain,
% 1.96/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[8754, 8753])).
% 1.96/2.14 tff(8756,plain,
% 1.96/2.14 ($false),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[8755, 45, 8749, 8740, 8728])).
% 1.96/2.14 tff(8757,plain,(r(s(s(s(elem!1))), s(s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)) | r(s(s(z)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.14 tff(8758,plain,
% 1.96/2.14 (~b(s(s(s(s(z)))), elem!1)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[8757, 8695, 8653, 8689, 1010])).
% 1.96/2.14 tff(8759,plain,
% 1.96/2.14 (r(s(s(s(s(z)))), elem!1)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[632, 8758, 243])).
% 1.96/2.14 tff(8760,plain,
% 1.96/2.14 ($false),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[1249, 8759, 8685, 8653, 199])).
% 1.96/2.15 tff(8761,plain,((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) | (~(s(s(elem!1)) = elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | r(s(s(z)), elem!1) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | r(elem!1, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.15 tff(8762,plain,
% 1.96/2.15 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[8761, 8620, 550, 8630, 8651, 8647, 8634, 8645])).
% 1.96/2.15 tff(8763,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(8764,plain,
% 1.96/2.15 (((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(8765,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[8764])).
% 1.96/2.15 tff(8766,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.96/2.15 inference(transitivity,[status(thm)],[8765, 8763])).
% 1.96/2.15 tff(8767,plain,
% 1.96/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))),
% 1.96/2.15 inference(quant_inst,[status(thm)],[])).
% 1.96/2.15 tff(8768,plain,
% 1.96/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z)))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[8767, 8766])).
% 1.96/2.15 tff(8769,plain,
% 1.96/2.15 (~b(s(s(s(elem!1))), z)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[8768, 128, 550, 3527, 2718])).
% 1.96/2.15 tff(8770,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(8771,plain,
% 1.96/2.15 (((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(8772,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[8771])).
% 1.96/2.15 tff(8773,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.96/2.15 inference(transitivity,[status(thm)],[8772, 8770])).
% 1.96/2.15 tff(8774,plain,
% 1.96/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.96/2.15 inference(quant_inst,[status(thm)],[])).
% 1.96/2.15 tff(8775,plain,
% 1.96/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[8774, 8773])).
% 1.96/2.15 tff(8776,plain,
% 1.96/2.15 (~b(s(s(s(s(elem!1)))), z)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[8775, 128, 550, 3527, 1841])).
% 1.96/2.15 tff(8777,plain,
% 1.96/2.15 (r(s(s(s(s(elem!1)))), z)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[2081, 8776])).
% 1.96/2.15 tff(8778,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(8779,plain,
% 1.96/2.15 (((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(8780,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[8779])).
% 1.96/2.15 tff(8781,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.96/2.15 inference(transitivity,[status(thm)],[8780, 8778])).
% 1.96/2.15 tff(8782,plain,
% 1.96/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.96/2.15 inference(quant_inst,[status(thm)],[])).
% 1.96/2.15 tff(8783,plain,
% 1.96/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[8782, 8781])).
% 1.96/2.15 tff(8784,plain,
% 1.96/2.15 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[8783, 128, 550, 3527, 2718, 1841])).
% 1.96/2.15 tff(8785,plain,
% 1.96/2.15 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[1820, 8784, 712])).
% 1.96/2.15 tff(8786,plain,
% 1.96/2.15 (~r(s(s(s(elem!1))), z)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[1780, 8785, 8777])).
% 1.96/2.15 tff(8787,plain,
% 1.96/2.15 ($false),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[547, 21, 382, 8786, 8769])).
% 1.96/2.15 tff(8788,plain,((~b(s(s(s(elem!1))), s(z))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.15 tff(8789,plain,
% 1.96/2.15 ((~b(s(s(s(elem!1))), s(z))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[8788, 7825])).
% 1.96/2.15 tff(8790,plain,
% 1.96/2.15 (~b(s(s(s(elem!1))), s(z))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[8789, 8762, 550, 8641])).
% 1.96/2.15 tff(8791,plain,
% 1.96/2.15 (r(s(s(s(elem!1))), s(z))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[196, 8790])).
% 1.96/2.15 tff(8792,plain,
% 1.96/2.15 (r(s(s(s(s(z)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), elem!1)),
% 1.96/2.15 inference(monotonicity,[status(thm)],[1091])).
% 1.96/2.15 tff(8793,plain,
% 1.96/2.15 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.96/2.15 inference(symmetry,[status(thm)],[8792])).
% 1.96/2.15 tff(8794,plain,
% 1.96/2.15 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[1414, 307])).
% 1.96/2.15 tff(8795,plain,
% 1.96/2.15 ((~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(s(s(z)))))), elem!1))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[1092])).
% 1.96/2.15 tff(8796,plain,
% 1.96/2.15 (r(z, s(s(elem!1))) <=> r(z, s(s(s(elem!1))))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[307])).
% 1.96/2.15 tff(8797,plain,
% 1.96/2.15 (r(z, s(s(s(elem!1))))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[88, 8796])).
% 1.96/2.15 tff(8798,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(s(s(s(z)))))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(8799,plain,
% 1.96/2.15 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), z))) <=> ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(8800,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(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~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(s(s(s(s(s(s(z)))))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[8799])).
% 1.96/2.15 tff(8801,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(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~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(s(s(s(s(s(s(z)))))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 1.96/2.15 inference(transitivity,[status(thm)],[8800, 8798])).
% 1.96/2.15 tff(8802,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(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 1.96/2.15 inference(quant_inst,[status(thm)],[])).
% 1.96/2.15 tff(8803,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(s(s(s(z)))))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[8802, 8801])).
% 1.96/2.15 tff(8804,plain,
% 1.96/2.15 (~r(s(s(s(s(s(s(z)))))), z)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[8803, 45, 424, 1197])).
% 1.96/2.15 tff(8805,plain,
% 1.96/2.15 (b(s(s(s(s(s(s(z)))))), z)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[1022, 21, 1019, 8804])).
% 1.96/2.15 tff(8806,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)))))), 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(X0, 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(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(8807,plain,
% 1.96/2.15 (((~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(8808,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), 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(X0, 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(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[8807])).
% 1.96/2.15 tff(8809,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), 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(X0, 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(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.96/2.15 inference(transitivity,[status(thm)],[8808, 8806])).
% 1.96/2.15 tff(8810,plain,
% 1.96/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.96/2.15 inference(quant_inst,[status(thm)],[])).
% 1.96/2.15 tff(8811,plain,
% 1.96/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[8810, 8809])).
% 1.96/2.15 tff(8812,plain,
% 1.96/2.15 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[8811, 128, 550, 3527, 8805])).
% 1.96/2.15 tff(8813,plain,
% 1.96/2.15 ((s(s(s(s(s(s(z)))))) = s(z)) | r(s(s(s(s(s(s(z)))))), s(z))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[1148, 21, 8812])).
% 1.96/2.15 tff(8814,plain,
% 1.96/2.15 (r(s(s(s(s(s(s(z)))))), s(z))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[8813, 1112])).
% 1.96/2.15 tff(8815,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(elem!1))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(8816,plain,
% 1.96/2.15 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(8817,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(elem!1))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[8816])).
% 1.96/2.15 tff(8818,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(elem!1))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 1.96/2.15 inference(transitivity,[status(thm)],[8817, 8815])).
% 1.96/2.15 tff(8819,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(elem!1))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 1.96/2.15 inference(quant_inst,[status(thm)],[])).
% 1.96/2.15 tff(8820,plain,
% 1.96/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[8819, 8818])).
% 1.96/2.15 tff(8821,plain,
% 1.96/2.15 ($false),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[8820, 45, 385, 1197, 8814])).
% 1.96/2.15 tff(8822,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.15 tff(8823,plain,
% 1.96/2.15 (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[8822, 8797, 550, 3527, 385])).
% 1.96/2.15 tff(8824,plain,
% 1.96/2.15 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[8823, 8795])).
% 1.96/2.15 tff(8825,plain,
% 1.96/2.15 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[1055, 8824, 8794])).
% 1.96/2.15 tff(8826,plain,
% 1.96/2.15 (~r(s(s(z)), s(z))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[6248, 518, 385])).
% 1.96/2.15 tff(8827,plain,
% 1.96/2.15 (b(s(s(z)), s(z))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[86, 8826])).
% 1.96/2.15 tff(8828,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(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(8829,plain,
% 1.96/2.15 (((~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(8830,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(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z)))))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[8829])).
% 1.96/2.15 tff(8831,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(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.96/2.15 inference(transitivity,[status(thm)],[8830, 8828])).
% 1.96/2.15 tff(8832,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(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))))),
% 1.96/2.15 inference(quant_inst,[status(thm)],[])).
% 1.96/2.15 tff(8833,plain,
% 1.96/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z)))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[8832, 8831])).
% 1.96/2.15 tff(8834,plain,
% 1.96/2.15 ($false),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[8833, 45, 385, 424, 519, 518])).
% 1.96/2.15 tff(8835,plain,((~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.15 tff(8836,plain,
% 1.96/2.15 (~r(z, s(s(z)))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[8835, 518, 424, 385])).
% 1.96/2.15 tff(8837,plain,
% 1.96/2.15 (b(z, s(s(z)))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[516, 8836])).
% 1.96/2.15 tff(8838,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z, s(s(z)))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(8839,plain,
% 1.96/2.15 (((~b(z, s(z))) | (~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(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(8840,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~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(X0, 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(z, s(s(z))))))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[8839])).
% 1.96/2.15 tff(8841,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~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(X0, 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(z, s(s(z)))))),
% 1.96/2.16 inference(transitivity,[status(thm)],[8840, 8838])).
% 1.96/2.16 tff(8842,plain,
% 1.96/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))),
% 1.96/2.16 inference(quant_inst,[status(thm)],[])).
% 1.96/2.16 tff(8843,plain,
% 1.96/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z))))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[8842, 8841])).
% 1.96/2.16 tff(8844,plain,
% 1.96/2.16 ($false),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[8843, 128, 550, 3527, 8837, 8827])).
% 1.96/2.16 tff(8845,plain,((~r(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.16 tff(8846,plain,
% 1.96/2.16 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[8845, 8797, 3527, 385, 550])).
% 1.96/2.16 tff(8847,plain,
% 1.96/2.16 (r(z, elem!1) <=> r(z, s(s(s(elem!1))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[1101])).
% 1.96/2.16 tff(8848,plain,
% 1.96/2.16 (r(z, s(s(s(elem!1)))) <=> r(z, elem!1)),
% 1.96/2.16 inference(symmetry,[status(thm)],[8847])).
% 1.96/2.16 tff(8849,plain,
% 1.96/2.16 (r(z, s(s(elem!1))) <=> r(z, elem!1)),
% 1.96/2.16 inference(transitivity,[status(thm)],[8796, 8848])).
% 1.96/2.16 tff(8850,plain,
% 1.96/2.16 (r(z, elem!1)),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[88, 8849])).
% 1.96/2.16 tff(8851,plain,
% 1.96/2.16 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[8845, 424, 3527, 385, 550])).
% 1.96/2.16 tff(8852,plain,
% 1.96/2.16 (~r(elem!1, s(s(z)))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[8851, 8704])).
% 1.96/2.16 tff(8853,plain,
% 1.96/2.16 (b(elem!1, s(s(z)))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[493, 8852, 8703])).
% 1.96/2.16 tff(8854,plain,
% 1.96/2.16 (b(s(s(s(elem!1))), s(s(z)))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[8853, 8697])).
% 1.96/2.16 tff(8855,plain,
% 1.96/2.16 (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[8822, 424, 550, 3527, 385])).
% 1.96/2.16 tff(8856,plain,
% 1.96/2.16 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[8855, 8795])).
% 1.96/2.16 tff(8857,plain,
% 1.96/2.16 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[1055, 8856, 8794])).
% 1.96/2.16 tff(8858,plain,
% 1.96/2.16 (b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[8857, 8710])).
% 1.96/2.16 tff(8859,plain,
% 1.96/2.16 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), elem!1)),
% 1.96/2.16 inference(symmetry,[status(thm)],[8712])).
% 1.96/2.16 tff(8860,plain,
% 1.96/2.16 ((~b(s(s(z)), s(s(s(elem!1))))) <=> (~b(s(s(z)), elem!1))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[8859])).
% 1.96/2.16 tff(8861,assumption,(b(elem!1, s(s(z)))), introduced(assumption)).
% 1.96/2.16 tff(8862,plain,
% 1.96/2.16 (b(s(s(s(elem!1))), s(s(z)))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[8861, 8697])).
% 1.96/2.16 tff(8863,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(8864,plain,
% 1.96/2.16 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(8865,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[8864])).
% 1.96/2.16 tff(8866,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.96/2.16 inference(transitivity,[status(thm)],[8865, 8863])).
% 1.96/2.16 tff(8867,plain,
% 1.96/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))))),
% 1.96/2.16 inference(quant_inst,[status(thm)],[])).
% 1.96/2.16 tff(8868,plain,
% 1.96/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[8867, 8866])).
% 1.96/2.16 tff(8869,plain,
% 1.96/2.16 ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[8868, 128, 549, 273])).
% 1.96/2.16 tff(8870,plain,
% 1.96/2.16 (~b(s(s(z)), s(s(s(elem!1))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[8869, 8862])).
% 1.96/2.16 tff(8871,plain,
% 1.96/2.16 (~b(s(s(z)), elem!1)),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[8870, 8860])).
% 1.96/2.16 tff(8872,plain,
% 1.96/2.16 (r(s(s(z)), elem!1)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[370, 8871, 8714])).
% 1.96/2.16 tff(8873,plain,
% 1.96/2.16 (r(s(s(z)), s(s(s(elem!1))))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[8872, 1102])).
% 1.96/2.16 tff(8874,plain,
% 1.96/2.16 (~b(z, s(s(z)))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[8843, 128, 550, 3527, 273])).
% 1.96/2.16 tff(8875,plain,
% 1.96/2.16 (r(z, s(s(z)))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[516, 8874])).
% 1.96/2.16 tff(8876,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(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(8877,plain,
% 1.96/2.16 (((~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(8878,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(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[8877])).
% 1.96/2.16 tff(8879,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(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.96/2.16 inference(transitivity,[status(thm)],[8878, 8876])).
% 1.96/2.16 tff(8880,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(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(z)))))),
% 1.96/2.16 inference(quant_inst,[status(thm)],[])).
% 1.96/2.16 tff(8881,plain,
% 1.96/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[8880, 8879])).
% 1.96/2.16 tff(8882,plain,
% 1.96/2.16 ($false),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[8881, 45, 424, 8875, 8873])).
% 1.96/2.16 tff(8883,plain,((~b(s(s(z)), s(z))) | (~r(z, s(s(s(elem!1))))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(z)))) | (~b(z, s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.16 tff(8884,plain,
% 1.96/2.16 (~b(s(s(z)), s(z))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[8883, 549, 307, 424, 8853, 550, 3527])).
% 1.96/2.16 tff(8885,plain,
% 1.96/2.16 (r(s(s(z)), s(z))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[86, 8884])).
% 1.96/2.16 tff(8886,plain,
% 1.96/2.16 (~r(s(s(z)), s(s(s(elem!1))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[8542, 45, 385, 8885])).
% 1.96/2.16 tff(8887,plain,
% 1.96/2.16 (~b(s(s(s(s(z)))), elem!1)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[8757, 8886, 307, 8851, 8857])).
% 1.96/2.16 tff(8888,plain,
% 1.96/2.16 (r(s(s(s(s(z)))), elem!1)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[632, 8887, 1412])).
% 1.96/2.16 tff(8889,plain,
% 1.96/2.16 (~r(s(s(z)), elem!1)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[1469, 8888, 1416])).
% 1.96/2.16 tff(8890,plain,
% 1.96/2.16 (b(s(s(z)), elem!1)),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[370, 8889, 8714])).
% 1.96/2.16 tff(8891,plain,
% 1.96/2.16 (b(s(s(z)), s(s(s(elem!1))))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[8890, 8712])).
% 1.96/2.16 tff(8892,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(8893,plain,
% 1.96/2.16 (((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(s(z))))))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(8894,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(s(z))))))))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[8893])).
% 1.96/2.16 tff(8895,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 1.96/2.16 inference(transitivity,[status(thm)],[8894, 8892])).
% 1.96/2.16 tff(8896,plain,
% 1.96/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 1.96/2.16 inference(quant_inst,[status(thm)],[])).
% 1.96/2.16 tff(8897,plain,
% 1.96/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(s(z))))))))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[8896, 8895])).
% 1.96/2.16 tff(8898,plain,
% 1.96/2.16 ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(z))))))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[8897, 128, 549, 8891, 8858])).
% 1.96/2.16 tff(8899,plain,
% 1.96/2.16 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[8898, 8854])).
% 1.96/2.16 tff(8900,plain,
% 1.96/2.16 (r(s(z), s(s(s(s(s(s(z)))))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[1041, 21, 1038, 8899])).
% 1.96/2.16 tff(8901,plain,
% 1.96/2.16 ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[8725, 128, 8891, 8858])).
% 1.96/2.16 tff(8902,plain,
% 1.96/2.16 (~b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[8901, 8854])).
% 1.96/2.16 tff(8903,plain,
% 1.96/2.16 (r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[1176, 21, 1123, 8902])).
% 1.96/2.16 tff(8904,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(8905,plain,
% 1.96/2.16 (((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(8906,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z))))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[8905])).
% 1.96/2.16 tff(8907,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))))),
% 1.96/2.16 inference(transitivity,[status(thm)],[8906, 8904])).
% 1.96/2.16 tff(8908,plain,
% 1.96/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))))),
% 1.96/2.16 inference(quant_inst,[status(thm)],[])).
% 1.96/2.16 tff(8909,plain,
% 1.96/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z))))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[8908, 8907])).
% 1.96/2.16 tff(8910,plain,
% 1.96/2.16 ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[8909, 128, 549, 8891])).
% 1.96/2.16 tff(8911,plain,
% 1.96/2.16 (~b(s(z), s(s(z)))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[8910, 8854])).
% 1.96/2.16 tff(8912,plain,
% 1.96/2.16 (r(s(z), s(s(z)))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[648, 8911])).
% 1.96/2.16 tff(8913,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(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(8914,plain,
% 1.96/2.16 (((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(8915,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(z)), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(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(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[8914])).
% 1.96/2.16 tff(8916,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(z)), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(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(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.96/2.16 inference(transitivity,[status(thm)],[8915, 8913])).
% 1.96/2.16 tff(8917,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(z)), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(z)))))),
% 1.96/2.16 inference(quant_inst,[status(thm)],[])).
% 1.96/2.16 tff(8918,plain,
% 1.96/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[8917, 8916])).
% 1.96/2.16 tff(8919,plain,
% 1.96/2.16 ($false),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[8918, 45, 8912, 8903, 8900])).
% 1.96/2.16 tff(8920,plain,((~b(s(z), s(s(s(elem!1))))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.16 tff(8921,plain,
% 1.96/2.16 (~b(s(z), s(s(s(elem!1))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[8920, 8850, 307, 385, 8797, 550, 3527])).
% 1.96/2.16 tff(8922,plain,
% 1.96/2.16 (r(s(z), s(s(s(elem!1))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[339, 8921])).
% 1.96/2.16 tff(8923,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(z)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(8924,plain,
% 1.96/2.16 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(8925,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(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[8924])).
% 1.96/2.16 tff(8926,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(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.96/2.16 inference(transitivity,[status(thm)],[8925, 8923])).
% 1.96/2.16 tff(8927,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(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))))),
% 1.96/2.16 inference(quant_inst,[status(thm)],[])).
% 1.96/2.16 tff(8928,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(z)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[8927, 8926])).
% 1.96/2.16 tff(8929,plain,
% 1.96/2.16 ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[8928, 45, 323])).
% 1.96/2.16 tff(8930,plain,
% 1.96/2.16 (~r(s(s(z)), s(z))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[8929, 1187])).
% 1.96/2.16 tff(8931,plain,
% 1.96/2.16 (b(s(s(z)), s(z))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[86, 8930])).
% 1.96/2.16 tff(8932,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(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(8933,plain,
% 1.96/2.16 (((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(8934,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(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(z))))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[8933])).
% 1.96/2.16 tff(8935,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(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))),
% 1.96/2.17 inference(transitivity,[status(thm)],[8934, 8932])).
% 1.96/2.17 tff(8936,plain,
% 1.96/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))),
% 1.96/2.17 inference(quant_inst,[status(thm)],[])).
% 1.96/2.17 tff(8937,plain,
% 1.96/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(z))))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[8936, 8935])).
% 1.96/2.17 tff(8938,plain,
% 1.96/2.17 ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(z))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[8937, 45, 323])).
% 1.96/2.17 tff(8939,plain,
% 1.96/2.17 (~r(s(z), s(s(z)))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[8938, 1187])).
% 1.96/2.17 tff(8940,plain,
% 1.96/2.17 (b(s(z), s(s(z)))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[648, 8939])).
% 1.96/2.17 tff(8941,plain,
% 1.96/2.17 ((~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[8881, 45, 424])).
% 1.96/2.17 tff(8942,plain,
% 1.96/2.17 (~r(z, s(s(z)))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[8941, 1187])).
% 1.96/2.17 tff(8943,plain,
% 1.96/2.17 (b(z, s(s(z)))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[516, 8942])).
% 1.96/2.17 tff(8944,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z, s(s(z)))))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(8945,plain,
% 1.96/2.17 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(8946,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z, s(s(z))))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[8945])).
% 1.96/2.17 tff(8947,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z, s(s(z)))))),
% 1.96/2.17 inference(transitivity,[status(thm)],[8946, 8944])).
% 1.96/2.17 tff(8948,plain,
% 1.96/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))),
% 1.96/2.17 inference(quant_inst,[status(thm)],[])).
% 1.96/2.17 tff(8949,plain,
% 1.96/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z))))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[8948, 8947])).
% 1.96/2.17 tff(8950,plain,
% 1.96/2.17 ($false),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[8949, 128, 3527, 495, 7476, 273])).
% 1.96/2.17 tff(8951,plain,((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.17 tff(8952,plain,
% 1.96/2.17 ($false),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[8951, 8943, 8940, 3527, 8931])).
% 1.96/2.17 tff(8953,plain,((~r(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.17 tff(8954,plain,
% 1.96/2.17 (~r(s(s(z)), s(s(s(elem!1))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[8953, 8922, 8797, 3527])).
% 1.96/2.17 tff(8955,plain,
% 1.96/2.17 (~b(s(s(s(s(z)))), elem!1)),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[8757, 8954, 307, 8846, 8825])).
% 1.96/2.17 tff(8956,plain,
% 1.96/2.17 (r(s(s(s(s(z)))), elem!1)),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[632, 8955, 1412])).
% 1.96/2.17 tff(8957,plain,
% 1.96/2.17 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[8956, 8793])).
% 1.96/2.17 tff(8958,plain,
% 1.96/2.17 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[8684, 8922, 8797, 550])).
% 1.96/2.17 tff(8959,plain,
% 1.96/2.17 ($false),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[8958, 8957])).
% 1.96/2.17 tff(8960,plain,((~r(z, s(s(elem!1)))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.17 tff(8961,plain,
% 1.96/2.17 ((~r(z, s(s(elem!1)))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(z, s(z))) | (~r(s(s(s(elem!1))), s(z)))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[8960, 7825])).
% 1.96/2.17 tff(8962,plain,
% 1.96/2.17 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[8961, 8791, 550, 88])).
% 1.96/2.17 tff(8963,plain,
% 1.96/2.17 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[803, 8962])).
% 1.96/2.17 tff(8964,plain,
% 1.96/2.17 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), elem!1)),
% 1.96/2.17 inference(monotonicity,[status(thm)],[8620])).
% 1.96/2.17 tff(8965,plain,
% 1.96/2.17 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.96/2.17 inference(symmetry,[status(thm)],[8964])).
% 1.96/2.17 tff(8966,plain,
% 1.96/2.17 (b(s(s(s(elem!1))), elem!1) <=> b(s(elem!1), elem!1)),
% 1.96/2.17 inference(monotonicity,[status(thm)],[8636])).
% 1.96/2.17 tff(8967,plain,
% 1.96/2.17 (b(s(elem!1), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 1.96/2.17 inference(symmetry,[status(thm)],[8966])).
% 1.96/2.17 tff(8968,plain,
% 1.96/2.17 (b(s(elem!1), elem!1) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.96/2.17 inference(transitivity,[status(thm)],[8967, 8965])).
% 1.96/2.17 tff(8969,plain,
% 1.96/2.17 ((~b(s(elem!1), elem!1)) <=> (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[8968])).
% 1.96/2.17 tff(8970,plain,
% 1.96/2.17 (r(s(s(s(elem!1))), s(z)) <=> r(s(elem!1), s(z))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[8636])).
% 1.96/2.17 tff(8971,plain,
% 1.96/2.17 (r(s(elem!1), s(z))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[8791, 8970])).
% 1.96/2.17 tff(8972,plain,
% 1.96/2.17 (~r(s(elem!1), s(s(z)))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[5035, 45, 35, 8971])).
% 1.96/2.17 tff(8973,plain,
% 1.96/2.17 ((s(s(s(elem!1))) = s(s(z))) <=> (s(elem!1) = s(s(z)))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[8636])).
% 1.96/2.17 tff(8974,plain,
% 1.96/2.17 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(elem!1) = s(s(z))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[8973])).
% 1.96/2.17 tff(8975,plain,
% 1.96/2.17 (~(s(elem!1) = s(s(z)))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[283, 8974])).
% 1.96/2.17 tff(8976,plain,
% 1.96/2.17 (b(s(elem!1), s(s(z)))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[473, 21, 8975, 8972])).
% 1.96/2.17 tff(8977,plain,
% 1.96/2.17 (b(s(s(elem!1)), s(s(z))) <=> b(elem!1, s(s(z)))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[8620])).
% 1.96/2.17 tff(8978,plain,
% 1.96/2.17 (b(elem!1, s(s(z)))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[8522, 8977])).
% 1.96/2.17 tff(8979,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(8980,plain,
% 1.96/2.17 (((~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(8981,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z))))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[8980])).
% 1.96/2.17 tff(8982,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))))),
% 1.96/2.17 inference(transitivity,[status(thm)],[8981, 8979])).
% 1.96/2.17 tff(8983,plain,
% 1.96/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), elem!1)))),
% 1.96/2.17 inference(quant_inst,[status(thm)],[])).
% 1.96/2.17 tff(8984,plain,
% 1.96/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z))))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[8983, 8982])).
% 1.96/2.17 tff(8985,plain,
% 1.96/2.17 (~b(s(elem!1), elem!1)),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[8984, 128, 8628, 8978, 8976])).
% 1.96/2.17 tff(8986,plain,
% 1.96/2.17 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[8985, 8969])).
% 1.96/2.17 tff(8987,plain,
% 1.96/2.17 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[889, 8986, 8963])).
% 1.96/2.17 tff(8988,plain,
% 1.96/2.17 (~r(s(z), s(s(s(elem!1))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[1802, 8987, 8635])).
% 1.96/2.17 tff(8989,plain,
% 1.96/2.17 (r(z, s(s(s(s(elem!1))))) <=> r(z, elem!1)),
% 1.96/2.17 inference(monotonicity,[status(thm)],[8638])).
% 1.96/2.17 tff(8990,plain,
% 1.96/2.17 (r(z, elem!1) <=> r(z, s(s(s(s(elem!1)))))),
% 1.96/2.17 inference(symmetry,[status(thm)],[8989])).
% 1.96/2.17 tff(8991,plain,
% 1.96/2.17 (r(z, s(s(s(s(elem!1)))))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[8647, 8990])).
% 1.96/2.17 tff(8992,plain,
% 1.96/2.17 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[8636])).
% 1.96/2.17 tff(8993,plain,
% 1.96/2.17 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.96/2.17 inference(symmetry,[status(thm)],[8992])).
% 1.96/2.17 tff(8994,plain,
% 1.96/2.17 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[8638])).
% 1.96/2.17 tff(8995,plain,
% 1.96/2.17 (b(elem!1, s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.96/2.17 inference(symmetry,[status(thm)],[8994])).
% 1.96/2.17 tff(8996,plain,
% 1.96/2.17 (b(elem!1, s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.96/2.17 inference(transitivity,[status(thm)],[8995, 8993])).
% 1.96/2.17 tff(8997,plain,
% 1.96/2.17 ((~b(elem!1, s(elem!1))) <=> (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[8996])).
% 1.96/2.17 tff(8998,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(z)))))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(8999,plain,
% 1.96/2.17 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(z)))))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(9000,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(z))))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[8999])).
% 1.96/2.17 tff(9001,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(z)))))),
% 1.96/2.17 inference(transitivity,[status(thm)],[9000, 8998])).
% 1.96/2.17 tff(9002,plain,
% 1.96/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1))))),
% 1.96/2.17 inference(quant_inst,[status(thm)],[])).
% 1.96/2.17 tff(9003,plain,
% 1.96/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(z))))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[9002, 9001])).
% 1.96/2.17 tff(9004,plain,
% 1.96/2.17 (~b(elem!1, s(elem!1))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[9003, 128, 8632, 8628, 8978, 8976])).
% 1.96/2.17 tff(9005,plain,
% 1.96/2.17 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[9004, 8997])).
% 1.96/2.17 tff(9006,plain,
% 1.96/2.17 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[1820, 9005, 8762])).
% 1.96/2.17 tff(9007,plain,
% 1.96/2.17 (~r(z, s(s(s(elem!1))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[1790, 9006, 8991])).
% 1.96/2.17 tff(9008,plain,
% 1.96/2.17 (r(s(s(s(s(elem!1)))), z) <=> r(elem!1, z)),
% 1.96/2.17 inference(monotonicity,[status(thm)],[8638])).
% 1.96/2.17 tff(9009,plain,
% 1.96/2.17 (r(elem!1, z) <=> r(s(s(s(s(elem!1)))), z)),
% 1.96/2.17 inference(symmetry,[status(thm)],[9008])).
% 1.96/2.17 tff(9010,plain,
% 1.96/2.17 (r(s(s(elem!1)), z) <=> r(elem!1, z)),
% 1.96/2.17 inference(monotonicity,[status(thm)],[8620])).
% 1.96/2.17 tff(9011,plain,
% 1.96/2.17 (r(elem!1, z)),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[1519, 9010])).
% 1.96/2.17 tff(9012,plain,
% 1.96/2.17 (r(s(s(s(s(elem!1)))), z)),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[9011, 9009])).
% 1.96/2.17 tff(9013,plain,
% 1.96/2.17 (~r(s(s(s(elem!1))), z)),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[1780, 9006, 9012])).
% 1.96/2.17 tff(9014,plain,
% 1.96/2.17 (~b(s(z), s(s(s(elem!1))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[561, 9013, 550, 9007])).
% 1.96/2.17 tff(9015,plain,
% 1.96/2.17 ($false),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[339, 9014, 8988])).
% 1.96/2.17 tff(9016,plain,((~r(s(s(z)), s(z))) | (~b(z, s(z))) | (~r(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | r(s(s(z)), s(s(elem!1))) | r(s(s(elem!1)), s(s(z))) | (~r(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | r(s(s(s(s(s(s(z)))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.96/2.17 tff(9017,plain,
% 1.96/2.17 (~r(s(s(z)), s(z))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[9016, 8521, 88, 550, 8512, 8519, 7345, 1519, 30, 29])).
% 1.96/2.17 tff(9018,plain,
% 1.96/2.17 (b(s(s(z)), s(z))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[86, 9017])).
% 1.96/2.17 tff(9019,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(9020,plain,
% 1.96/2.17 (((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(9021,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z))))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[9020])).
% 1.96/2.17 tff(9022,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.96/2.17 inference(transitivity,[status(thm)],[9021, 9019])).
% 1.96/2.17 tff(9023,plain,
% 1.96/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.96/2.17 inference(quant_inst,[status(thm)],[])).
% 1.96/2.17 tff(9024,plain,
% 1.96/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z))))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[9023, 9022])).
% 1.96/2.17 tff(9025,plain,
% 1.96/2.17 ($false),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[9024, 128, 30, 550, 7825, 9018, 8512])).
% 1.96/2.17 tff(9026,plain,((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | r(s(s(s(s(s(s(z)))))), elem!1) | (s(s(elem!1)) = s(s(z))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.17 tff(9027,plain,
% 1.96/2.17 (~b(s(s(elem!1)), s(z))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[9026, 29, 88, 1519, 550, 1, 28])).
% 1.96/2.17 tff(9028,plain,
% 1.96/2.17 (r(s(s(elem!1)), s(z))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[292, 9027])).
% 1.96/2.17 tff(9029,plain,
% 1.96/2.17 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[2141, 2095, 325])).
% 1.96/2.17 tff(9030,plain,
% 1.96/2.17 (b(s(s(s(s(elem!1)))), s(z))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[1828, 9029])).
% 1.96/2.17 tff(9031,plain,
% 1.96/2.17 (~b(z, s(s(s(s(elem!1)))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[4144, 128, 416, 3527, 9030])).
% 1.96/2.17 tff(9032,plain,
% 1.96/2.17 ((z = s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1)))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[2047, 21, 9031])).
% 1.96/2.17 tff(9033,plain,
% 1.96/2.17 (r(z, s(s(s(s(elem!1)))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[9032, 2276])).
% 1.96/2.17 tff(9034,plain,
% 1.96/2.17 ($false),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[2307, 45, 88, 2095, 9033])).
% 1.96/2.17 tff(9035,plain,((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~b(s(z), z)) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.17 tff(9036,plain,
% 1.96/2.17 ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z)))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[9035, 7825])).
% 1.96/2.17 tff(9037,plain,
% 1.96/2.17 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[9036, 9028, 88])).
% 1.96/2.17 tff(9038,plain,
% 1.96/2.17 (r(s(s(elem!1)), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[307])).
% 1.96/2.17 tff(9039,plain,
% 1.96/2.17 (r(s(s(s(elem!1))), s(z))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[325, 9038])).
% 1.96/2.17 tff(9040,plain,
% 1.96/2.17 (b(z, s(s(elem!1))) <=> b(z, s(s(s(elem!1))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[307])).
% 1.96/2.17 tff(9041,plain,
% 1.96/2.17 (~r(z, s(s(elem!1)))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[8960, 307, 550, 3527, 9039])).
% 1.96/2.17 tff(9042,plain,
% 1.96/2.17 (b(z, s(s(elem!1)))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[160, 9041])).
% 1.96/2.17 tff(9043,plain,
% 1.96/2.17 (b(z, s(s(s(elem!1))))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[9042, 9040])).
% 1.96/2.17 tff(9044,plain,
% 1.96/2.17 (~r(z, s(s(elem!1)))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[8960, 307, 550, 3527, 385])).
% 1.96/2.17 tff(9045,plain,
% 1.96/2.17 (b(z, s(s(elem!1)))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[160, 9044])).
% 1.96/2.17 tff(9046,plain,
% 1.96/2.17 (b(z, s(s(s(elem!1))))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[9045, 9040])).
% 1.96/2.17 tff(9047,plain,
% 1.96/2.17 ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) <=> (~b(s(s(s(s(z)))), elem!1))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[8729])).
% 1.96/2.17 tff(9048,plain,
% 1.96/2.17 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[6248, 35, 385])).
% 1.96/2.17 tff(9049,plain,
% 1.96/2.17 (~r(elem!1, s(s(z)))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[9048, 8704])).
% 1.96/2.17 tff(9050,plain,
% 1.96/2.17 (b(elem!1, s(s(z)))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[493, 9049, 8703])).
% 1.96/2.17 tff(9051,plain,
% 1.96/2.17 (b(s(s(s(elem!1))), s(s(z)))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[9050, 8697])).
% 1.96/2.17 tff(9052,plain,
% 1.96/2.17 (~r(s(s(z)), elem!1)),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[8543, 8716])).
% 1.96/2.17 tff(9053,plain,
% 1.96/2.17 (b(s(s(z)), elem!1)),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[370, 9052, 8714])).
% 1.96/2.17 tff(9054,plain,
% 1.96/2.17 (b(s(s(z)), s(s(s(elem!1))))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[9053, 8712])).
% 1.96/2.17 tff(9055,assumption,(b(s(s(s(s(z)))), s(s(s(elem!1))))), introduced(assumption)).
% 1.96/2.17 tff(9056,assumption,(b(s(s(s(elem!1))), s(s(z)))), introduced(assumption)).
% 1.96/2.17 tff(9057,plain,
% 1.96/2.17 ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[8746, 128, 8557, 9056])).
% 1.96/2.17 tff(9058,plain,
% 1.96/2.17 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[9057, 9055])).
% 1.96/2.17 tff(9059,plain,
% 1.96/2.17 (r(s(s(z)), s(s(s(s(z)))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[610, 21, 607, 9058])).
% 1.96/2.17 tff(9060,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(9061,plain,
% 1.96/2.17 (((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(9062,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 1.96/2.18 inference(monotonicity,[status(thm)],[9061])).
% 1.96/2.18 tff(9063,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.96/2.18 inference(transitivity,[status(thm)],[9062, 9060])).
% 1.96/2.18 tff(9064,plain,
% 1.96/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)))),
% 1.96/2.18 inference(quant_inst,[status(thm)],[])).
% 1.96/2.18 tff(9065,plain,
% 1.96/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[9064, 9063])).
% 1.96/2.18 tff(9066,plain,
% 1.96/2.18 ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[9065, 128, 874, 8557, 9056])).
% 1.96/2.18 tff(9067,plain,
% 1.96/2.18 (~b(s(s(s(s(z)))), z)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[9066, 9055])).
% 1.96/2.18 tff(9068,plain,
% 1.96/2.18 (r(s(s(s(s(z)))), z)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[589, 21, 586, 9067])).
% 1.96/2.18 tff(9069,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(9070,plain,
% 1.96/2.18 (((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(9071,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 1.96/2.18 inference(monotonicity,[status(thm)],[9070])).
% 1.96/2.18 tff(9072,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.96/2.18 inference(transitivity,[status(thm)],[9071, 9069])).
% 1.96/2.18 tff(9073,plain,
% 1.96/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z)))),
% 1.96/2.18 inference(quant_inst,[status(thm)],[])).
% 1.96/2.18 tff(9074,plain,
% 1.96/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[9073, 9072])).
% 1.96/2.18 tff(9075,plain,
% 1.96/2.18 ((~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[9074, 128, 874, 8557])).
% 1.96/2.18 tff(9076,plain,
% 1.96/2.18 (~b(s(s(z)), z)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[9075, 9056])).
% 1.96/2.18 tff(9077,plain,
% 1.96/2.18 (r(s(s(z)), z)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[25, 9076])).
% 1.96/2.18 tff(9078,plain,
% 1.96/2.18 ($false),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[625, 45, 9077, 9068, 9059])).
% 1.96/2.18 tff(9079,plain,((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.18 tff(9080,plain,
% 1.96/2.18 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[9079, 9054, 874, 9051])).
% 1.96/2.18 tff(9081,plain,
% 1.96/2.18 (~b(s(s(s(s(z)))), elem!1)),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[9080, 9047])).
% 1.96/2.18 tff(9082,plain,
% 1.96/2.18 (r(s(s(s(s(z)))), elem!1)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[632, 9081, 1412])).
% 1.96/2.18 tff(9083,plain,
% 1.96/2.18 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[9082, 8793])).
% 1.96/2.18 tff(9084,plain,
% 1.96/2.18 (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[7548, 9083, 323])).
% 1.96/2.18 tff(9085,plain,
% 1.96/2.18 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[1098, 9084, 307])).
% 1.96/2.18 tff(9086,plain,
% 1.96/2.18 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[1055, 9085, 8794])).
% 1.96/2.18 tff(9087,plain,
% 1.96/2.18 (b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[9086, 8710])).
% 1.96/2.18 tff(9088,plain,
% 1.96/2.18 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(z)))))),
% 1.96/2.18 inference(monotonicity,[status(thm)],[1091])).
% 1.96/2.18 tff(9089,plain,
% 1.96/2.18 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 1.96/2.18 inference(transitivity,[status(thm)],[9088, 3009])).
% 1.96/2.18 tff(9090,plain,
% 1.96/2.18 ((s(s(s(s(z)))) = elem!1) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 1.96/2.18 inference(symmetry,[status(thm)],[9089])).
% 1.96/2.18 tff(9091,plain,
% 1.96/2.18 ((~(s(s(s(s(z)))) = elem!1)) <=> (~(s(s(s(elem!1))) = s(s(s(s(z))))))),
% 1.96/2.18 inference(monotonicity,[status(thm)],[9090])).
% 1.96/2.18 tff(9092,plain,
% 1.96/2.18 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[1412, 9091])).
% 1.96/2.18 tff(9093,plain,
% 1.96/2.18 (~r(s(s(s(s(z)))), s(z))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[7521, 45, 323, 9083])).
% 1.96/2.18 tff(9094,plain,
% 1.96/2.18 (b(s(s(s(s(z)))), s(z))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[782, 21, 779, 9093])).
% 1.96/2.18 tff(9095,plain,
% 1.96/2.18 (~r(s(z), s(s(s(s(z)))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[7529, 45, 323, 9083])).
% 1.96/2.18 tff(9096,plain,
% 1.96/2.18 (b(s(z), s(s(s(s(z)))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[684, 21, 681, 9095])).
% 1.96/2.18 tff(9097,plain,
% 1.96/2.18 (~b(s(s(s(s(z)))), z)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[8682, 128, 550, 9096, 9094])).
% 1.96/2.18 tff(9098,plain,
% 1.96/2.18 (r(s(s(s(s(z)))), z)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[589, 21, 586, 9097])).
% 1.96/2.18 tff(9099,plain,
% 1.96/2.18 ((~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[9074, 128, 874, 9054])).
% 1.96/2.18 tff(9100,plain,
% 1.96/2.18 (~b(s(s(z)), z)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[9099, 9051])).
% 1.96/2.18 tff(9101,plain,
% 1.96/2.18 (r(s(s(z)), z)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[25, 9100])).
% 1.96/2.18 tff(9102,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(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(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(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(9103,plain,
% 1.96/2.18 (((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(9104,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(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z))))),
% 1.96/2.18 inference(monotonicity,[status(thm)],[9103])).
% 1.96/2.18 tff(9105,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(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 1.96/2.18 inference(transitivity,[status(thm)],[9104, 9102])).
% 1.96/2.18 tff(9106,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(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.96/2.18 inference(quant_inst,[status(thm)],[])).
% 1.96/2.18 tff(9107,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(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[9106, 9105])).
% 1.96/2.18 tff(9108,plain,
% 1.96/2.18 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[9107, 45, 35, 9101, 9098])).
% 1.96/2.18 tff(9109,plain,
% 1.96/2.18 ((s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z)))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[971, 21, 9108])).
% 1.96/2.18 tff(9110,plain,
% 1.96/2.18 (b(s(s(s(s(z)))), s(s(z)))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[9109, 921])).
% 1.96/2.18 tff(9111,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(9112,plain,
% 1.96/2.18 (((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(9113,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 1.96/2.18 inference(monotonicity,[status(thm)],[9112])).
% 1.96/2.18 tff(9114,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.96/2.18 inference(transitivity,[status(thm)],[9113, 9111])).
% 1.96/2.18 tff(9115,plain,
% 1.96/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.96/2.18 inference(quant_inst,[status(thm)],[])).
% 1.96/2.18 tff(9116,plain,
% 1.96/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[9115, 9114])).
% 1.96/2.18 tff(9117,plain,
% 1.96/2.18 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[9116, 128, 9054, 9051, 9110])).
% 1.96/2.18 tff(9118,plain,
% 1.96/2.18 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(9119,plain,
% 1.96/2.18 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 1.96/2.18 inference(quant_inst,[status(thm)],[])).
% 1.96/2.18 tff(9120,plain,
% 1.96/2.18 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[9119, 9118])).
% 1.96/2.18 tff(9121,plain,
% 1.96/2.18 ((s(s(s(elem!1))) = s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[9120, 21, 9117])).
% 1.96/2.18 tff(9122,plain,
% 1.96/2.18 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[9121, 9092])).
% 1.96/2.18 tff(9123,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(9124,plain,
% 1.96/2.18 (((~b(s(s(s(s(z)))), s(z))) | (~b(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(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(9125,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 1.96/2.18 inference(monotonicity,[status(thm)],[9124])).
% 1.96/2.18 tff(9126,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.96/2.18 inference(transitivity,[status(thm)],[9125, 9123])).
% 1.96/2.18 tff(9127,plain,
% 1.96/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(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)))))))),
% 1.96/2.18 inference(quant_inst,[status(thm)],[])).
% 1.96/2.18 tff(9128,plain,
% 1.96/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[9127, 9126])).
% 1.96/2.18 tff(9129,plain,
% 1.96/2.18 (~b(z, s(s(s(s(z)))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[9128, 128, 550, 9096, 9094])).
% 1.96/2.18 tff(9130,plain,
% 1.96/2.18 ((z = s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[2905, 21, 9129])).
% 1.96/2.18 tff(9131,plain,
% 1.96/2.18 (r(z, s(s(s(s(z)))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[9130, 2895])).
% 1.96/2.18 tff(9132,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(9133,plain,
% 1.96/2.18 (((~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(9134,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z))))))),
% 1.96/2.18 inference(monotonicity,[status(thm)],[9133])).
% 1.96/2.18 tff(9135,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))))),
% 1.96/2.18 inference(transitivity,[status(thm)],[9134, 9132])).
% 1.96/2.18 tff(9136,plain,
% 1.96/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))))),
% 1.96/2.18 inference(quant_inst,[status(thm)],[])).
% 1.96/2.18 tff(9137,plain,
% 1.96/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z))))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[9136, 9135])).
% 1.96/2.18 tff(9138,plain,
% 1.96/2.18 ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[9137, 128, 874, 9054])).
% 1.96/2.18 tff(9139,plain,
% 1.96/2.18 (~b(z, s(s(z)))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[9138, 9051])).
% 1.96/2.18 tff(9140,plain,
% 1.96/2.18 (r(z, s(s(z)))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[516, 9139])).
% 1.96/2.18 tff(9141,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(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(9142,plain,
% 1.96/2.18 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(9143,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(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 1.96/2.18 inference(monotonicity,[status(thm)],[9142])).
% 1.96/2.18 tff(9144,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(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.96/2.18 inference(transitivity,[status(thm)],[9143, 9141])).
% 1.96/2.18 tff(9145,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(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)))),
% 1.96/2.19 inference(quant_inst,[status(thm)],[])).
% 1.96/2.19 tff(9146,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(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[9145, 9144])).
% 1.96/2.19 tff(9147,plain,
% 1.96/2.19 (~r(s(s(s(elem!1))), z)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[9146, 45, 9140, 9131, 9122])).
% 1.96/2.19 tff(9148,plain,
% 1.96/2.19 (b(s(s(s(elem!1))), z)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[547, 21, 382, 9147])).
% 1.96/2.19 tff(9149,plain,
% 1.96/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(9150,plain,
% 1.96/2.19 (((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), z))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(9151,plain,
% 1.96/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[9150])).
% 1.96/2.19 tff(9152,plain,
% 1.96/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 1.96/2.19 inference(transitivity,[status(thm)],[9151, 9149])).
% 1.96/2.19 tff(9153,plain,
% 1.96/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 1.96/2.19 inference(quant_inst,[status(thm)],[])).
% 1.96/2.19 tff(9154,plain,
% 1.96/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[9153, 9152])).
% 1.96/2.19 tff(9155,plain,
% 1.96/2.19 ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[9154, 128, 874, 9148])).
% 1.96/2.19 tff(9156,plain,
% 1.96/2.19 (~b(s(s(s(s(s(s(z)))))), z)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[9155, 9087])).
% 1.96/2.19 tff(9157,plain,
% 1.96/2.19 (r(s(s(s(s(s(s(z)))))), z)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[1022, 21, 1019, 9156])).
% 1.96/2.19 tff(9158,plain,
% 1.96/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(9159,plain,
% 1.96/2.19 (((~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(9160,plain,
% 1.96/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[9159])).
% 1.96/2.19 tff(9161,plain,
% 1.96/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 1.96/2.19 inference(transitivity,[status(thm)],[9160, 9158])).
% 1.96/2.19 tff(9162,plain,
% 1.96/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.96/2.19 inference(quant_inst,[status(thm)],[])).
% 1.96/2.19 tff(9163,plain,
% 1.96/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[9162, 9161])).
% 1.96/2.19 tff(9164,plain,
% 1.96/2.19 ((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[9163, 128, 874, 9148, 9054])).
% 1.96/2.19 tff(9165,plain,
% 1.96/2.19 (~b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[9164, 9087])).
% 1.96/2.19 tff(9166,plain,
% 1.96/2.19 (r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[1176, 21, 1123, 9165])).
% 1.96/2.19 tff(9167,plain,
% 1.96/2.19 ($false),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[7567, 45, 9101, 9166, 9157])).
% 1.96/2.19 tff(9168,plain,((~r(s(s(z)), s(z))) | (~b(z, s(s(s(elem!1))))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.19 tff(9169,plain,
% 1.96/2.19 (~r(s(s(z)), s(z))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[9168, 323, 307, 550, 9046, 385])).
% 1.96/2.19 tff(9170,plain,
% 1.96/2.19 (b(s(s(z)), s(z))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[86, 9169])).
% 1.96/2.19 tff(9171,plain,
% 1.96/2.19 (((~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(9172,plain,
% 1.96/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[9171])).
% 1.96/2.19 tff(9173,plain,
% 1.96/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.96/2.19 inference(transitivity,[status(thm)],[9172, 8806])).
% 1.96/2.19 tff(9174,plain,
% 1.96/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 1.96/2.19 inference(quant_inst,[status(thm)],[])).
% 1.96/2.19 tff(9175,plain,
% 1.96/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[9174, 9173])).
% 1.96/2.19 tff(9176,plain,
% 1.96/2.19 (~b(s(s(s(s(s(s(z)))))), z)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[9175, 128, 550, 3527, 7637])).
% 1.96/2.19 tff(9177,plain,
% 1.96/2.19 (r(s(s(s(s(s(s(z)))))), z)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[1022, 21, 1019, 9176])).
% 1.96/2.19 tff(9178,plain,
% 1.96/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(s(s(s(s(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(X0, 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)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(9179,plain,
% 1.96/2.19 (((~b(z, s(z))) | (~b(s(s(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(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(9180,plain,
% 1.96/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, 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)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[9179])).
% 1.96/2.19 tff(9181,plain,
% 1.96/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, 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)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.96/2.19 inference(transitivity,[status(thm)],[9180, 9178])).
% 1.96/2.19 tff(9182,plain,
% 1.96/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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)))))))))),
% 1.96/2.19 inference(quant_inst,[status(thm)],[])).
% 1.96/2.19 tff(9183,plain,
% 1.96/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[9182, 9181])).
% 1.96/2.19 tff(9184,plain,
% 1.96/2.19 (~b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[9183, 128, 550, 3527, 273, 7637])).
% 1.96/2.19 tff(9185,plain,
% 1.96/2.19 (r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[1176, 21, 1123, 9184])).
% 1.96/2.19 tff(9186,plain,
% 1.96/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)), s(z))))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(9187,plain,
% 1.96/2.19 (((~b(z, s(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))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(9188,plain,
% 1.96/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, 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(s(z)), s(z)))))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[9187])).
% 1.96/2.19 tff(9189,plain,
% 1.96/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, 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(s(z)), s(z))))),
% 1.96/2.19 inference(transitivity,[status(thm)],[9188, 9186])).
% 1.96/2.19 tff(9190,plain,
% 1.96/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.96/2.19 inference(quant_inst,[status(thm)],[])).
% 1.96/2.19 tff(9191,plain,
% 1.96/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[9190, 9189])).
% 1.96/2.19 tff(9192,plain,
% 1.96/2.19 (~b(s(s(z)), z)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[9191, 128, 550, 3527, 273])).
% 1.96/2.19 tff(9193,plain,
% 1.96/2.19 (r(s(s(z)), z)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[25, 9192])).
% 1.96/2.19 tff(9194,plain,
% 1.96/2.19 ($false),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[7567, 45, 9193, 9185, 9177])).
% 1.96/2.19 tff(9195,plain,((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.19 tff(9196,plain,
% 1.96/2.19 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[9195, 9170, 3527, 550])).
% 1.96/2.19 tff(9197,plain,
% 1.96/2.19 ((s(s(s(s(s(s(z)))))) = s(z)) | r(s(s(s(s(s(s(z)))))), s(z))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[1148, 21, 9196])).
% 1.96/2.19 tff(9198,plain,
% 1.96/2.19 (r(s(s(s(s(s(s(z)))))), s(z))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[9197, 1112])).
% 1.96/2.19 tff(9199,plain,
% 1.96/2.19 (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[8820, 45, 385, 9198])).
% 1.96/2.19 tff(9200,plain,
% 1.96/2.19 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[1098, 9199, 307])).
% 1.96/2.19 tff(9201,plain,
% 1.96/2.19 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[1055, 9200, 8794])).
% 1.96/2.19 tff(9202,plain,
% 1.96/2.19 (b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[9201, 8710])).
% 1.96/2.19 tff(9203,plain,
% 1.96/2.19 ((s(s(s(elem!1))) = s(s(s(s(s(s(z))))))) <=> (elem!1 = s(s(s(s(s(s(z)))))))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[1091])).
% 1.96/2.19 tff(9204,plain,
% 1.96/2.19 ((s(s(s(elem!1))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = elem!1)),
% 1.96/2.19 inference(transitivity,[status(thm)],[9203, 4622])).
% 1.96/2.19 tff(9205,plain,
% 1.96/2.19 ((s(s(s(s(s(s(z)))))) = elem!1) <=> (s(s(s(elem!1))) = s(s(s(s(s(s(z)))))))),
% 1.96/2.19 inference(symmetry,[status(thm)],[9204])).
% 1.96/2.19 tff(9206,plain,
% 1.96/2.19 ((~(s(s(s(s(s(s(z)))))) = elem!1)) <=> (~(s(s(s(elem!1))) = s(s(s(s(s(s(z))))))))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[9205])).
% 1.96/2.19 tff(9207,plain,
% 1.96/2.19 (~(s(s(s(elem!1))) = s(s(s(s(s(s(z)))))))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[8794, 9206])).
% 1.96/2.19 tff(9208,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(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(9209,plain,
% 1.96/2.19 (((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(9210,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(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(z))))))))))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[9209])).
% 1.96/2.19 tff(9211,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(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))),
% 1.96/2.19 inference(transitivity,[status(thm)],[9210, 9208])).
% 1.96/2.19 tff(9212,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(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))),
% 1.96/2.19 inference(quant_inst,[status(thm)],[])).
% 1.96/2.19 tff(9213,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(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(z))))))))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[9212, 9211])).
% 1.96/2.19 tff(9214,plain,
% 1.96/2.19 (~r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[9213, 45, 385, 9198])).
% 1.96/2.19 tff(9215,plain,
% 1.96/2.19 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(s(s(z))))))) | b(s(s(s(elem!1))), s(s(s(s(s(s(z))))))) | r(s(s(s(elem!1))), s(s(s(s(s(s(z))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(s(s(z))))))) | b(s(s(s(elem!1))), s(s(s(s(s(s(z))))))) | r(s(s(s(elem!1))), s(s(s(s(s(s(z))))))))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(9216,plain,
% 1.96/2.19 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(s(s(z))))))) | b(s(s(s(elem!1))), s(s(s(s(s(s(z))))))) | r(s(s(s(elem!1))), s(s(s(s(s(s(z))))))))),
% 1.96/2.19 inference(quant_inst,[status(thm)],[])).
% 1.96/2.19 tff(9217,plain,
% 1.96/2.19 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(s(s(z))))))) | b(s(s(s(elem!1))), s(s(s(s(s(s(z))))))) | r(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[9216, 9215])).
% 1.96/2.19 tff(9218,plain,
% 1.96/2.19 ((s(s(s(elem!1))) = s(s(s(s(s(s(z))))))) | b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[9217, 21, 9214])).
% 1.96/2.19 tff(9219,plain,
% 1.96/2.19 (b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[9218, 9207])).
% 1.96/2.19 tff(9220,plain,
% 1.96/2.19 ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(z)))), elem!1))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[8792])).
% 1.96/2.19 tff(9221,plain,
% 1.96/2.19 (~b(s(s(z)), z)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[9191, 128, 550, 3527, 9170])).
% 1.96/2.19 tff(9222,plain,
% 1.96/2.19 (r(s(s(z)), z)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[25, 9221])).
% 1.96/2.19 tff(9223,plain,
% 1.96/2.19 (((~b(s(s(s(s(z)))), s(z))) | (~b(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(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(9224,plain,
% 1.96/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[9223])).
% 1.96/2.19 tff(9225,plain,
% 1.96/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.96/2.19 inference(transitivity,[status(thm)],[9224, 1284])).
% 1.96/2.19 tff(9226,plain,
% 1.96/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(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)))))))),
% 1.96/2.20 inference(quant_inst,[status(thm)],[])).
% 1.96/2.20 tff(9227,plain,
% 1.96/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 1.96/2.20 inference(modus_ponens,[status(thm)],[9226, 9225])).
% 1.96/2.20 tff(9228,plain,
% 1.96/2.20 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.96/2.20 inference(unit_resolution,[status(thm)],[9227, 128, 273, 7531, 7523])).
% 1.96/2.20 tff(9229,plain,
% 1.96/2.20 (r(s(s(z)), s(s(s(s(z)))))),
% 1.96/2.20 inference(unit_resolution,[status(thm)],[610, 21, 607, 9228])).
% 1.96/2.20 tff(9230,plain,
% 1.96/2.20 (~b(s(s(s(s(z)))), z)),
% 1.96/2.20 inference(unit_resolution,[status(thm)],[8682, 128, 550, 7531, 7523])).
% 1.96/2.20 tff(9231,plain,
% 1.96/2.20 (r(s(s(s(s(z)))), z)),
% 1.96/2.20 inference(unit_resolution,[status(thm)],[589, 21, 586, 9230])).
% 1.96/2.20 tff(9232,plain,
% 1.96/2.20 ($false),
% 1.96/2.20 inference(unit_resolution,[status(thm)],[625, 45, 28, 9231, 9229])).
% 1.96/2.20 tff(9233,plain,((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.20 tff(9234,plain,
% 1.96/2.20 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.96/2.20 inference(unit_resolution,[status(thm)],[9233, 9222, 550, 9170, 323])).
% 1.96/2.20 tff(9235,plain,
% 1.96/2.20 (~r(s(s(s(s(z)))), elem!1)),
% 1.96/2.20 inference(modus_ponens,[status(thm)],[9234, 9220])).
% 1.96/2.20 tff(9236,plain,
% 1.96/2.20 (b(s(s(s(s(z)))), elem!1)),
% 1.96/2.20 inference(unit_resolution,[status(thm)],[632, 9235, 1412])).
% 1.96/2.20 tff(9237,plain,
% 1.96/2.20 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.96/2.20 inference(modus_ponens,[status(thm)],[9236, 8730])).
% 1.96/2.20 tff(9238,plain,
% 1.96/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))),
% 1.96/2.20 inference(rewrite,[status(thm)],[])).
% 1.96/2.20 tff(9239,plain,
% 1.96/2.20 (((~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(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)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))),
% 1.96/2.20 inference(rewrite,[status(thm)],[])).
% 1.96/2.20 tff(9240,plain,
% 1.96/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z))))))))))),
% 1.96/2.20 inference(monotonicity,[status(thm)],[9239])).
% 1.96/2.20 tff(9241,plain,
% 1.96/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))),
% 2.03/2.20 inference(transitivity,[status(thm)],[9240, 9238])).
% 2.03/2.20 tff(9242,plain,
% 2.03/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.03/2.20 inference(quant_inst,[status(thm)],[])).
% 2.03/2.20 tff(9243,plain,
% 2.03/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z))))))))),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[9242, 9241])).
% 2.03/2.20 tff(9244,plain,
% 2.03/2.20 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[9243, 128, 9237, 9219, 9202])).
% 2.03/2.20 tff(9245,plain,
% 2.03/2.20 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[1215, 21, 1212, 9244])).
% 2.03/2.20 tff(9246,plain,
% 2.03/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))),
% 2.03/2.20 inference(rewrite,[status(thm)],[])).
% 2.03/2.20 tff(9247,plain,
% 2.03/2.20 (((~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), z))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))),
% 2.03/2.20 inference(rewrite,[status(thm)],[])).
% 2.03/2.20 tff(9248,plain,
% 2.03/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z))))))))))),
% 2.03/2.20 inference(monotonicity,[status(thm)],[9247])).
% 2.03/2.20 tff(9249,plain,
% 2.03/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))),
% 2.03/2.20 inference(transitivity,[status(thm)],[9248, 9246])).
% 2.03/2.20 tff(9250,plain,
% 2.03/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 2.03/2.20 inference(quant_inst,[status(thm)],[])).
% 2.03/2.20 tff(9251,plain,
% 2.03/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z))))))))),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[9250, 9249])).
% 2.03/2.20 tff(9252,plain,
% 2.03/2.20 ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[9251, 128, 9046, 9219])).
% 2.03/2.20 tff(9253,plain,
% 2.03/2.20 (~b(s(s(s(s(s(s(z)))))), z)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[9252, 9202])).
% 2.03/2.20 tff(9254,plain,
% 2.03/2.20 (r(s(s(s(s(s(s(z)))))), z)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[1022, 21, 1019, 9253])).
% 2.03/2.20 tff(9255,plain,
% 2.03/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))),
% 2.03/2.20 inference(rewrite,[status(thm)],[])).
% 2.03/2.20 tff(9256,plain,
% 2.03/2.20 (((~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))),
% 2.03/2.20 inference(rewrite,[status(thm)],[])).
% 2.03/2.20 tff(9257,plain,
% 2.03/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z))))))))))),
% 2.03/2.20 inference(monotonicity,[status(thm)],[9256])).
% 2.03/2.20 tff(9258,plain,
% 2.03/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))))),
% 2.03/2.20 inference(transitivity,[status(thm)],[9257, 9255])).
% 2.03/2.20 tff(9259,plain,
% 2.03/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)))),
% 2.03/2.20 inference(quant_inst,[status(thm)],[])).
% 2.03/2.20 tff(9260,plain,
% 2.03/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(z))))))))),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[9259, 9258])).
% 2.03/2.20 tff(9261,plain,
% 2.03/2.20 (~b(s(s(s(s(z)))), z)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[9260, 128, 9046, 9237, 9219, 9202])).
% 2.03/2.20 tff(9262,plain,
% 2.03/2.20 (r(s(s(s(s(z)))), z)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[589, 21, 586, 9261])).
% 2.03/2.20 tff(9263,plain,
% 2.03/2.20 ($false),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[7506, 45, 9262, 9254, 9245])).
% 2.03/2.20 tff(9264,plain,((~r(s(z), s(s(s(elem!1))))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.20 tff(9265,plain,
% 2.03/2.20 (~r(s(z), s(s(s(elem!1))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[9264, 307, 550, 9039, 3527])).
% 2.03/2.20 tff(9266,plain,
% 2.03/2.20 (b(s(z), s(s(s(elem!1))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[339, 9265])).
% 2.03/2.20 tff(9267,plain,
% 2.03/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.03/2.20 inference(rewrite,[status(thm)],[])).
% 2.03/2.20 tff(9268,plain,
% 2.03/2.20 (((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.03/2.20 inference(rewrite,[status(thm)],[])).
% 2.03/2.20 tff(9269,plain,
% 2.03/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 2.03/2.20 inference(monotonicity,[status(thm)],[9268])).
% 2.03/2.20 tff(9270,plain,
% 2.03/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.03/2.20 inference(transitivity,[status(thm)],[9269, 9267])).
% 2.03/2.20 tff(9271,plain,
% 2.03/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))),
% 2.03/2.20 inference(quant_inst,[status(thm)],[])).
% 2.03/2.20 tff(9272,plain,
% 2.03/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[9271, 9270])).
% 2.03/2.20 tff(9273,plain,
% 2.03/2.20 ($false),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[9272, 128, 3527, 549, 874, 9054, 9051])).
% 2.03/2.20 tff(9274,plain,((~r(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.20 tff(9275,plain,
% 2.03/2.20 (~r(s(s(z)), s(z))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[9274, 9266, 3527, 9043, 307, 9039])).
% 2.03/2.20 tff(9276,plain,
% 2.03/2.20 (b(s(s(z)), s(z))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[86, 9275])).
% 2.03/2.20 tff(9277,plain,
% 2.03/2.20 (~b(z, s(s(z)))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[8843, 128, 550, 3527, 9276])).
% 2.03/2.20 tff(9278,plain,
% 2.03/2.20 (r(z, s(s(z)))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[516, 9277])).
% 2.03/2.20 tff(9279,plain,
% 2.03/2.20 ((~r(z, s(s(elem!1)))) <=> (~r(z, s(s(s(elem!1)))))),
% 2.03/2.20 inference(monotonicity,[status(thm)],[8796])).
% 2.03/2.20 tff(9280,plain,
% 2.03/2.20 (~r(z, s(s(s(elem!1))))),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[9041, 9279])).
% 2.03/2.20 tff(9281,plain,
% 2.03/2.20 (r(s(s(s(elem!1))), z)),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[561, 9266, 550, 9280])).
% 2.03/2.20 tff(9282,plain,
% 2.03/2.20 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[528, 9281, 9278])).
% 2.03/2.20 tff(9283,plain,
% 2.03/2.20 (~r(elem!1, s(s(z)))),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[9282, 8704])).
% 2.03/2.20 tff(9284,plain,
% 2.03/2.20 (b(elem!1, s(s(z)))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[493, 9283, 8703])).
% 2.03/2.20 tff(9285,plain,
% 2.03/2.20 (b(s(s(s(elem!1))), s(s(z)))),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[9284, 8697])).
% 2.03/2.20 tff(9286,plain,
% 2.03/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.03/2.20 inference(rewrite,[status(thm)],[])).
% 2.03/2.20 tff(9287,plain,
% 2.03/2.20 (((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.03/2.20 inference(rewrite,[status(thm)],[])).
% 2.03/2.20 tff(9288,plain,
% 2.03/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 2.03/2.20 inference(monotonicity,[status(thm)],[9287])).
% 2.03/2.20 tff(9289,plain,
% 2.03/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.03/2.20 inference(transitivity,[status(thm)],[9288, 9286])).
% 2.03/2.20 tff(9290,plain,
% 2.03/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))),
% 2.03/2.20 inference(quant_inst,[status(thm)],[])).
% 2.03/2.20 tff(9291,plain,
% 2.03/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[9290, 9289])).
% 2.03/2.20 tff(9292,plain,
% 2.03/2.20 ($false),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[9291, 128, 550, 9266, 9043, 9276, 9285])).
% 2.03/2.20 tff(9293,plain,((~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.20 tff(9294,plain,
% 2.03/2.20 ((~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(z, s(z))) | (~r(s(s(elem!1)), s(z)))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[9293, 7825])).
% 2.03/2.20 tff(9295,plain,
% 2.03/2.20 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[9294, 9028, 550])).
% 2.03/2.20 tff(9296,plain,
% 2.03/2.20 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[438, 9028, 88])).
% 2.03/2.20 tff(9297,plain,
% 2.03/2.20 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[321, 9296, 9295])).
% 2.03/2.20 tff(9298,plain,
% 2.03/2.20 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(z)))),
% 2.03/2.20 inference(commutativity,[status(thm)],[])).
% 2.03/2.20 tff(9299,plain,
% 2.03/2.20 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(elem!1)))))),
% 2.03/2.20 inference(symmetry,[status(thm)],[9298])).
% 2.03/2.20 tff(9300,plain,
% 2.03/2.20 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(s(elem!1))))))),
% 2.03/2.20 inference(monotonicity,[status(thm)],[9299])).
% 2.03/2.20 tff(9301,plain,
% 2.03/2.20 (~(s(s(z)) = s(s(s(s(elem!1)))))),
% 2.03/2.20 inference(modus_ponens,[status(thm)],[239, 9300])).
% 2.03/2.20 tff(9302,plain,
% 2.03/2.20 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.03/2.20 inference(unit_resolution,[status(thm)],[1897, 2023, 1892])).
% 2.03/2.20 tff(9303,plain,
% 2.03/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.03/2.20 inference(rewrite,[status(thm)],[])).
% 2.03/2.20 tff(9304,plain,
% 2.03/2.20 (((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.03/2.20 inference(rewrite,[status(thm)],[])).
% 2.03/2.20 tff(9305,plain,
% 2.03/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))))),
% 2.03/2.20 inference(monotonicity,[status(thm)],[9304])).
% 2.03/2.20 tff(9306,plain,
% 2.03/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.03/2.21 inference(transitivity,[status(thm)],[9305, 9303])).
% 2.03/2.21 tff(9307,plain,
% 2.03/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 2.03/2.21 inference(quant_inst,[status(thm)],[])).
% 2.03/2.21 tff(9308,plain,
% 2.03/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[9307, 9306])).
% 2.03/2.21 tff(9309,plain,
% 2.03/2.21 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[9308, 128, 9302, 8522, 8523])).
% 2.03/2.21 tff(9310,plain,
% 2.03/2.21 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(elem!1))))) | b(s(s(z)), s(s(s(s(elem!1))))) | r(s(s(z)), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(elem!1))))) | b(s(s(z)), s(s(s(s(elem!1))))) | r(s(s(z)), s(s(s(s(elem!1))))))),
% 2.03/2.21 inference(rewrite,[status(thm)],[])).
% 2.03/2.21 tff(9311,plain,
% 2.03/2.21 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(elem!1))))) | b(s(s(z)), s(s(s(s(elem!1))))) | r(s(s(z)), s(s(s(s(elem!1))))))),
% 2.03/2.21 inference(quant_inst,[status(thm)],[])).
% 2.03/2.21 tff(9312,plain,
% 2.03/2.21 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(elem!1))))) | b(s(s(z)), s(s(s(s(elem!1))))) | r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[9311, 9310])).
% 2.03/2.21 tff(9313,plain,
% 2.03/2.21 ((s(s(z)) = s(s(s(s(elem!1))))) | r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[9312, 21, 9309])).
% 2.03/2.21 tff(9314,plain,
% 2.03/2.21 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[9313, 9301])).
% 2.03/2.21 tff(9315,plain,
% 2.03/2.21 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[9294, 325, 550])).
% 2.03/2.21 tff(9316,plain,
% 2.03/2.21 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[803, 9315])).
% 2.03/2.21 tff(9317,plain,
% 2.03/2.21 (~r(z, s(z))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[53, 28, 35])).
% 2.03/2.21 tff(9318,plain,
% 2.03/2.21 (b(z, s(z))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[415, 9317])).
% 2.03/2.21 tff(9319,plain,
% 2.03/2.21 (~b(s(s(s(elem!1))), z)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[8768, 128, 9318, 7825, 2718])).
% 2.03/2.21 tff(9320,plain,
% 2.03/2.21 (r(s(s(s(elem!1))), z)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[5301, 9319])).
% 2.03/2.21 tff(9321,plain,
% 2.03/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(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(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z)))),
% 2.03/2.21 inference(rewrite,[status(thm)],[])).
% 2.03/2.21 tff(9322,plain,
% 2.03/2.21 (((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z)))),
% 2.03/2.21 inference(rewrite,[status(thm)],[])).
% 2.03/2.21 tff(9323,plain,
% 2.03/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[9322])).
% 2.03/2.21 tff(9324,plain,
% 2.03/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z)))),
% 2.03/2.21 inference(transitivity,[status(thm)],[9323, 9321])).
% 2.03/2.21 tff(9325,plain,
% 2.03/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.03/2.21 inference(quant_inst,[status(thm)],[])).
% 2.03/2.21 tff(9326,plain,
% 2.03/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[9325, 9324])).
% 2.03/2.21 tff(9327,plain,
% 2.03/2.21 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[9326, 45, 9320, 28])).
% 2.03/2.21 tff(9328,plain,
% 2.03/2.21 ((s(s(z)) = s(s(s(elem!1)))) | b(s(s(z)), s(s(s(elem!1))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[4283, 21, 9327])).
% 2.03/2.21 tff(9329,plain,
% 2.03/2.21 (b(s(s(z)), s(s(s(elem!1))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[9328, 4271])).
% 2.03/2.21 tff(9330,plain,
% 2.03/2.21 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[8789, 9318, 2718, 2073])).
% 2.03/2.21 tff(9331,plain,
% 2.03/2.21 (r(s(s(s(s(elem!1)))), s(z))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1828, 9330])).
% 2.03/2.21 tff(9332,plain,
% 2.03/2.21 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[2141, 9331, 325])).
% 2.03/2.21 tff(9333,plain,
% 2.03/2.21 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1897, 9332, 2023])).
% 2.03/2.21 tff(9334,plain,
% 2.03/2.21 (~b(z, s(s(s(elem!1))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[8605, 128, 9318, 7825, 2718])).
% 2.03/2.21 tff(9335,plain,
% 2.03/2.21 (r(z, s(s(s(elem!1))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[858, 9334])).
% 2.03/2.21 tff(9336,plain,
% 2.03/2.21 (~r(z, s(s(elem!1)))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[438, 324, 325])).
% 2.03/2.21 tff(9337,plain,
% 2.03/2.21 (b(z, s(s(elem!1)))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[160, 9336])).
% 2.03/2.21 tff(9338,plain,
% 2.03/2.21 (~r(s(s(elem!1)), z)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[4572, 45, 324, 424])).
% 2.03/2.21 tff(9339,plain,
% 2.03/2.21 (b(s(s(elem!1)), z)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[2018, 21, 154, 9338])).
% 2.03/2.21 tff(9340,plain,
% 2.03/2.21 (~b(s(s(s(s(elem!1)))), z)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[2092, 9339, 2084, 9337])).
% 2.03/2.21 tff(9341,plain,
% 2.03/2.21 (r(s(s(s(s(elem!1)))), z)),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[2081, 9340])).
% 2.03/2.21 tff(9342,plain,
% 2.03/2.21 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1780, 9341, 520])).
% 2.03/2.21 tff(9343,plain,
% 2.03/2.21 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1820, 9342, 712])).
% 2.03/2.21 tff(9344,plain,
% 2.03/2.21 (b(s(z), s(s(s(elem!1))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[339, 396])).
% 2.03/2.21 tff(9345,plain,
% 2.03/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.03/2.21 inference(rewrite,[status(thm)],[])).
% 2.03/2.21 tff(9346,plain,
% 2.03/2.21 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.03/2.21 inference(rewrite,[status(thm)],[])).
% 2.03/2.21 tff(9347,plain,
% 2.03/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z))))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[9346])).
% 2.03/2.21 tff(9348,plain,
% 2.03/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.03/2.21 inference(transitivity,[status(thm)],[9347, 9345])).
% 2.03/2.21 tff(9349,plain,
% 2.03/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.03/2.21 inference(quant_inst,[status(thm)],[])).
% 2.03/2.21 tff(9350,plain,
% 2.03/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[9349, 9348])).
% 2.03/2.21 tff(9351,plain,
% 2.03/2.21 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[9350, 128, 9344, 9343, 2718, 8557])).
% 2.03/2.21 tff(9352,plain,
% 2.03/2.21 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[4377, 45, 1737, 35])).
% 2.03/2.21 tff(9353,plain,
% 2.03/2.21 ($false),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[4309, 21, 239, 9352, 9351])).
% 2.03/2.21 tff(9354,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(z)), s(z))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.21 tff(9355,plain,
% 2.03/2.21 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[9354, 9329, 2718, 9331, 35, 2073, 9320, 9333, 9335, 325])).
% 2.03/2.21 tff(9356,plain,
% 2.03/2.21 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[321, 9355, 2024])).
% 2.03/2.21 tff(9357,plain,
% 2.03/2.21 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[7309, 45, 1737, 385])).
% 2.03/2.21 tff(9358,plain,
% 2.03/2.21 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1820, 9357, 712])).
% 2.03/2.21 tff(9359,plain,
% 2.03/2.21 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[889, 7276, 1691])).
% 2.03/2.21 tff(9360,plain,
% 2.03/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.03/2.21 inference(rewrite,[status(thm)],[])).
% 2.03/2.21 tff(9361,plain,
% 2.03/2.21 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.03/2.21 inference(rewrite,[status(thm)],[])).
% 2.03/2.21 tff(9362,plain,
% 2.03/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[9361])).
% 2.03/2.21 tff(9363,plain,
% 2.03/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.03/2.21 inference(transitivity,[status(thm)],[9362, 9360])).
% 2.03/2.21 tff(9364,plain,
% 2.03/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.03/2.21 inference(quant_inst,[status(thm)],[])).
% 2.03/2.21 tff(9365,plain,
% 2.03/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[9364, 9363])).
% 2.03/2.21 tff(9366,plain,
% 2.03/2.21 ($false),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[9365, 128, 2106, 9359, 9358, 4293])).
% 2.03/2.21 tff(9367,plain,((~r(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (s(s(s(elem!1))) = s(s(elem!1))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.21 tff(9368,plain,
% 2.03/2.21 (~r(s(s(s(elem!1))), s(z))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[9367, 2525, 2106, 1691, 712, 325, 1737])).
% 2.03/2.21 tff(9369,plain,
% 2.03/2.21 (b(s(s(s(elem!1))), s(z))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[195, 9368, 191])).
% 2.03/2.21 tff(9370,plain,
% 2.03/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.03/2.21 inference(rewrite,[status(thm)],[])).
% 2.03/2.21 tff(9371,plain,
% 2.03/2.21 (((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.03/2.21 inference(rewrite,[status(thm)],[])).
% 2.03/2.21 tff(9372,plain,
% 2.03/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[9371])).
% 2.03/2.21 tff(9373,plain,
% 2.03/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.03/2.21 inference(transitivity,[status(thm)],[9372, 9370])).
% 2.03/2.21 tff(9374,plain,
% 2.03/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.03/2.21 inference(quant_inst,[status(thm)],[])).
% 2.03/2.21 tff(9375,plain,
% 2.03/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[9374, 9373])).
% 2.03/2.21 tff(9376,plain,
% 2.03/2.21 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[9375, 128, 876, 2106, 9369, 2084])).
% 2.03/2.21 tff(9377,plain,
% 2.03/2.21 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1820, 9376, 712])).
% 2.03/2.21 tff(9378,plain,
% 2.03/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 2.03/2.21 inference(rewrite,[status(thm)],[])).
% 2.03/2.21 tff(9379,plain,
% 2.03/2.21 (((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1))))))) <=> ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 2.03/2.21 inference(rewrite,[status(thm)],[])).
% 2.03/2.21 tff(9380,plain,
% 2.03/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[9379])).
% 2.03/2.21 tff(9381,plain,
% 2.03/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 2.03/2.21 inference(transitivity,[status(thm)],[9380, 9378])).
% 2.03/2.21 tff(9382,plain,
% 2.03/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 2.03/2.21 inference(quant_inst,[status(thm)],[])).
% 2.03/2.21 tff(9383,plain,
% 2.03/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[9382, 9381])).
% 2.03/2.21 tff(9384,plain,
% 2.03/2.21 ($false),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[9383, 45, 2534, 323, 9377])).
% 2.03/2.21 tff(9385,plain,((~b(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (s(s(elem!1)) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.21 tff(9386,plain,
% 2.03/2.21 (~b(s(z), s(s(elem!1)))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[9385, 323, 712, 2106, 2084, 1691, 325, 1737, 1069])).
% 2.03/2.21 tff(9387,plain,
% 2.03/2.21 (r(s(z), s(s(elem!1)))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[117, 9386])).
% 2.03/2.21 tff(9388,plain,
% 2.03/2.21 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1802, 9387, 323])).
% 2.03/2.21 tff(9389,plain,
% 2.03/2.21 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[889, 9388, 1691])).
% 2.03/2.21 tff(9390,plain,
% 2.03/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.03/2.21 inference(rewrite,[status(thm)],[])).
% 2.03/2.21 tff(9391,plain,
% 2.03/2.21 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.03/2.21 inference(rewrite,[status(thm)],[])).
% 2.03/2.21 tff(9392,plain,
% 2.03/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 2.03/2.21 inference(monotonicity,[status(thm)],[9391])).
% 2.03/2.21 tff(9393,plain,
% 2.03/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.03/2.21 inference(transitivity,[status(thm)],[9392, 9390])).
% 2.03/2.21 tff(9394,plain,
% 2.03/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.03/2.21 inference(quant_inst,[status(thm)],[])).
% 2.03/2.21 tff(9395,plain,
% 2.03/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 2.03/2.21 inference(modus_ponens,[status(thm)],[9394, 9393])).
% 2.03/2.21 tff(9396,plain,
% 2.03/2.21 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[9395, 128, 2106, 9389, 2084])).
% 2.03/2.21 tff(9397,plain,
% 2.03/2.21 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.03/2.21 inference(unit_resolution,[status(thm)],[1820, 9396, 712])).
% 2.03/2.21 tff(9398,plain,
% 2.03/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 2.03/2.21 inference(rewrite,[status(thm)],[])).
% 2.03/2.21 tff(9399,plain,
% 2.03/2.21 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z)))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 2.03/2.21 inference(rewrite,[status(thm)],[])).
% 2.03/2.21 tff(9400,plain,
% 2.03/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[9399])).
% 2.03/2.22 tff(9401,plain,
% 2.03/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 2.03/2.22 inference(transitivity,[status(thm)],[9400, 9398])).
% 2.03/2.22 tff(9402,plain,
% 2.03/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 2.03/2.22 inference(quant_inst,[status(thm)],[])).
% 2.03/2.22 tff(9403,plain,
% 2.03/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[9402, 9401])).
% 2.03/2.22 tff(9404,plain,
% 2.03/2.22 ($false),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[9403, 45, 9387, 1737, 323, 9397])).
% 2.03/2.22 tff(9405,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (s(s(elem!1)) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.22 tff(9406,plain,
% 2.03/2.22 (~r(s(z), s(s(s(elem!1))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[9405, 9356, 325, 9333, 2073, 2025, 9331, 1069])).
% 2.03/2.22 tff(9407,plain,
% 2.03/2.22 (b(s(z), s(s(s(elem!1))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[339, 9406])).
% 2.03/2.22 tff(9408,plain,
% 2.03/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(9409,plain,
% 2.03/2.22 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(9410,plain,
% 2.03/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1))))))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[9409])).
% 2.03/2.22 tff(9411,plain,
% 2.03/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.03/2.22 inference(transitivity,[status(thm)],[9410, 9408])).
% 2.03/2.22 tff(9412,plain,
% 2.03/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.03/2.22 inference(quant_inst,[status(thm)],[])).
% 2.03/2.22 tff(9413,plain,
% 2.03/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1))))),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[9412, 9411])).
% 2.03/2.22 tff(9414,plain,
% 2.03/2.22 (~b(s(s(z)), s(s(elem!1)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[9413, 128, 9356, 9407, 2718, 9329])).
% 2.03/2.22 tff(9415,plain,
% 2.03/2.22 (~r(s(s(z)), s(s(elem!1)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[4431, 45, 325, 35])).
% 2.03/2.22 tff(9416,plain,
% 2.03/2.22 ((s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[138, 21, 9415])).
% 2.03/2.22 tff(9417,plain,
% 2.03/2.22 (s(s(z)) = s(s(elem!1))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[9416, 9414])).
% 2.03/2.22 tff(9418,plain,
% 2.03/2.22 (s(s(elem!1)) = s(s(z))),
% 2.03/2.22 inference(symmetry,[status(thm)],[9417])).
% 2.03/2.22 tff(9419,plain,
% 2.03/2.22 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[9417])).
% 2.03/2.22 tff(9420,plain,
% 2.03/2.22 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[9419])).
% 2.03/2.22 tff(9421,plain,
% 2.03/2.22 (s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[9420])).
% 2.03/2.22 tff(9422,plain,
% 2.03/2.22 (s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(elem!1))))))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[9421])).
% 2.03/2.22 tff(9423,plain,
% 2.03/2.22 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z))))))),
% 2.03/2.22 inference(symmetry,[status(thm)],[9422])).
% 2.03/2.22 tff(9424,plain,
% 2.03/2.22 ((s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) <=> (s(s(s(s(s(s(z)))))) = s(s(z)))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[9423, 9418])).
% 2.03/2.22 tff(9425,plain,
% 2.03/2.22 ((s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) <=> (s(s(z)) = s(s(s(s(s(s(z)))))))),
% 2.03/2.22 inference(transitivity,[status(thm)],[9424, 1113])).
% 2.03/2.22 tff(9426,plain,
% 2.03/2.22 ((s(s(z)) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 2.03/2.22 inference(symmetry,[status(thm)],[9425])).
% 2.03/2.22 tff(9427,plain,
% 2.03/2.22 ((~(s(s(z)) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[9426])).
% 2.03/2.22 tff(9428,plain,
% 2.03/2.22 (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[1123, 9427])).
% 2.03/2.22 tff(9429,plain,
% 2.03/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(9430,plain,
% 2.03/2.22 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(9431,plain,
% 2.03/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z))))))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[9430])).
% 2.03/2.22 tff(9432,plain,
% 2.03/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.03/2.22 inference(transitivity,[status(thm)],[9431, 9429])).
% 2.03/2.22 tff(9433,plain,
% 2.03/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.03/2.22 inference(quant_inst,[status(thm)],[])).
% 2.03/2.22 tff(9434,plain,
% 2.03/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z))))),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[9433, 9432])).
% 2.03/2.22 tff(9435,plain,
% 2.03/2.22 (~b(s(s(elem!1)), s(s(z)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[9434, 128, 9356, 9407, 2718, 9329])).
% 2.03/2.22 tff(9436,plain,
% 2.03/2.22 (~r(s(s(elem!1)), s(s(z)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[5461, 45, 325, 35])).
% 2.03/2.22 tff(9437,plain,
% 2.03/2.22 ((s(s(elem!1)) = s(s(z))) | b(s(s(elem!1)), s(s(z)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[4339, 21, 9436])).
% 2.03/2.22 tff(9438,plain,
% 2.03/2.22 (s(s(elem!1)) = s(s(z))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[9437, 9435])).
% 2.03/2.22 tff(9439,plain,
% 2.03/2.22 (z = elem!1),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[4260, 9438])).
% 2.03/2.22 tff(9440,plain,
% 2.03/2.22 ((s(s(s(s(s(s(z)))))) = z) <=> (s(s(s(s(s(s(z)))))) = elem!1)),
% 2.03/2.22 inference(monotonicity,[status(thm)],[9439])).
% 2.03/2.22 tff(9441,plain,
% 2.03/2.22 ((~(s(s(s(s(s(s(z)))))) = z)) <=> (~(s(s(s(s(s(s(z)))))) = elem!1))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[9440])).
% 2.03/2.22 tff(9442,plain,
% 2.03/2.22 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[1019, 9441])).
% 2.03/2.22 tff(9443,plain,
% 2.03/2.22 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[9417])).
% 2.03/2.22 tff(9444,plain,
% 2.03/2.22 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 2.03/2.22 inference(symmetry,[status(thm)],[9443])).
% 2.03/2.22 tff(9445,plain,
% 2.03/2.22 (s(elem!1) = s(z)),
% 2.03/2.22 inference(transitivity,[status(thm)],[106, 9444, 69])).
% 2.03/2.22 tff(9446,plain,
% 2.03/2.22 (b(s(elem!1), elem!1) <=> b(s(z), elem!1)),
% 2.03/2.22 inference(monotonicity,[status(thm)],[9445])).
% 2.03/2.22 tff(9447,plain,
% 2.03/2.22 (b(s(z), elem!1) <=> b(s(elem!1), elem!1)),
% 2.03/2.22 inference(symmetry,[status(thm)],[9446])).
% 2.03/2.22 tff(9448,plain,
% 2.03/2.22 (b(s(z), z) <=> b(s(z), elem!1)),
% 2.03/2.22 inference(monotonicity,[status(thm)],[9439])).
% 2.03/2.22 tff(9449,plain,
% 2.03/2.22 (b(s(z), elem!1)),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[7825, 9448])).
% 2.03/2.22 tff(9450,plain,
% 2.03/2.22 (b(s(elem!1), elem!1)),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[9449, 9447])).
% 2.03/2.22 tff(9451,plain,
% 2.03/2.22 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 2.03/2.22 inference(monotonicity,[status(thm)],[9439])).
% 2.03/2.22 tff(9452,plain,
% 2.03/2.22 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[9293, 325, 3527, 550])).
% 2.03/2.22 tff(9453,plain,
% 2.03/2.22 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[693, 9452])).
% 2.03/2.22 tff(9454,plain,
% 2.03/2.22 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[700, 9453])).
% 2.03/2.22 tff(9455,plain,
% 2.03/2.22 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[8788, 2718, 3527, 9454, 550])).
% 2.03/2.22 tff(9456,plain,
% 2.03/2.22 (r(s(s(s(s(elem!1)))), s(z))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[1828, 9455])).
% 2.03/2.22 tff(9457,plain,
% 2.03/2.22 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[2141, 9456, 325])).
% 2.03/2.22 tff(9458,plain,
% 2.03/2.22 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[1897, 9457, 2023])).
% 2.03/2.22 tff(9459,plain,
% 2.03/2.22 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[803, 9452])).
% 2.03/2.22 tff(9460,plain,
% 2.03/2.22 (~r(s(z), s(s(s(elem!1))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[9405, 9458, 2106, 9454, 9456, 9459, 325, 1069])).
% 2.03/2.22 tff(9461,plain,
% 2.03/2.22 (b(s(z), s(s(s(elem!1))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[339, 9460])).
% 2.03/2.22 tff(9462,plain,
% 2.03/2.22 ($false),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[5853, 128, 2106, 9461, 1842, 2718, 9458])).
% 2.03/2.22 tff(9463,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.22 tff(9464,plain,
% 2.03/2.22 ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~b(z, s(z)))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[9463, 7825])).
% 2.03/2.22 tff(9465,plain,
% 2.03/2.22 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[9464, 9356, 2718, 325, 1069, 9318])).
% 2.03/2.22 tff(9466,plain,
% 2.03/2.22 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[1820, 9465, 2073])).
% 2.03/2.22 tff(9467,plain,
% 2.03/2.22 (~r(s(s(s(s(elem!1)))), z)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[1780, 9466, 9320])).
% 2.03/2.22 tff(9468,plain,
% 2.03/2.22 (b(s(s(s(s(elem!1)))), z)),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[2081, 9467])).
% 2.03/2.22 tff(9469,plain,
% 2.03/2.22 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[9468, 9451])).
% 2.03/2.22 tff(9470,plain,
% 2.03/2.22 (elem!1 = z),
% 2.03/2.22 inference(symmetry,[status(thm)],[9439])).
% 2.03/2.22 tff(9471,plain,
% 2.03/2.22 ((elem!1 = s(s(s(s(elem!1))))) <=> (z = s(s(s(s(elem!1)))))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[9470])).
% 2.03/2.22 tff(9472,plain,
% 2.03/2.22 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = z)),
% 2.03/2.22 inference(transitivity,[status(thm)],[9471, 1694])).
% 2.03/2.22 tff(9473,plain,
% 2.03/2.22 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 2.03/2.22 inference(symmetry,[status(thm)],[9472])).
% 2.03/2.22 tff(9474,plain,
% 2.03/2.22 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[9473])).
% 2.03/2.22 tff(9475,plain,
% 2.03/2.22 (~(elem!1 = s(s(s(s(elem!1)))))),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[176, 9474])).
% 2.03/2.22 tff(9476,plain,
% 2.03/2.22 (r(z, s(s(s(s(elem!1))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[9439])).
% 2.03/2.22 tff(9477,plain,
% 2.03/2.22 ((~r(z, s(s(s(s(elem!1)))))) <=> (~r(elem!1, s(s(s(s(elem!1))))))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[9476])).
% 2.03/2.22 tff(9478,plain,
% 2.03/2.22 (~r(z, s(s(s(s(elem!1)))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[1790, 9466, 9335])).
% 2.03/2.22 tff(9479,plain,
% 2.03/2.22 (~r(elem!1, s(s(s(s(elem!1)))))),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[9478, 9477])).
% 2.03/2.22 tff(9480,plain,
% 2.03/2.22 (b(elem!1, s(s(s(s(elem!1)))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[1766, 9479, 9475])).
% 2.03/2.22 tff(9481,plain,
% 2.03/2.22 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1)))))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[3124, 9439])).
% 2.03/2.22 tff(9482,plain,
% 2.03/2.22 (~(s(elem!1) = s(s(s(s(s(s(elem!1)))))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[3337, 9439])).
% 2.03/2.22 tff(9483,plain,
% 2.03/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(9484,plain,
% 2.03/2.22 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(9485,plain,
% 2.03/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[9484])).
% 2.03/2.22 tff(9486,plain,
% 2.03/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.03/2.22 inference(transitivity,[status(thm)],[9485, 9483])).
% 2.03/2.22 tff(9487,plain,
% 2.03/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.03/2.22 inference(quant_inst,[status(thm)],[])).
% 2.03/2.22 tff(9488,plain,
% 2.03/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1))))))),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[9487, 9486])).
% 2.03/2.22 tff(9489,plain,
% 2.03/2.22 (~b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[9488, 128, 9480, 9469, 9450])).
% 2.03/2.22 tff(9490,plain,
% 2.03/2.22 (s(z) = s(elem!1)),
% 2.03/2.22 inference(transitivity,[status(thm)],[70, 9443, 105])).
% 2.03/2.22 tff(9491,plain,
% 2.03/2.22 ((s(s(s(s(elem!1)))) = s(z)) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[9490])).
% 2.03/2.22 tff(9492,plain,
% 2.03/2.22 ((s(s(s(s(elem!1)))) = s(z)) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 2.03/2.22 inference(transitivity,[status(thm)],[9491, 1712])).
% 2.03/2.22 tff(9493,plain,
% 2.03/2.22 ((~(s(s(s(s(elem!1)))) = s(z))) <=> (~(s(elem!1) = s(s(s(s(elem!1))))))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[9492])).
% 2.03/2.22 tff(9494,plain,
% 2.03/2.22 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[1723, 9493])).
% 2.03/2.22 tff(9495,plain,
% 2.03/2.22 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[1727, 21, 9494, 9489])).
% 2.03/2.22 tff(9496,assumption,(b(elem!1, s(s(s(s(elem!1)))))), introduced(assumption)).
% 2.03/2.22 tff(9497,plain,
% 2.03/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(9498,plain,
% 2.03/2.22 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(9499,plain,
% 2.03/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(elem!1))))))))))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[9498])).
% 2.03/2.22 tff(9500,plain,
% 2.03/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))))),
% 2.03/2.22 inference(transitivity,[status(thm)],[9499, 9497])).
% 2.03/2.22 tff(9501,plain,
% 2.03/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))))),
% 2.03/2.22 inference(quant_inst,[status(thm)],[])).
% 2.03/2.22 tff(9502,plain,
% 2.03/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(elem!1))))))))),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[9501, 9500])).
% 2.03/2.22 tff(9503,plain,
% 2.03/2.22 (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[9502, 128, 9496, 2656, 4791, 3239])).
% 2.03/2.22 tff(9504,plain,
% 2.03/2.22 (r(s(elem!1), s(s(s(s(s(s(elem!1)))))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[3341, 21, 3400, 9503])).
% 2.03/2.22 tff(9505,plain,
% 2.03/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(9506,plain,
% 2.03/2.22 (((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))),
% 2.03/2.22 inference(rewrite,[status(thm)],[])).
% 2.03/2.22 tff(9507,plain,
% 2.03/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))))))),
% 2.03/2.22 inference(monotonicity,[status(thm)],[9506])).
% 2.03/2.22 tff(9508,plain,
% 2.03/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))),
% 2.03/2.22 inference(transitivity,[status(thm)],[9507, 9505])).
% 2.03/2.22 tff(9509,plain,
% 2.03/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))),
% 2.03/2.22 inference(quant_inst,[status(thm)],[])).
% 2.03/2.22 tff(9510,plain,
% 2.03/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))))),
% 2.03/2.22 inference(modus_ponens,[status(thm)],[9509, 9508])).
% 2.03/2.22 tff(9511,plain,
% 2.03/2.22 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[9510, 128, 9496, 2084, 2656, 3239])).
% 2.03/2.22 tff(9512,plain,
% 2.03/2.22 (r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))),
% 2.03/2.22 inference(unit_resolution,[status(thm)],[3969, 21, 3391, 9511])).
% 2.03/2.23 tff(9513,assumption,(r(s(elem!1), s(s(s(s(elem!1)))))), introduced(assumption)).
% 2.03/2.23 tff(9514,plain,
% 2.03/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))))),
% 2.03/2.23 inference(rewrite,[status(thm)],[])).
% 2.03/2.23 tff(9515,plain,
% 2.03/2.23 (((~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))))),
% 2.03/2.23 inference(rewrite,[status(thm)],[])).
% 2.03/2.23 tff(9516,plain,
% 2.03/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(elem!1), s(s(s(s(s(s(elem!1))))))))))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[9515])).
% 2.03/2.23 tff(9517,plain,
% 2.03/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))))),
% 2.03/2.23 inference(transitivity,[status(thm)],[9516, 9514])).
% 2.03/2.23 tff(9518,plain,
% 2.03/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 2.03/2.23 inference(quant_inst,[status(thm)],[])).
% 2.03/2.23 tff(9519,plain,
% 2.03/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(elem!1), s(s(s(s(s(s(elem!1))))))))),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[9518, 9517])).
% 2.03/2.23 tff(9520,plain,
% 2.03/2.23 ($false),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[9519, 45, 9513, 9512, 9504])).
% 2.03/2.23 tff(9521,plain,((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (s(elem!1) = s(s(s(s(s(s(elem!1))))))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1))))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.23 tff(9522,plain,
% 2.03/2.23 (~b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[9521, 9495, 9482, 9481, 9480, 9469, 9450, 9333])).
% 2.03/2.23 tff(9523,plain,
% 2.03/2.23 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[3304, 9522, 9439])).
% 2.03/2.23 tff(9524,plain,
% 2.03/2.23 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[1055, 9523, 9442])).
% 2.03/2.23 tff(9525,plain,
% 2.03/2.23 (r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[3926, 9524, 9439])).
% 2.03/2.23 tff(9526,plain,
% 2.03/2.23 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 2.03/2.23 inference(monotonicity,[status(thm)],[9439])).
% 2.03/2.23 tff(9527,plain,
% 2.03/2.23 (r(s(s(z)), z) <=> r(s(s(elem!1)), z)),
% 2.03/2.23 inference(monotonicity,[status(thm)],[9417])).
% 2.03/2.23 tff(9528,plain,
% 2.03/2.23 (r(s(s(elem!1)), z)),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[28, 9527])).
% 2.03/2.23 tff(9529,plain,
% 2.03/2.23 (r(s(s(elem!1)), elem!1)),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[9528, 9526])).
% 2.03/2.23 tff(9530,plain,
% 2.03/2.23 (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[3899, 45, 9529, 9525])).
% 2.03/2.23 tff(9531,plain,
% 2.03/2.23 ((s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[3269, 21, 9530])).
% 2.03/2.23 tff(9532,plain,
% 2.03/2.23 (b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[9531, 9428])).
% 2.03/2.23 tff(9533,plain,
% 2.03/2.23 (r(s(s(s(elem!1))), elem!1)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[2558, 9439, 9320])).
% 2.03/2.23 tff(9534,plain,
% 2.03/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))),
% 2.03/2.23 inference(rewrite,[status(thm)],[])).
% 2.03/2.23 tff(9535,plain,
% 2.03/2.23 (((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))),
% 2.03/2.23 inference(rewrite,[status(thm)],[])).
% 2.03/2.23 tff(9536,plain,
% 2.03/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1))))))))))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[9535])).
% 2.03/2.23 tff(9537,plain,
% 2.03/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))),
% 2.03/2.23 inference(transitivity,[status(thm)],[9536, 9534])).
% 2.03/2.23 tff(9538,plain,
% 2.03/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))),
% 2.03/2.23 inference(quant_inst,[status(thm)],[])).
% 2.03/2.23 tff(9539,plain,
% 2.03/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1))))))))),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[9538, 9537])).
% 2.03/2.23 tff(9540,plain,
% 2.03/2.23 (~r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[9539, 45, 9533, 9525])).
% 2.03/2.23 tff(9541,plain,
% 2.03/2.23 (~(s(s(s(elem!1))) = s(s(s(s(s(s(elem!1)))))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[3236, 9494])).
% 2.03/2.23 tff(9542,plain,
% 2.03/2.23 (b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[3980, 21, 9541, 9540])).
% 2.03/2.23 tff(9543,plain,
% 2.03/2.23 ((s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(z)) = s(s(s(s(s(s(z)))))))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[9418, 9423])).
% 2.03/2.23 tff(9544,plain,
% 2.03/2.23 ((s(s(z)) = s(s(s(s(s(s(z))))))) <=> (s(s(elem!1)) = s(s(s(s(s(s(elem!1)))))))),
% 2.03/2.23 inference(symmetry,[status(thm)],[9543])).
% 2.03/2.23 tff(9545,plain,
% 2.03/2.23 ((~(s(s(z)) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[9544])).
% 2.03/2.23 tff(9546,plain,
% 2.03/2.23 (~(s(s(elem!1)) = s(s(s(s(s(s(elem!1)))))))),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[1123, 9545])).
% 2.03/2.23 tff(9547,plain,
% 2.03/2.23 (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[3909, 45, 9529, 9525])).
% 2.03/2.23 tff(9548,plain,
% 2.03/2.23 ((s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) | b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[3287, 21, 9547])).
% 2.03/2.23 tff(9549,plain,
% 2.03/2.23 (b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[9548, 9546])).
% 2.03/2.23 tff(9550,plain,
% 2.03/2.23 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[9417])).
% 2.03/2.23 tff(9551,plain,
% 2.03/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), z)))),
% 2.03/2.23 inference(rewrite,[status(thm)],[])).
% 2.03/2.23 tff(9552,plain,
% 2.03/2.23 (((~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), z)))),
% 2.03/2.23 inference(rewrite,[status(thm)],[])).
% 2.03/2.23 tff(9553,plain,
% 2.03/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), z))))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[9552])).
% 2.03/2.23 tff(9554,plain,
% 2.03/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), z)))),
% 2.03/2.23 inference(transitivity,[status(thm)],[9553, 9551])).
% 2.03/2.23 tff(9555,plain,
% 2.03/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.03/2.23 inference(quant_inst,[status(thm)],[])).
% 2.03/2.23 tff(9556,plain,
% 2.03/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), z))),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[9555, 9554])).
% 2.03/2.23 tff(9557,plain,
% 2.03/2.23 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[9556, 45, 9320, 35, 28])).
% 2.03/2.23 tff(9558,plain,
% 2.03/2.23 (b(s(s(s(elem!1))), s(s(z)))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[4350, 21, 9557, 283])).
% 2.03/2.23 tff(9559,plain,
% 2.03/2.23 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[9558, 9550])).
% 2.03/2.23 tff(9560,plain,
% 2.03/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 2.03/2.23 inference(rewrite,[status(thm)],[])).
% 2.03/2.23 tff(9561,plain,
% 2.03/2.23 (((~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 2.03/2.23 inference(rewrite,[status(thm)],[])).
% 2.03/2.23 tff(9562,plain,
% 2.03/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[9561])).
% 2.03/2.23 tff(9563,plain,
% 2.03/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 2.03/2.23 inference(transitivity,[status(thm)],[9562, 9560])).
% 2.03/2.23 tff(9564,plain,
% 2.03/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.03/2.23 inference(quant_inst,[status(thm)],[])).
% 2.03/2.23 tff(9565,plain,
% 2.03/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[9564, 9563])).
% 2.03/2.23 tff(9566,plain,
% 2.03/2.23 ($false),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[9565, 128, 9559, 9549, 9542, 9532])).
% 2.03/2.23 tff(9567,plain,((~r(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.23 tff(9568,plain,
% 2.03/2.23 (~r(s(s(z)), s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[9567, 2718, 28, 325, 1069])).
% 2.03/2.23 tff(9569,plain,
% 2.03/2.23 (b(s(s(z)), s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[86, 9568])).
% 2.03/2.23 tff(9570,plain,
% 2.03/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.03/2.23 inference(rewrite,[status(thm)],[])).
% 2.03/2.23 tff(9571,plain,
% 2.03/2.23 (((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.03/2.23 inference(rewrite,[status(thm)],[])).
% 2.03/2.23 tff(9572,plain,
% 2.03/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[9571])).
% 2.03/2.23 tff(9573,plain,
% 2.03/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.03/2.23 inference(transitivity,[status(thm)],[9572, 9570])).
% 2.03/2.23 tff(9574,plain,
% 2.03/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.03/2.23 inference(quant_inst,[status(thm)],[])).
% 2.03/2.23 tff(9575,plain,
% 2.03/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[9574, 9573])).
% 2.03/2.23 tff(9576,plain,
% 2.03/2.23 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[9575, 128, 550, 7825, 2718, 9569])).
% 2.03/2.23 tff(9577,plain,
% 2.03/2.23 (~b(s(s(s(elem!1))), z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[8768, 128, 550, 7825, 2718])).
% 2.03/2.23 tff(9578,plain,
% 2.03/2.23 (r(s(s(s(elem!1))), z)),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[5301, 9577])).
% 2.03/2.23 tff(9579,plain,
% 2.03/2.23 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[693, 9315])).
% 2.03/2.23 tff(9580,plain,
% 2.03/2.23 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[700, 9579])).
% 2.03/2.23 tff(9581,plain,
% 2.03/2.23 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[8789, 2718, 550, 9580])).
% 2.03/2.23 tff(9582,plain,
% 2.03/2.23 (r(s(s(s(s(elem!1)))), s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[1828, 9581])).
% 2.03/2.23 tff(9583,plain,
% 2.03/2.23 (~r(s(z), s(s(s(elem!1))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[9405, 9582, 325, 2106, 9580, 9316, 2084, 1069])).
% 2.03/2.23 tff(9584,plain,
% 2.03/2.23 (b(s(z), s(s(s(elem!1))))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[339, 9583])).
% 2.03/2.23 tff(9585,plain,
% 2.03/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 2.03/2.23 inference(rewrite,[status(thm)],[])).
% 2.03/2.23 tff(9586,plain,
% 2.03/2.23 (((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z))))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 2.03/2.23 inference(rewrite,[status(thm)],[])).
% 2.03/2.23 tff(9587,plain,
% 2.03/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z))))))),
% 2.03/2.23 inference(monotonicity,[status(thm)],[9586])).
% 2.03/2.23 tff(9588,plain,
% 2.03/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 2.03/2.23 inference(transitivity,[status(thm)],[9587, 9585])).
% 2.03/2.23 tff(9589,plain,
% 2.03/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))),
% 2.03/2.23 inference(quant_inst,[status(thm)],[])).
% 2.03/2.23 tff(9590,plain,
% 2.03/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z))))),
% 2.03/2.23 inference(modus_ponens,[status(thm)],[9589, 9588])).
% 2.03/2.23 tff(9591,plain,
% 2.03/2.23 (~b(z, s(s(z)))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[9590, 128, 550, 9584, 2718, 9569])).
% 2.03/2.23 tff(9592,plain,
% 2.03/2.23 (r(z, s(s(z)))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[516, 9591])).
% 2.03/2.23 tff(9593,plain,
% 2.03/2.23 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[528, 9592, 9578])).
% 2.03/2.23 tff(9594,plain,
% 2.03/2.23 ($false),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[4350, 21, 9593, 9576, 283])).
% 2.03/2.23 tff(9595,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.23 tff(9596,plain,
% 2.03/2.23 (~b(s(s(s(elem!1))), s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[9595, 9302, 325, 2106, 550, 1069, 28])).
% 2.03/2.23 tff(9597,plain,
% 2.03/2.23 (r(s(s(s(elem!1))), s(z))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[196, 9596])).
% 2.03/2.23 tff(9598,plain,
% 2.03/2.23 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[7275, 45, 325, 9597])).
% 2.03/2.23 tff(9599,plain,
% 2.03/2.23 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.03/2.23 inference(unit_resolution,[status(thm)],[889, 9598, 9316])).
% 2.03/2.23 tff(9600,plain,
% 2.03/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(9601,plain,
% 2.03/2.24 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(9602,plain,
% 2.03/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[9601])).
% 2.03/2.24 tff(9603,plain,
% 2.03/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.03/2.24 inference(transitivity,[status(thm)],[9602, 9600])).
% 2.03/2.24 tff(9604,plain,
% 2.03/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.03/2.24 inference(quant_inst,[status(thm)],[])).
% 2.03/2.24 tff(9605,plain,
% 2.03/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[9604, 9603])).
% 2.03/2.24 tff(9606,plain,
% 2.03/2.24 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[9605, 128, 2106, 9599, 8523])).
% 2.03/2.24 tff(9607,plain,
% 2.03/2.24 (r(s(s(s(elem!1))), s(s(z)))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[4350, 21, 9606, 283])).
% 2.03/2.24 tff(9608,plain,
% 2.03/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(9609,plain,
% 2.03/2.24 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(9610,plain,
% 2.03/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[9609])).
% 2.03/2.24 tff(9611,plain,
% 2.03/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.03/2.24 inference(transitivity,[status(thm)],[9610, 9608])).
% 2.03/2.24 tff(9612,plain,
% 2.03/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.03/2.24 inference(quant_inst,[status(thm)],[])).
% 2.03/2.24 tff(9613,plain,
% 2.03/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[9612, 9611])).
% 2.03/2.24 tff(9614,plain,
% 2.03/2.24 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[9613, 128, 2106, 9599, 9302])).
% 2.03/2.24 tff(9615,plain,
% 2.03/2.24 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1856, 9614, 9579])).
% 2.03/2.24 tff(9616,plain,
% 2.03/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(9617,plain,
% 2.03/2.24 (((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z))))) <=> ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(9618,plain,
% 2.03/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(elem!1))))))))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[9617])).
% 2.03/2.24 tff(9619,plain,
% 2.03/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 2.03/2.24 inference(transitivity,[status(thm)],[9618, 9616])).
% 2.03/2.24 tff(9620,plain,
% 2.03/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.03/2.24 inference(quant_inst,[status(thm)],[])).
% 2.03/2.24 tff(9621,plain,
% 2.03/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(elem!1))))))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[9620, 9619])).
% 2.03/2.24 tff(9622,plain,
% 2.03/2.24 ($false),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[9621, 45, 9615, 28, 9607, 9314])).
% 2.03/2.24 tff(9623,plain,((s(s(elem!1)) = s(s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(s(z)))) | r(s(s(s(s(elem!1)))), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.24 tff(9624,plain,
% 2.03/2.24 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[9623, 9297, 28, 8521, 9028, 550, 8512, 9037])).
% 2.03/2.24 tff(9625,plain,
% 2.03/2.24 (s(s(elem!1)) = elem!1),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1089, 9624])).
% 2.03/2.24 tff(9626,plain,
% 2.03/2.24 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[245, 9625])).
% 2.03/2.24 tff(9627,plain,
% 2.03/2.24 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1055, 9626, 29])).
% 2.03/2.24 tff(9628,plain,
% 2.03/2.24 (b(s(s(elem!1)), s(s(z))) <=> b(elem!1, s(s(z)))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[9625])).
% 2.03/2.24 tff(9629,plain,
% 2.03/2.24 (b(elem!1, s(s(z)))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[8512, 9628])).
% 2.03/2.24 tff(9630,plain,
% 2.03/2.24 (b(s(s(z)), s(s(elem!1))) <=> b(s(s(z)), elem!1)),
% 2.03/2.24 inference(monotonicity,[status(thm)],[9625])).
% 2.03/2.24 tff(9631,plain,
% 2.03/2.24 (b(s(s(z)), elem!1)),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[8521, 9630])).
% 2.03/2.24 tff(9632,plain,
% 2.03/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(9633,plain,
% 2.03/2.24 (((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))) <=> ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(9634,plain,
% 2.03/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[9633])).
% 2.03/2.24 tff(9635,plain,
% 2.03/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 2.03/2.24 inference(transitivity,[status(thm)],[9634, 9632])).
% 2.03/2.24 tff(9636,plain,
% 2.03/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 2.03/2.24 inference(quant_inst,[status(thm)],[])).
% 2.03/2.24 tff(9637,plain,
% 2.03/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[9636, 9635])).
% 2.03/2.24 tff(9638,plain,
% 2.03/2.24 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[9637, 128, 9631, 9629, 9627])).
% 2.03/2.24 tff(9639,plain,
% 2.03/2.24 ((s(s(s(s(s(s(z)))))) = s(s(z))) | r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1134, 21, 9638])).
% 2.03/2.24 tff(9640,plain,
% 2.03/2.24 (r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[9639, 1124])).
% 2.03/2.24 tff(9641,plain,
% 2.03/2.24 (b(s(z), s(s(elem!1))) <=> b(s(z), elem!1)),
% 2.03/2.24 inference(monotonicity,[status(thm)],[9625])).
% 2.03/2.24 tff(9642,plain,
% 2.03/2.24 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[803, 9295])).
% 2.03/2.24 tff(9643,plain,
% 2.03/2.24 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), elem!1)),
% 2.03/2.24 inference(monotonicity,[status(thm)],[9625])).
% 2.03/2.24 tff(9644,plain,
% 2.03/2.24 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.03/2.24 inference(symmetry,[status(thm)],[9643])).
% 2.03/2.24 tff(9645,plain,
% 2.03/2.24 (s(s(s(elem!1))) = s(elem!1)),
% 2.03/2.24 inference(monotonicity,[status(thm)],[9625])).
% 2.03/2.24 tff(9646,plain,
% 2.03/2.24 (b(s(s(s(elem!1))), elem!1) <=> b(s(elem!1), elem!1)),
% 2.03/2.24 inference(monotonicity,[status(thm)],[9645])).
% 2.03/2.24 tff(9647,plain,
% 2.03/2.24 (b(s(elem!1), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 2.03/2.24 inference(symmetry,[status(thm)],[9646])).
% 2.03/2.24 tff(9648,plain,
% 2.03/2.24 (b(s(elem!1), elem!1) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.03/2.24 inference(transitivity,[status(thm)],[9647, 9644])).
% 2.03/2.24 tff(9649,plain,
% 2.03/2.24 ((~b(s(elem!1), elem!1)) <=> (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[9648])).
% 2.03/2.24 tff(9650,assumption,(s(s(s(s(s(s(z)))))) = s(elem!1)), introduced(assumption)).
% 2.03/2.24 tff(9651,plain,
% 2.03/2.24 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(elem!1))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[9650])).
% 2.03/2.24 tff(9652,plain,
% 2.03/2.24 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 2.03/2.24 inference(transitivity,[status(thm)],[208, 9651, 201, 202])).
% 2.03/2.24 tff(9653,plain,
% 2.03/2.24 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(elem!1)))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[9652])).
% 2.03/2.24 tff(9654,plain,
% 2.03/2.24 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(z))))))),
% 2.03/2.24 inference(symmetry,[status(thm)],[9653])).
% 2.03/2.24 tff(9655,plain,
% 2.03/2.24 (s(elem!1) = s(s(s(s(z))))),
% 2.03/2.24 inference(transitivity,[status(thm)],[106, 9654, 163])).
% 2.03/2.24 tff(9656,plain,
% 2.03/2.24 ($false),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[762, 9655])).
% 2.03/2.24 tff(9657,plain,((~(s(s(s(s(s(s(z)))))) = s(elem!1))) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.24 tff(9658,plain,
% 2.03/2.24 (~(s(s(s(s(s(s(z)))))) = s(elem!1))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[9657, 9625])).
% 2.03/2.24 tff(9659,plain,
% 2.03/2.24 ((s(s(s(elem!1))) = s(s(z))) <=> (s(elem!1) = s(s(z)))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[9645])).
% 2.03/2.24 tff(9660,plain,
% 2.03/2.24 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(elem!1) = s(s(z))))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[9659])).
% 2.03/2.24 tff(9661,plain,
% 2.03/2.24 (~(s(elem!1) = s(s(z)))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[283, 9660])).
% 2.03/2.24 tff(9662,plain,
% 2.03/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(9663,plain,
% 2.03/2.24 (((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(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(s(elem!1), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(9664,plain,
% 2.03/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1)))))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[9663])).
% 2.03/2.24 tff(9665,plain,
% 2.03/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 2.03/2.24 inference(transitivity,[status(thm)],[9664, 9662])).
% 2.03/2.24 tff(9666,plain,
% 2.03/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(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))))),
% 2.03/2.24 inference(quant_inst,[status(thm)],[])).
% 2.03/2.24 tff(9667,plain,
% 2.03/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1)))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[9666, 9665])).
% 2.03/2.24 tff(9668,plain,
% 2.03/2.24 (~b(s(s(s(s(s(s(z)))))), s(elem!1))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[9667, 128, 591, 8861, 1010, 4791])).
% 2.03/2.24 tff(9669,assumption,(~(s(s(s(s(s(s(z)))))) = s(elem!1))), introduced(assumption)).
% 2.03/2.24 tff(9670,plain,
% 2.03/2.24 (r(s(s(s(s(s(s(z)))))), s(elem!1))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[7815, 21, 9669, 9668])).
% 2.03/2.24 tff(9671,plain,
% 2.03/2.24 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[9637, 128, 591, 8861, 1010])).
% 2.03/2.24 tff(9672,plain,
% 2.03/2.24 ((s(s(s(s(s(s(z)))))) = s(s(z))) | r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1134, 21, 9671])).
% 2.03/2.24 tff(9673,plain,
% 2.03/2.24 (r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[9672, 1124])).
% 2.03/2.24 tff(9674,plain,
% 2.03/2.24 (((~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z))))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(9675,plain,
% 2.03/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z))))))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[9674])).
% 2.03/2.24 tff(9676,plain,
% 2.03/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))))),
% 2.03/2.24 inference(transitivity,[status(thm)],[9675, 8979])).
% 2.03/2.24 tff(9677,plain,
% 2.03/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))))),
% 2.03/2.24 inference(quant_inst,[status(thm)],[])).
% 2.03/2.24 tff(9678,plain,
% 2.03/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z))))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[9677, 9676])).
% 2.03/2.24 tff(9679,plain,
% 2.03/2.24 (~b(s(elem!1), s(s(z)))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[9678, 128, 591, 8861, 4791])).
% 2.03/2.24 tff(9680,plain,
% 2.03/2.24 (r(s(elem!1), s(s(z)))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[473, 21, 759, 9679])).
% 2.03/2.24 tff(9681,plain,
% 2.03/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(elem!1), 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(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(9682,plain,
% 2.03/2.24 (((~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1)))) <=> ((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 2.03/2.24 inference(rewrite,[status(thm)],[])).
% 2.03/2.24 tff(9683,plain,
% 2.03/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(elem!1), 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(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1)))))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[9682])).
% 2.03/2.24 tff(9684,plain,
% 2.03/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(elem!1), 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(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 2.03/2.24 inference(transitivity,[status(thm)],[9683, 9681])).
% 2.03/2.24 tff(9685,plain,
% 2.03/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 2.03/2.24 inference(quant_inst,[status(thm)],[])).
% 2.03/2.24 tff(9686,plain,
% 2.03/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(elem!1)))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[9685, 9684])).
% 2.03/2.24 tff(9687,plain,
% 2.03/2.24 ($false),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[9686, 45, 9680, 9673, 9670])).
% 2.03/2.24 tff(9688,plain,((~b(s(elem!1), elem!1)) | (s(elem!1) = s(s(z))) | (s(s(s(s(s(s(z)))))) = s(elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.24 tff(9689,plain,
% 2.03/2.24 (~b(s(elem!1), elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[9688, 9661, 9658, 9631, 9629, 9627])).
% 2.03/2.24 tff(9690,plain,
% 2.03/2.24 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[9689, 9649])).
% 2.03/2.24 tff(9691,plain,
% 2.03/2.24 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[889, 9690, 9642])).
% 2.03/2.24 tff(9692,plain,
% 2.03/2.24 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[2509, 9625])).
% 2.03/2.24 tff(9693,plain,
% 2.03/2.24 (s(s(s(s(elem!1)))) = elem!1),
% 2.03/2.24 inference(transitivity,[status(thm)],[9692, 9625])).
% 2.03/2.24 tff(9694,plain,
% 2.03/2.24 (r(s(s(s(s(elem!1)))), z) <=> r(elem!1, z)),
% 2.03/2.24 inference(monotonicity,[status(thm)],[9693])).
% 2.03/2.24 tff(9695,plain,
% 2.03/2.24 (r(elem!1, z) <=> r(s(s(s(s(elem!1)))), z)),
% 2.03/2.24 inference(symmetry,[status(thm)],[9694])).
% 2.03/2.24 tff(9696,plain,
% 2.03/2.24 (r(s(s(elem!1)), z) <=> r(elem!1, z)),
% 2.03/2.24 inference(monotonicity,[status(thm)],[9625])).
% 2.03/2.24 tff(9697,plain,
% 2.03/2.24 (r(elem!1, z)),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[1519, 9696])).
% 2.03/2.24 tff(9698,plain,
% 2.03/2.24 (r(s(s(s(s(elem!1)))), z)),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[9697, 9695])).
% 2.03/2.24 tff(9699,plain,
% 2.03/2.24 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[693, 9295])).
% 2.03/2.24 tff(9700,plain,
% 2.03/2.24 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), elem!1)),
% 2.03/2.24 inference(monotonicity,[status(thm)],[9693])).
% 2.03/2.24 tff(9701,plain,
% 2.03/2.24 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.24 inference(symmetry,[status(thm)],[9700])).
% 2.03/2.24 tff(9702,plain,
% 2.03/2.24 (b(s(elem!1), elem!1) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.24 inference(transitivity,[status(thm)],[9647, 9701])).
% 2.03/2.24 tff(9703,plain,
% 2.03/2.24 ((~b(s(elem!1), elem!1)) <=> (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[9702])).
% 2.03/2.24 tff(9704,plain,
% 2.03/2.24 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.24 inference(modus_ponens,[status(thm)],[9689, 9703])).
% 2.03/2.24 tff(9705,plain,
% 2.03/2.24 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1856, 9704, 9699])).
% 2.03/2.24 tff(9706,plain,
% 2.03/2.24 (~r(s(s(s(elem!1))), z)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[1874, 9705, 9698])).
% 2.03/2.24 tff(9707,plain,
% 2.03/2.24 (s(elem!1) = s(s(s(elem!1)))),
% 2.03/2.24 inference(symmetry,[status(thm)],[9645])).
% 2.03/2.24 tff(9708,plain,
% 2.03/2.24 (r(z, s(elem!1)) <=> r(z, s(s(s(elem!1))))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[9707])).
% 2.03/2.24 tff(9709,plain,
% 2.03/2.24 ((~r(z, s(elem!1))) <=> (~r(z, s(s(s(elem!1)))))),
% 2.03/2.24 inference(monotonicity,[status(thm)],[9708])).
% 2.03/2.24 tff(9710,plain,
% 2.03/2.24 (r(s(elem!1), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 2.03/2.24 inference(monotonicity,[status(thm)],[9707])).
% 2.03/2.24 tff(9711,plain,
% 2.03/2.24 (r(s(s(s(elem!1))), elem!1) <=> r(s(elem!1), elem!1)),
% 2.03/2.24 inference(symmetry,[status(thm)],[9710])).
% 2.03/2.24 tff(9712,plain,
% 2.03/2.24 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[700, 9699])).
% 2.03/2.24 tff(9713,plain,
% 2.03/2.24 (~(s(s(s(elem!1))) = elem!1)),
% 2.03/2.24 inference(unit_resolution,[status(thm)],[714, 9625, 9712])).
% 2.03/2.24 tff(9714,plain,
% 2.03/2.24 ((~b(s(elem!1), elem!1)) <=> (~b(s(s(s(elem!1))), elem!1))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[9647])).
% 2.03/2.25 tff(9715,plain,
% 2.03/2.25 (~b(s(s(s(elem!1))), elem!1)),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[9689, 9714])).
% 2.03/2.25 tff(9716,plain,
% 2.03/2.25 (r(s(s(s(elem!1))), elem!1)),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[742, 9715, 9713])).
% 2.03/2.25 tff(9717,plain,
% 2.03/2.25 (r(s(elem!1), elem!1)),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[9716, 9711])).
% 2.03/2.25 tff(9718,plain,
% 2.03/2.25 (r(z, s(s(elem!1))) <=> r(z, elem!1)),
% 2.03/2.25 inference(monotonicity,[status(thm)],[9625])).
% 2.03/2.25 tff(9719,plain,
% 2.03/2.25 (r(z, elem!1)),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[88, 9718])).
% 2.03/2.25 tff(9720,plain,
% 2.03/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(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))))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(9721,plain,
% 2.03/2.25 (((~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))))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(9722,plain,
% 2.03/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(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)))))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[9721])).
% 2.03/2.25 tff(9723,plain,
% 2.03/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(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))))),
% 2.03/2.25 inference(transitivity,[status(thm)],[9722, 9720])).
% 2.03/2.25 tff(9724,plain,
% 2.03/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))))),
% 2.03/2.25 inference(quant_inst,[status(thm)],[])).
% 2.03/2.25 tff(9725,plain,
% 2.03/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1)))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[9724, 9723])).
% 2.03/2.25 tff(9726,plain,
% 2.03/2.25 (~r(z, s(elem!1))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[9725, 45, 9719, 9717])).
% 2.03/2.25 tff(9727,plain,
% 2.03/2.25 (~r(z, s(s(s(elem!1))))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[9726, 9709])).
% 2.03/2.25 tff(9728,plain,
% 2.03/2.25 (~b(s(z), s(s(s(elem!1))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[561, 9727, 550, 9706])).
% 2.03/2.25 tff(9729,plain,
% 2.03/2.25 (r(s(z), s(s(s(elem!1))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[339, 9728])).
% 2.03/2.25 tff(9730,plain,
% 2.03/2.25 (~r(s(z), s(s(elem!1)))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[1802, 9729, 9691])).
% 2.03/2.25 tff(9731,plain,
% 2.03/2.25 (b(s(z), s(s(elem!1)))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[117, 9730])).
% 2.03/2.25 tff(9732,plain,
% 2.03/2.25 (b(s(z), elem!1)),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[9731, 9641])).
% 2.03/2.25 tff(9733,plain,
% 2.03/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(9734,plain,
% 2.03/2.25 (((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(9735,plain,
% 2.03/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[9734])).
% 2.03/2.25 tff(9736,plain,
% 2.03/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.03/2.25 inference(transitivity,[status(thm)],[9735, 9733])).
% 2.03/2.25 tff(9737,plain,
% 2.03/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.03/2.25 inference(quant_inst,[status(thm)],[])).
% 2.03/2.25 tff(9738,plain,
% 2.03/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[9737, 9736])).
% 2.03/2.25 tff(9739,plain,
% 2.03/2.25 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[9738, 128, 9732, 9631, 9629, 9627])).
% 2.03/2.25 tff(9740,plain,
% 2.03/2.25 (r(s(s(s(s(s(s(z)))))), s(z))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[1148, 21, 9739, 8155])).
% 2.03/2.25 tff(9741,plain,
% 2.03/2.25 (((~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(9742,plain,
% 2.03/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1))))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[9741])).
% 2.03/2.25 tff(9743,plain,
% 2.03/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 2.03/2.25 inference(transitivity,[status(thm)],[9742, 655])).
% 2.03/2.25 tff(9744,plain,
% 2.03/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))))),
% 2.03/2.25 inference(quant_inst,[status(thm)],[])).
% 2.03/2.25 tff(9745,plain,
% 2.03/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[9744, 9743])).
% 2.03/2.25 tff(9746,plain,
% 2.03/2.25 (~b(s(z), s(s(z)))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[9745, 128, 9732, 9631, 9629])).
% 2.03/2.25 tff(9747,plain,
% 2.03/2.25 (r(s(z), s(s(z)))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[648, 9746])).
% 2.03/2.25 tff(9748,plain,
% 2.03/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(9749,plain,
% 2.03/2.25 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(9750,plain,
% 2.03/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(z)))))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[9749])).
% 2.03/2.25 tff(9751,plain,
% 2.03/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 2.03/2.25 inference(transitivity,[status(thm)],[9750, 9748])).
% 2.03/2.25 tff(9752,plain,
% 2.03/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 2.03/2.25 inference(quant_inst,[status(thm)],[])).
% 2.03/2.25 tff(9753,plain,
% 2.03/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(z)))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[9752, 9751])).
% 2.03/2.25 tff(9754,plain,
% 2.03/2.25 ($false),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[9753, 45, 9747, 9740, 9640])).
% 2.03/2.25 tff(9755,plain,(r(s(s(s(s(s(s(z)))))), elem!1) | (~b(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (s(s(elem!1)) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.25 tff(9756,plain,
% 2.03/2.25 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[9755, 88, 1519, 550, 28, 1])).
% 2.03/2.25 tff(9757,plain,
% 2.03/2.25 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[438, 325, 88])).
% 2.03/2.25 tff(9758,plain,
% 2.03/2.25 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[321, 9757, 9315])).
% 2.03/2.25 tff(9759,plain,
% 2.03/2.25 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[9036, 325, 88])).
% 2.03/2.25 tff(9760,plain,
% 2.03/2.25 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[9623, 9759, 9758, 8523, 325, 550, 8522, 28])).
% 2.03/2.25 tff(9761,plain,
% 2.03/2.25 (s(s(elem!1)) = elem!1),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[1089, 9760])).
% 2.03/2.25 tff(9762,plain,
% 2.03/2.25 (r(s(s(elem!1)), s(z)) <=> r(elem!1, s(z))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[9761])).
% 2.03/2.25 tff(9763,plain,
% 2.03/2.25 (r(elem!1, s(z))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[325, 9762])).
% 2.03/2.25 tff(9764,plain,
% 2.03/2.25 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[7620, 9763, 1094])).
% 2.03/2.25 tff(9765,plain,
% 2.03/2.25 (r(z, s(s(elem!1))) <=> r(z, elem!1)),
% 2.03/2.25 inference(monotonicity,[status(thm)],[9761])).
% 2.03/2.25 tff(9766,plain,
% 2.03/2.25 (r(z, elem!1)),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[88, 9765])).
% 2.03/2.25 tff(9767,plain,
% 2.03/2.25 (~r(s(s(s(s(s(s(z)))))), z)),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[1423, 45, 9766, 1094])).
% 2.03/2.25 tff(9768,plain,
% 2.03/2.25 (b(s(s(s(s(s(s(z)))))), z)),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[1022, 21, 1019, 9767])).
% 2.03/2.25 tff(9769,plain,
% 2.03/2.25 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[8811, 128, 550, 7825, 9768])).
% 2.03/2.25 tff(9770,plain,
% 2.03/2.25 ($false),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[1148, 21, 9769, 9764, 8155])).
% 2.03/2.25 tff(9771,plain,((~r(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.25 tff(9772,plain,
% 2.03/2.25 (~r(s(s(elem!1)), s(z))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[9771, 9756, 550, 88, 8521, 8512, 28])).
% 2.03/2.25 tff(9773,plain,
% 2.03/2.25 (b(s(s(elem!1)), s(z))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[292, 9772])).
% 2.03/2.25 tff(9774,plain,
% 2.03/2.25 ($false),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[9024, 128, 30, 550, 7825, 273, 8522])).
% 2.03/2.25 tff(9775,plain,((~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.25 tff(9776,plain,
% 2.03/2.25 (~b(s(s(z)), s(z))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[9775, 9773, 550, 8512])).
% 2.03/2.25 tff(9777,plain,
% 2.03/2.25 (r(s(s(z)), s(z))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[86, 9776])).
% 2.03/2.25 tff(9778,plain,
% 2.03/2.25 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[8617, 9777, 9773, 550, 8521, 8512, 88])).
% 2.03/2.25 tff(9779,plain,
% 2.03/2.25 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[1073, 9778])).
% 2.03/2.25 tff(9780,plain,
% 2.03/2.25 (s(s(elem!1)) = elem!1),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[1089, 9779])).
% 2.03/2.25 tff(9781,plain,
% 2.03/2.25 (~(s(s(s(s(z)))) = elem!1)),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[242, 9780])).
% 2.03/2.25 tff(9782,plain,
% 2.03/2.25 (b(s(s(z)), s(s(elem!1))) <=> b(s(s(z)), elem!1)),
% 2.03/2.25 inference(monotonicity,[status(thm)],[9780])).
% 2.03/2.25 tff(9783,plain,
% 2.03/2.25 (b(s(s(z)), elem!1)),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[8521, 9782])).
% 2.03/2.25 tff(9784,plain,
% 2.03/2.25 (b(s(s(elem!1)), s(z)) <=> b(elem!1, s(z))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[9780])).
% 2.03/2.25 tff(9785,plain,
% 2.03/2.25 (b(elem!1, s(z))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[9773, 9784])).
% 2.03/2.25 tff(9786,plain,
% 2.03/2.25 ((s(s(elem!1)) = s(z)) <=> (elem!1 = s(z))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[9780])).
% 2.03/2.25 tff(9787,plain,
% 2.03/2.25 ((s(s(elem!1)) = s(z)) <=> (s(z) = elem!1)),
% 2.03/2.25 inference(transitivity,[status(thm)],[9786, 253])).
% 2.03/2.25 tff(9788,plain,
% 2.03/2.25 ((~(s(s(elem!1)) = s(z))) <=> (~(s(z) = elem!1))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[9787])).
% 2.03/2.25 tff(9789,plain,
% 2.03/2.25 (~(s(z) = elem!1)),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[111, 9788])).
% 2.03/2.25 tff(9790,plain,
% 2.03/2.25 ((s(s(s(s(s(s(z)))))) = elem!1) <=> (elem!1 = s(s(s(s(s(s(z)))))))),
% 2.03/2.25 inference(symmetry,[status(thm)],[4622])).
% 2.03/2.25 tff(9791,plain,
% 2.03/2.25 ((~(s(s(s(s(s(s(z)))))) = elem!1)) <=> (~(elem!1 = s(s(s(s(s(s(z))))))))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[9790])).
% 2.03/2.25 tff(9792,plain,
% 2.03/2.25 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[245, 9780])).
% 2.03/2.25 tff(9793,plain,
% 2.03/2.25 (~(elem!1 = s(s(s(s(s(s(z)))))))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[9792, 9791])).
% 2.03/2.25 tff(9794,plain,
% 2.03/2.25 (r(z, s(s(elem!1))) <=> r(z, elem!1)),
% 2.03/2.25 inference(monotonicity,[status(thm)],[9780])).
% 2.03/2.25 tff(9795,plain,
% 2.03/2.25 (r(z, elem!1)),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[88, 9794])).
% 2.03/2.25 tff(9796,plain,
% 2.03/2.25 (~r(s(s(s(s(s(s(z)))))), z)),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[1423, 45, 9795, 9756])).
% 2.03/2.25 tff(9797,plain,
% 2.03/2.25 (b(s(s(s(s(s(s(z)))))), z)),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[1022, 21, 1019, 9796])).
% 2.03/2.25 tff(9798,plain,
% 2.03/2.25 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[8811, 128, 550, 7825, 9797])).
% 2.03/2.25 tff(9799,plain,
% 2.03/2.25 (r(s(s(s(s(s(s(z)))))), s(z))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[1148, 21, 9798, 8155])).
% 2.03/2.25 tff(9800,plain,
% 2.03/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), 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(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(9801,plain,
% 2.03/2.25 (((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(9802,plain,
% 2.03/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), 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(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[9801])).
% 2.03/2.25 tff(9803,plain,
% 2.03/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), 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(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.03/2.25 inference(transitivity,[status(thm)],[9802, 9800])).
% 2.03/2.25 tff(9804,plain,
% 2.03/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.03/2.25 inference(quant_inst,[status(thm)],[])).
% 2.03/2.25 tff(9805,plain,
% 2.03/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[9804, 9803])).
% 2.03/2.25 tff(9806,plain,
% 2.03/2.25 (~r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[9805, 45, 9777, 9799])).
% 2.03/2.25 tff(9807,plain,
% 2.03/2.25 (b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[1176, 21, 1123, 9806])).
% 2.03/2.25 tff(9808,plain,
% 2.03/2.25 (b(s(s(elem!1)), s(s(z))) <=> b(elem!1, s(s(z)))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[9780])).
% 2.03/2.25 tff(9809,plain,
% 2.03/2.25 (b(elem!1, s(s(z)))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[8512, 9808])).
% 2.03/2.25 tff(9810,plain,
% 2.03/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(elem!1, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(9811,plain,
% 2.03/2.25 (((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(z))))) <=> ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(9812,plain,
% 2.03/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(elem!1, s(s(s(s(s(s(z))))))))))),
% 2.03/2.25 inference(monotonicity,[status(thm)],[9811])).
% 2.03/2.25 tff(9813,plain,
% 2.03/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(elem!1, s(s(s(s(s(s(z)))))))))),
% 2.03/2.25 inference(transitivity,[status(thm)],[9812, 9810])).
% 2.03/2.25 tff(9814,plain,
% 2.03/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(z)))))),
% 2.03/2.25 inference(quant_inst,[status(thm)],[])).
% 2.03/2.25 tff(9815,plain,
% 2.03/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(elem!1, s(s(s(s(s(s(z))))))))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[9814, 9813])).
% 2.03/2.25 tff(9816,plain,
% 2.03/2.25 (~b(elem!1, s(s(s(s(s(s(z)))))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[9815, 128, 9785, 550, 9809, 9797, 9807])).
% 2.03/2.25 tff(9817,plain,
% 2.03/2.25 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(s(s(z))))))) | b(elem!1, s(s(s(s(s(s(z))))))) | r(elem!1, s(s(s(s(s(s(z))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(s(s(z))))))) | b(elem!1, s(s(s(s(s(s(z))))))) | r(elem!1, s(s(s(s(s(s(z))))))))),
% 2.03/2.25 inference(rewrite,[status(thm)],[])).
% 2.03/2.25 tff(9818,plain,
% 2.03/2.25 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(s(s(z))))))) | b(elem!1, s(s(s(s(s(s(z))))))) | r(elem!1, s(s(s(s(s(s(z))))))))),
% 2.03/2.25 inference(quant_inst,[status(thm)],[])).
% 2.03/2.25 tff(9819,plain,
% 2.03/2.25 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(s(s(z))))))) | b(elem!1, s(s(s(s(s(s(z))))))) | r(elem!1, s(s(s(s(s(s(z)))))))),
% 2.03/2.25 inference(modus_ponens,[status(thm)],[9818, 9817])).
% 2.03/2.25 tff(9820,plain,
% 2.03/2.25 ((elem!1 = s(s(s(s(s(s(z))))))) | r(elem!1, s(s(s(s(s(s(z)))))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[9819, 21, 9816])).
% 2.03/2.25 tff(9821,plain,
% 2.03/2.25 (r(elem!1, s(s(s(s(s(s(z)))))))),
% 2.03/2.25 inference(unit_resolution,[status(thm)],[9820, 9793])).
% 2.03/2.25 tff(9822,plain,
% 2.03/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 2.03/2.26 inference(rewrite,[status(thm)],[])).
% 2.03/2.26 tff(9823,plain,
% 2.03/2.26 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z))))))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 2.03/2.26 inference(rewrite,[status(thm)],[])).
% 2.03/2.26 tff(9824,plain,
% 2.03/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z))))))))))),
% 2.03/2.26 inference(monotonicity,[status(thm)],[9823])).
% 2.03/2.26 tff(9825,plain,
% 2.03/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 2.03/2.26 inference(transitivity,[status(thm)],[9824, 9822])).
% 2.03/2.26 tff(9826,plain,
% 2.03/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 2.03/2.26 inference(quant_inst,[status(thm)],[])).
% 2.03/2.26 tff(9827,plain,
% 2.03/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z))))))))),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[9826, 9825])).
% 2.03/2.26 tff(9828,plain,
% 2.03/2.26 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[9827, 128, 550, 7825, 9797])).
% 2.03/2.26 tff(9829,plain,
% 2.03/2.26 (r(s(z), s(s(s(s(s(s(z)))))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[1041, 21, 1038, 9828])).
% 2.03/2.26 tff(9830,plain,
% 2.03/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(elem!1, 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(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))))),
% 2.03/2.26 inference(rewrite,[status(thm)],[])).
% 2.03/2.26 tff(9831,plain,
% 2.03/2.26 (((~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(z), elem!1))) <=> ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))))),
% 2.03/2.26 inference(rewrite,[status(thm)],[])).
% 2.03/2.26 tff(9832,plain,
% 2.03/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z))))))))))),
% 2.03/2.26 inference(monotonicity,[status(thm)],[9831])).
% 2.03/2.26 tff(9833,plain,
% 2.03/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))))),
% 2.03/2.26 inference(transitivity,[status(thm)],[9832, 9830])).
% 2.03/2.26 tff(9834,plain,
% 2.03/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z)))))))) | (~r(s(z), elem!1)))),
% 2.03/2.26 inference(quant_inst,[status(thm)],[])).
% 2.03/2.26 tff(9835,plain,
% 2.03/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(elem!1, s(s(s(s(s(s(z))))))))),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[9834, 9833])).
% 2.03/2.26 tff(9836,plain,
% 2.03/2.26 (~r(s(z), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[9835, 45, 9829, 9821])).
% 2.03/2.26 tff(9837,plain,
% 2.03/2.26 (b(s(z), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[665, 9836, 9789])).
% 2.03/2.26 tff(9838,plain,
% 2.03/2.26 (~b(s(s(s(s(z)))), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[2819, 9837, 9785, 9783])).
% 2.03/2.26 tff(9839,plain,
% 2.03/2.26 (r(s(s(s(s(z)))), elem!1)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[632, 9838, 9781])).
% 2.03/2.26 tff(9840,plain,
% 2.03/2.26 (~r(s(s(s(s(z)))), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[1459, 45, 9795, 9839])).
% 2.03/2.26 tff(9841,plain,
% 2.03/2.26 (b(s(s(s(s(z)))), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[589, 21, 586, 9840])).
% 2.03/2.26 tff(9842,plain,
% 2.03/2.26 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[2986, 45, 9839, 9756])).
% 2.03/2.26 tff(9843,plain,
% 2.03/2.26 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[1215, 21, 1212, 9842])).
% 2.03/2.26 tff(9844,plain,
% 2.03/2.26 ((z = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = z)),
% 2.03/2.26 inference(commutativity,[status(thm)],[])).
% 2.03/2.26 tff(9845,plain,
% 2.03/2.26 ((s(s(s(s(s(s(z)))))) = z) <=> (z = s(s(s(s(s(s(z)))))))),
% 2.03/2.26 inference(symmetry,[status(thm)],[9844])).
% 2.03/2.26 tff(9846,plain,
% 2.03/2.26 ((~(s(s(s(s(s(s(z)))))) = z)) <=> (~(z = s(s(s(s(s(s(z))))))))),
% 2.03/2.26 inference(monotonicity,[status(thm)],[9845])).
% 2.03/2.26 tff(9847,plain,
% 2.03/2.26 (~(z = s(s(s(s(s(s(z)))))))),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[1019, 9846])).
% 2.03/2.26 tff(9848,plain,
% 2.03/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(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(z, elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 2.03/2.26 inference(rewrite,[status(thm)],[])).
% 2.03/2.26 tff(9849,plain,
% 2.03/2.26 (((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(z, s(s(s(s(s(s(z))))))))) <=> ((~r(z, elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 2.03/2.26 inference(rewrite,[status(thm)],[])).
% 2.03/2.26 tff(9850,plain,
% 2.03/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(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(z, elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(z, s(s(s(s(s(s(z))))))))))),
% 2.03/2.26 inference(monotonicity,[status(thm)],[9849])).
% 2.03/2.26 tff(9851,plain,
% 2.03/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(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(z, elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 2.03/2.26 inference(transitivity,[status(thm)],[9850, 9848])).
% 2.03/2.26 tff(9852,plain,
% 2.03/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 2.03/2.26 inference(quant_inst,[status(thm)],[])).
% 2.03/2.26 tff(9853,plain,
% 2.03/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(z, s(s(s(s(s(s(z))))))))),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[9852, 9851])).
% 2.03/2.26 tff(9854,plain,
% 2.03/2.26 (~r(z, s(s(s(s(s(s(z)))))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[9853, 45, 9795, 9756])).
% 2.03/2.26 tff(9855,plain,
% 2.03/2.26 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(s(z))))))) | b(z, s(s(s(s(s(s(z))))))) | r(z, s(s(s(s(s(s(z))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(s(z))))))) | b(z, s(s(s(s(s(s(z))))))) | r(z, s(s(s(s(s(s(z))))))))),
% 2.03/2.26 inference(rewrite,[status(thm)],[])).
% 2.03/2.26 tff(9856,plain,
% 2.03/2.26 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(s(z))))))) | b(z, s(s(s(s(s(s(z))))))) | r(z, s(s(s(s(s(s(z))))))))),
% 2.03/2.26 inference(quant_inst,[status(thm)],[])).
% 2.03/2.26 tff(9857,plain,
% 2.03/2.26 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(s(z))))))) | b(z, s(s(s(s(s(s(z))))))) | r(z, s(s(s(s(s(s(z)))))))),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[9856, 9855])).
% 2.03/2.26 tff(9858,plain,
% 2.03/2.26 ((z = s(s(s(s(s(s(z))))))) | b(z, s(s(s(s(s(s(z)))))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[9857, 21, 9854])).
% 2.03/2.26 tff(9859,plain,
% 2.03/2.26 (b(z, s(s(s(s(s(s(z)))))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[9858, 9847])).
% 2.03/2.26 tff(9860,plain,
% 2.03/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.03/2.26 inference(rewrite,[status(thm)],[])).
% 2.03/2.26 tff(9861,plain,
% 2.03/2.26 (((~b(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)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.03/2.26 inference(rewrite,[status(thm)],[])).
% 2.03/2.26 tff(9862,plain,
% 2.03/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 2.03/2.26 inference(monotonicity,[status(thm)],[9861])).
% 2.03/2.26 tff(9863,plain,
% 2.03/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.03/2.26 inference(transitivity,[status(thm)],[9862, 9860])).
% 2.03/2.26 tff(9864,plain,
% 2.03/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.03/2.26 inference(quant_inst,[status(thm)],[])).
% 2.03/2.26 tff(9865,plain,
% 2.03/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[9864, 9863])).
% 2.03/2.26 tff(9866,plain,
% 2.03/2.26 ($false),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[9865, 128, 9797, 9859, 9843, 9841])).
% 2.03/2.26 tff(9867,plain,((~r(z, s(s(elem!1)))) | (~b(z, s(z))) | (~r(s(s(z)), z)) | (s(s(elem!1)) = s(s(z))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.26 tff(9868,plain,
% 2.03/2.26 (~r(z, s(s(elem!1)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[9867, 1519, 28, 1, 550])).
% 2.03/2.26 tff(9869,plain,
% 2.03/2.26 (b(z, s(s(elem!1)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[160, 9868])).
% 2.03/2.26 tff(9870,plain,
% 2.03/2.26 ((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[3535, 7825])).
% 2.03/2.26 tff(9871,plain,
% 2.03/2.26 (~b(s(s(elem!1)), s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[9870, 9869, 550])).
% 2.03/2.26 tff(9872,plain,
% 2.03/2.26 (r(s(s(elem!1)), s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[292, 9871])).
% 2.03/2.26 tff(9873,plain,
% 2.03/2.26 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[9294, 9872, 550])).
% 2.03/2.26 tff(9874,plain,
% 2.03/2.26 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[693, 9873])).
% 2.03/2.26 tff(9875,plain,
% 2.03/2.26 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[700, 9874])).
% 2.03/2.26 tff(9876,plain,
% 2.03/2.26 (~b(s(s(elem!1)), s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[9870, 453, 550])).
% 2.03/2.26 tff(9877,plain,
% 2.03/2.26 (r(s(s(elem!1)), s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[292, 9876])).
% 2.03/2.26 tff(9878,plain,
% 2.03/2.26 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[9294, 9877, 550])).
% 2.03/2.26 tff(9879,plain,
% 2.03/2.26 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[803, 9878])).
% 2.03/2.26 tff(9880,plain,
% 2.03/2.26 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[7275, 45, 9877, 385])).
% 2.03/2.26 tff(9881,plain,
% 2.03/2.26 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[889, 9880, 9879])).
% 2.03/2.26 tff(9882,plain,
% 2.03/2.26 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[393, 385, 9877])).
% 2.03/2.26 tff(9883,plain,
% 2.03/2.26 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[321, 9882, 9878])).
% 2.03/2.26 tff(9884,plain,
% 2.03/2.26 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[9605, 128, 9883, 9881, 8523])).
% 2.03/2.26 tff(9885,plain,
% 2.03/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))),
% 2.03/2.26 inference(rewrite,[status(thm)],[])).
% 2.03/2.26 tff(9886,plain,
% 2.03/2.26 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))),
% 2.03/2.26 inference(rewrite,[status(thm)],[])).
% 2.03/2.26 tff(9887,plain,
% 2.03/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1)))))))),
% 2.03/2.26 inference(monotonicity,[status(thm)],[9886])).
% 2.03/2.26 tff(9888,plain,
% 2.03/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))))),
% 2.03/2.26 inference(transitivity,[status(thm)],[9887, 9885])).
% 2.03/2.26 tff(9889,plain,
% 2.03/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 2.03/2.26 inference(quant_inst,[status(thm)],[])).
% 2.03/2.26 tff(9890,plain,
% 2.03/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1)))))),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[9889, 9888])).
% 2.03/2.26 tff(9891,plain,
% 2.03/2.26 (~b(z, s(s(s(elem!1))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[9890, 128, 453, 9883, 9881])).
% 2.03/2.26 tff(9892,plain,
% 2.03/2.26 (r(z, s(s(s(elem!1))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[858, 9891])).
% 2.03/2.26 tff(9893,plain,
% 2.03/2.26 ((~r(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1)))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[8845, 7825])).
% 2.03/2.26 tff(9894,plain,
% 2.03/2.26 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[9893, 9892, 385, 550])).
% 2.03/2.26 tff(9895,plain,
% 2.03/2.26 ($false),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[4350, 21, 9894, 9884, 283])).
% 2.03/2.26 tff(9896,plain,((~r(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.26 tff(9897,plain,
% 2.03/2.26 (~r(s(s(s(elem!1))), s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[9896, 8521, 550, 9869])).
% 2.03/2.26 tff(9898,plain,
% 2.03/2.26 (b(s(s(s(elem!1))), s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[196, 9897])).
% 2.03/2.26 tff(9899,plain,
% 2.03/2.26 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[8789, 9898, 550, 9875])).
% 2.03/2.26 tff(9900,plain,
% 2.03/2.26 (r(s(s(s(s(elem!1)))), s(z))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[1828, 9899])).
% 2.03/2.26 tff(9901,plain,
% 2.03/2.26 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[2141, 9900, 9872])).
% 2.03/2.26 tff(9902,plain,
% 2.03/2.26 (~b(s(s(s(elem!1))), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[8768, 128, 550, 7825, 9898])).
% 2.03/2.26 tff(9903,plain,
% 2.03/2.26 (r(s(s(s(elem!1))), z)),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[5301, 9902])).
% 2.03/2.26 tff(9904,plain,
% 2.03/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.03/2.26 inference(rewrite,[status(thm)],[])).
% 2.03/2.26 tff(9905,plain,
% 2.03/2.26 (((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.03/2.26 inference(rewrite,[status(thm)],[])).
% 2.03/2.26 tff(9906,plain,
% 2.03/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 2.03/2.26 inference(monotonicity,[status(thm)],[9905])).
% 2.03/2.26 tff(9907,plain,
% 2.03/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.03/2.26 inference(transitivity,[status(thm)],[9906, 9904])).
% 2.03/2.26 tff(9908,plain,
% 2.03/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.03/2.26 inference(quant_inst,[status(thm)],[])).
% 2.03/2.26 tff(9909,plain,
% 2.03/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[9908, 9907])).
% 2.03/2.26 tff(9910,plain,
% 2.03/2.26 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[9909, 45, 9903, 1519])).
% 2.03/2.26 tff(9911,plain,
% 2.03/2.26 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[321, 9910, 9873])).
% 2.03/2.26 tff(9912,plain,
% 2.03/2.26 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[9623, 9911, 9901, 8521, 9872, 550, 8512, 28])).
% 2.03/2.26 tff(9913,plain,
% 2.03/2.26 (s(s(elem!1)) = elem!1),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[1089, 9912])).
% 2.03/2.26 tff(9914,plain,
% 2.03/2.26 (s(s(s(elem!1))) = s(elem!1)),
% 2.03/2.26 inference(monotonicity,[status(thm)],[9913])).
% 2.03/2.26 tff(9915,plain,
% 2.03/2.26 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(elem!1), s(s(z)))),
% 2.03/2.26 inference(monotonicity,[status(thm)],[9914])).
% 2.03/2.26 tff(9916,plain,
% 2.03/2.26 ((~r(s(s(s(elem!1))), s(s(z)))) <=> (~r(s(elem!1), s(s(z))))),
% 2.03/2.26 inference(monotonicity,[status(thm)],[9915])).
% 2.03/2.26 tff(9917,plain,
% 2.03/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.03/2.26 inference(rewrite,[status(thm)],[])).
% 2.03/2.26 tff(9918,plain,
% 2.03/2.26 (((~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.03/2.26 inference(rewrite,[status(thm)],[])).
% 2.03/2.26 tff(9919,plain,
% 2.03/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))))),
% 2.03/2.26 inference(monotonicity,[status(thm)],[9918])).
% 2.03/2.26 tff(9920,plain,
% 2.03/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.03/2.26 inference(transitivity,[status(thm)],[9919, 9917])).
% 2.03/2.26 tff(9921,plain,
% 2.03/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))))),
% 2.03/2.26 inference(quant_inst,[status(thm)],[])).
% 2.03/2.26 tff(9922,plain,
% 2.03/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[9921, 9920])).
% 2.03/2.26 tff(9923,plain,
% 2.03/2.26 (~b(z, s(s(z)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[9922, 128, 9869, 8512, 8521])).
% 2.03/2.26 tff(9924,plain,
% 2.03/2.26 (r(z, s(s(z)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[516, 9923])).
% 2.03/2.26 tff(9925,plain,
% 2.03/2.26 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[528, 9903, 9924])).
% 2.03/2.26 tff(9926,plain,
% 2.03/2.26 (~r(s(elem!1), s(s(z)))),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[9925, 9916])).
% 2.03/2.26 tff(9927,plain,
% 2.03/2.26 ((s(s(s(elem!1))) = s(s(z))) <=> (s(elem!1) = s(s(z)))),
% 2.03/2.26 inference(monotonicity,[status(thm)],[9914])).
% 2.03/2.26 tff(9928,plain,
% 2.03/2.26 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(elem!1) = s(s(z))))),
% 2.03/2.26 inference(monotonicity,[status(thm)],[9927])).
% 2.03/2.26 tff(9929,plain,
% 2.03/2.26 (~(s(elem!1) = s(s(z)))),
% 2.03/2.26 inference(modus_ponens,[status(thm)],[283, 9928])).
% 2.03/2.26 tff(9930,plain,
% 2.03/2.26 (b(s(elem!1), s(s(z)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[473, 21, 9929, 9926])).
% 2.03/2.26 tff(9931,plain,
% 2.03/2.26 (b(s(s(s(elem!1))), elem!1) <=> b(s(elem!1), elem!1)),
% 2.03/2.26 inference(monotonicity,[status(thm)],[9914])).
% 2.03/2.26 tff(9932,plain,
% 2.03/2.26 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), elem!1)),
% 2.03/2.26 inference(monotonicity,[status(thm)],[9913])).
% 2.03/2.26 tff(9933,plain,
% 2.03/2.26 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.03/2.26 inference(unit_resolution,[status(thm)],[803, 9873])).
% 2.03/2.26 tff(9934,plain,
% 2.03/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.03/2.26 inference(rewrite,[status(thm)],[])).
% 2.03/2.26 tff(9935,plain,
% 2.03/2.26 (((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.03/2.26 inference(rewrite,[status(thm)],[])).
% 2.03/2.26 tff(9936,plain,
% 2.03/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1))))))),
% 2.03/2.26 inference(monotonicity,[status(thm)],[9935])).
% 2.03/2.26 tff(9937,plain,
% 2.03/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.03/2.27 inference(transitivity,[status(thm)],[9936, 9934])).
% 2.03/2.27 tff(9938,plain,
% 2.03/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.03/2.27 inference(quant_inst,[status(thm)],[])).
% 2.03/2.27 tff(9939,plain,
% 2.03/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[9938, 9937])).
% 2.03/2.27 tff(9940,plain,
% 2.03/2.27 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[9939, 45, 9872, 9903, 1519])).
% 2.03/2.27 tff(9941,plain,
% 2.03/2.27 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[889, 9940, 9933])).
% 2.03/2.27 tff(9942,plain,
% 2.03/2.27 (b(s(s(s(elem!1))), elem!1)),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[9941, 9932])).
% 2.03/2.27 tff(9943,plain,
% 2.03/2.27 (b(s(elem!1), elem!1)),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[9942, 9931])).
% 2.03/2.27 tff(9944,plain,
% 2.03/2.27 (b(s(s(elem!1)), s(s(z))) <=> b(elem!1, s(s(z)))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[9913])).
% 2.03/2.27 tff(9945,plain,
% 2.03/2.27 (b(elem!1, s(s(z)))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[8512, 9944])).
% 2.03/2.27 tff(9946,plain,
% 2.03/2.27 (b(s(s(z)), s(s(elem!1))) <=> b(s(s(z)), elem!1)),
% 2.03/2.27 inference(monotonicity,[status(thm)],[9913])).
% 2.03/2.27 tff(9947,plain,
% 2.03/2.27 (b(s(s(z)), elem!1)),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[8521, 9946])).
% 2.03/2.27 tff(9948,plain,
% 2.03/2.27 ($false),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[9678, 128, 9947, 9945, 9943, 9930])).
% 2.03/2.27 tff(9949,plain,((~r(s(s(elem!1)), z)) | (~b(z, s(z))) | (~r(s(s(z)), z)) | (s(s(elem!1)) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.27 tff(9950,plain,
% 2.03/2.27 (~r(s(s(elem!1)), z)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[9949, 1, 28, 550])).
% 2.03/2.27 tff(9951,plain,
% 2.03/2.27 (b(s(s(elem!1)), z)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[7835, 9950])).
% 2.03/2.27 tff(9952,plain,
% 2.03/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(9953,plain,
% 2.03/2.27 (((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(9954,plain,
% 2.03/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[9953])).
% 2.03/2.27 tff(9955,plain,
% 2.03/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 2.03/2.27 inference(transitivity,[status(thm)],[9954, 9952])).
% 2.03/2.27 tff(9956,plain,
% 2.03/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 2.03/2.27 inference(quant_inst,[status(thm)],[])).
% 2.03/2.27 tff(9957,plain,
% 2.03/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[9956, 9955])).
% 2.03/2.27 tff(9958,plain,
% 2.03/2.27 (~b(s(s(elem!1)), s(z))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[9957, 128, 550, 7825, 9951])).
% 2.03/2.27 tff(9959,plain,
% 2.03/2.27 (r(s(s(elem!1)), s(z))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[292, 9958])).
% 2.03/2.27 tff(9960,plain,
% 2.03/2.27 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[9294, 9959, 550])).
% 2.03/2.27 tff(9961,plain,
% 2.03/2.27 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[693, 9960])).
% 2.03/2.27 tff(9962,plain,
% 2.03/2.27 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[700, 9961])).
% 2.03/2.27 tff(9963,plain,
% 2.03/2.27 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[2141, 9582, 325])).
% 2.03/2.27 tff(9964,plain,
% 2.03/2.27 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[1897, 9963, 2023])).
% 2.03/2.27 tff(9965,plain,
% 2.03/2.27 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[9595, 9964, 325, 1069, 550, 2718, 28])).
% 2.03/2.27 tff(9966,plain,
% 2.03/2.27 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[321, 9965, 9315])).
% 2.03/2.27 tff(9967,plain,
% 2.03/2.27 (~r(s(z), s(s(s(elem!1))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[333, 9966, 325])).
% 2.03/2.27 tff(9968,plain,
% 2.03/2.27 (b(s(z), s(s(s(elem!1))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[339, 9967])).
% 2.03/2.27 tff(9969,plain,
% 2.03/2.27 (~b(z, s(s(z)))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[9590, 128, 550, 9968, 2718, 9569])).
% 2.03/2.27 tff(9970,plain,
% 2.03/2.27 (r(z, s(s(z)))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[516, 9969])).
% 2.03/2.27 tff(9971,plain,
% 2.03/2.27 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[528, 9578, 9970])).
% 2.03/2.27 tff(9972,plain,
% 2.03/2.27 ($false),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[4350, 21, 9971, 9576, 283])).
% 2.03/2.27 tff(9973,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.27 tff(9974,plain,
% 2.03/2.27 (~b(s(s(s(elem!1))), s(z))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[9973, 1069, 9959, 550, 28])).
% 2.03/2.27 tff(9975,plain,
% 2.03/2.27 (r(s(s(s(elem!1))), s(z))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[196, 9974])).
% 2.03/2.27 tff(9976,plain,
% 2.03/2.27 (~b(s(s(z)), s(s(elem!1)))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[9896, 453, 9975, 550])).
% 2.03/2.27 tff(9977,plain,
% 2.03/2.27 ((s(s(z)) = s(s(elem!1))) | r(s(s(z)), s(s(elem!1)))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[138, 21, 9976])).
% 2.03/2.27 tff(9978,plain,
% 2.03/2.27 (r(s(s(z)), s(s(elem!1)))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[9977, 34])).
% 2.03/2.27 tff(9979,plain,
% 2.03/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(9980,plain,
% 2.03/2.27 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(9981,plain,
% 2.03/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z)))))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[9980])).
% 2.03/2.27 tff(9982,plain,
% 2.03/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))))),
% 2.03/2.27 inference(transitivity,[status(thm)],[9981, 9979])).
% 2.03/2.27 tff(9983,plain,
% 2.03/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))),
% 2.03/2.27 inference(quant_inst,[status(thm)],[])).
% 2.03/2.27 tff(9984,plain,
% 2.03/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z)))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[9983, 9982])).
% 2.03/2.27 tff(9985,plain,
% 2.03/2.27 (~b(s(z), s(s(elem!1)))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[9984, 128, 550, 7825, 9951])).
% 2.03/2.27 tff(9986,plain,
% 2.03/2.27 (r(s(z), s(s(elem!1)))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[117, 9985])).
% 2.03/2.27 tff(9987,plain,
% 2.03/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(9988,plain,
% 2.03/2.27 (((~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(9989,plain,
% 2.03/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1))))))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[9988])).
% 2.03/2.27 tff(9990,plain,
% 2.03/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))),
% 2.03/2.27 inference(transitivity,[status(thm)],[9989, 9987])).
% 2.03/2.27 tff(9991,plain,
% 2.03/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))))),
% 2.03/2.27 inference(quant_inst,[status(thm)],[])).
% 2.03/2.27 tff(9992,plain,
% 2.03/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1))))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[9991, 9990])).
% 2.03/2.27 tff(9993,plain,
% 2.03/2.27 (~r(s(s(z)), s(z))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[9992, 45, 9986, 9978])).
% 2.03/2.27 tff(9994,plain,
% 2.03/2.27 (b(s(s(z)), s(z))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[86, 9993])).
% 2.03/2.27 tff(9995,plain,
% 2.03/2.27 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[803, 9960])).
% 2.03/2.27 tff(9996,plain,
% 2.03/2.27 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[393, 9975, 9959])).
% 2.03/2.27 tff(9997,plain,
% 2.03/2.27 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[321, 9996, 9960])).
% 2.03/2.27 tff(9998,plain,
% 2.03/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(9999,plain,
% 2.03/2.27 (((~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(10000,plain,
% 2.03/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(elem!1))))))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[9999])).
% 2.03/2.27 tff(10001,plain,
% 2.03/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))))),
% 2.03/2.27 inference(transitivity,[status(thm)],[10000, 9998])).
% 2.03/2.27 tff(10002,plain,
% 2.03/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(z)))))),
% 2.03/2.27 inference(quant_inst,[status(thm)],[])).
% 2.03/2.27 tff(10003,plain,
% 2.03/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(elem!1))))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[10002, 10001])).
% 2.03/2.27 tff(10004,plain,
% 2.03/2.27 (~r(s(z), s(s(z)))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[10003, 45, 9986, 9978])).
% 2.03/2.27 tff(10005,plain,
% 2.03/2.27 (b(s(z), s(s(z)))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[648, 10004])).
% 2.03/2.27 tff(10006,plain,
% 2.03/2.27 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[7275, 45, 9959, 9975])).
% 2.03/2.27 tff(10007,plain,
% 2.03/2.27 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[889, 10006, 9995])).
% 2.03/2.27 tff(10008,plain,
% 2.03/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(10009,plain,
% 2.03/2.27 (((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(10010,plain,
% 2.03/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[10009])).
% 2.03/2.27 tff(10011,plain,
% 2.03/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))),
% 2.03/2.27 inference(transitivity,[status(thm)],[10010, 10008])).
% 2.03/2.27 tff(10012,plain,
% 2.03/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))),
% 2.03/2.27 inference(quant_inst,[status(thm)],[])).
% 2.03/2.27 tff(10013,plain,
% 2.03/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[10012, 10011])).
% 2.03/2.27 tff(10014,plain,
% 2.03/2.27 (~b(s(s(s(elem!1))), z)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[10013, 128, 453, 9951, 10007])).
% 2.03/2.27 tff(10015,plain,
% 2.03/2.27 (r(s(s(s(elem!1))), z)),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[5301, 10014])).
% 2.03/2.27 tff(10016,plain,
% 2.03/2.27 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[9326, 45, 10015, 28])).
% 2.03/2.27 tff(10017,plain,
% 2.03/2.27 ((s(s(z)) = s(s(s(elem!1)))) | b(s(s(z)), s(s(s(elem!1))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[4283, 21, 10016])).
% 2.03/2.27 tff(10018,plain,
% 2.03/2.27 (b(s(s(z)), s(s(s(elem!1))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[10017, 4271])).
% 2.03/2.27 tff(10019,plain,
% 2.03/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(10020,plain,
% 2.03/2.27 (((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(10021,plain,
% 2.03/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(z))))))),
% 2.03/2.27 inference(monotonicity,[status(thm)],[10020])).
% 2.03/2.27 tff(10022,plain,
% 2.03/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))))),
% 2.03/2.27 inference(transitivity,[status(thm)],[10021, 10019])).
% 2.03/2.27 tff(10023,plain,
% 2.03/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))))),
% 2.03/2.27 inference(quant_inst,[status(thm)],[])).
% 2.03/2.27 tff(10024,plain,
% 2.03/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(z))))),
% 2.03/2.27 inference(modus_ponens,[status(thm)],[10023, 10022])).
% 2.03/2.27 tff(10025,plain,
% 2.03/2.27 ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[10024, 128, 7825, 9951, 10007, 10018])).
% 2.03/2.27 tff(10026,plain,
% 2.03/2.27 (~b(s(z), s(s(s(elem!1))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[10025, 10005])).
% 2.03/2.27 tff(10027,plain,
% 2.03/2.27 (r(s(z), s(s(s(elem!1))))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[339, 10026])).
% 2.03/2.27 tff(10028,plain,
% 2.03/2.27 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[9405, 1737, 325, 2106, 712, 1691, 323, 1069])).
% 2.03/2.27 tff(10029,plain,
% 2.03/2.27 ($false),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[1897, 10028, 2163, 2023])).
% 2.03/2.27 tff(10030,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.27 tff(10031,plain,
% 2.03/2.27 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[10030, 10027, 9997, 9962, 9995, 9959, 1069])).
% 2.03/2.27 tff(10032,plain,
% 2.03/2.27 (b(s(s(s(s(elem!1)))), s(z))),
% 2.03/2.27 inference(unit_resolution,[status(thm)],[1828, 10031])).
% 2.03/2.27 tff(10033,plain,
% 2.03/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(10034,plain,
% 2.03/2.27 (((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.03/2.27 inference(rewrite,[status(thm)],[])).
% 2.03/2.27 tff(10035,plain,
% 2.03/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z))))))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[10034])).
% 2.03/2.28 tff(10036,plain,
% 2.03/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.03/2.28 inference(transitivity,[status(thm)],[10035, 10033])).
% 2.03/2.28 tff(10037,plain,
% 2.03/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.03/2.28 inference(quant_inst,[status(thm)],[])).
% 2.03/2.28 tff(10038,plain,
% 2.03/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[10037, 10036])).
% 2.03/2.28 tff(10039,plain,
% 2.03/2.28 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[10038, 128, 550, 7825, 10032, 9994])).
% 2.03/2.28 tff(10040,plain,
% 2.03/2.28 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[4309, 21, 239, 10039])).
% 2.03/2.28 tff(10041,plain,
% 2.03/2.28 ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[8951, 7825])).
% 2.03/2.28 tff(10042,plain,
% 2.03/2.28 (~b(z, s(s(z)))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[10041, 10005, 9994])).
% 2.03/2.28 tff(10043,plain,
% 2.03/2.28 (r(z, s(s(z)))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[516, 10042])).
% 2.03/2.28 tff(10044,plain,
% 2.03/2.28 (~b(z, s(s(s(s(elem!1)))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[4144, 128, 550, 7825, 10032])).
% 2.03/2.28 tff(10045,plain,
% 2.03/2.28 (r(z, s(s(s(s(elem!1)))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[2047, 21, 10044, 178])).
% 2.03/2.28 tff(10046,plain,
% 2.03/2.28 (~b(s(s(s(s(elem!1)))), z)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[8775, 128, 550, 7825, 10032])).
% 2.03/2.28 tff(10047,plain,
% 2.03/2.28 (r(s(s(s(s(elem!1)))), z)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[2081, 10046])).
% 2.03/2.28 tff(10048,plain,
% 2.03/2.28 ($false),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[8582, 45, 10047, 10045, 10043, 10040])).
% 2.03/2.28 tff(10049,plain,((~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(z))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.28 tff(10050,plain,
% 2.03/2.28 (~b(z, s(s(elem!1)))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[10049, 1069, 550, 1, 28])).
% 2.03/2.28 tff(10051,plain,
% 2.03/2.28 (r(z, s(s(elem!1)))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[160, 10050])).
% 2.03/2.28 tff(10052,plain,
% 2.03/2.28 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[9036, 10051, 9959])).
% 2.03/2.28 tff(10053,plain,
% 2.03/2.28 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[1897, 10052, 2023])).
% 2.03/2.28 tff(10054,plain,
% 2.03/2.28 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[9395, 128, 9997, 10007, 10053])).
% 2.03/2.28 tff(10055,plain,
% 2.03/2.28 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[1820, 10054, 9962])).
% 2.03/2.28 tff(10056,plain,
% 2.03/2.28 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[9613, 128, 9997, 10007, 10053])).
% 2.03/2.28 tff(10057,plain,
% 2.03/2.28 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[1856, 10056, 9961])).
% 2.03/2.28 tff(10058,plain,
% 2.03/2.28 ($false),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[3951, 45, 1737, 1866, 385])).
% 2.03/2.28 tff(10059,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.28 tff(10060,plain,
% 2.03/2.28 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[10059, 10057, 9975])).
% 2.03/2.28 tff(10061,plain,
% 2.03/2.28 (b(s(s(s(s(elem!1)))), s(z))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[1828, 10060])).
% 2.03/2.28 tff(10062,plain,
% 2.03/2.28 (~b(s(s(s(s(elem!1)))), z)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[8775, 128, 550, 7825, 10061])).
% 2.03/2.28 tff(10063,plain,
% 2.03/2.28 (r(s(s(s(s(elem!1)))), z)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[2081, 10062])).
% 2.03/2.28 tff(10064,plain,
% 2.03/2.28 (~r(s(s(s(elem!1))), z)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[1780, 10063, 10055])).
% 2.03/2.28 tff(10065,plain,
% 2.03/2.28 (b(s(s(s(elem!1))), z)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[5301, 10064])).
% 2.03/2.28 tff(10066,plain,
% 2.03/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(10067,plain,
% 2.03/2.28 (((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(10068,plain,
% 2.03/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[10067])).
% 2.03/2.28 tff(10069,plain,
% 2.03/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 2.03/2.28 inference(transitivity,[status(thm)],[10068, 10066])).
% 2.03/2.28 tff(10070,plain,
% 2.03/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.03/2.28 inference(quant_inst,[status(thm)],[])).
% 2.03/2.28 tff(10071,plain,
% 2.03/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[10070, 10069])).
% 2.03/2.28 tff(10072,plain,
% 2.03/2.28 ($false),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[10071, 128, 550, 7825, 9951, 9997, 10065])).
% 2.03/2.28 tff(10073,plain,((s(s(elem!1)) = s(s(s(s(elem!1))))) | (~b(z, s(z))) | (s(s(elem!1)) = s(s(z))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.28 tff(10074,plain,
% 2.03/2.28 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[10073, 1, 550, 28])).
% 2.03/2.28 tff(10075,plain,
% 2.03/2.28 (s(s(elem!1)) = elem!1),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[1089, 10074])).
% 2.03/2.28 tff(10076,plain,
% 2.03/2.28 (s(s(s(elem!1))) = s(elem!1)),
% 2.03/2.28 inference(monotonicity,[status(thm)],[10075])).
% 2.03/2.28 tff(10077,plain,
% 2.03/2.28 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[10076])).
% 2.03/2.28 tff(10078,plain,
% 2.03/2.28 (s(s(s(s(elem!1)))) = elem!1),
% 2.03/2.28 inference(transitivity,[status(thm)],[10077, 10075])).
% 2.03/2.28 tff(10079,plain,
% 2.03/2.28 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(elem!1), elem!1)),
% 2.03/2.28 inference(monotonicity,[status(thm)],[10078])).
% 2.03/2.28 tff(10080,plain,
% 2.03/2.28 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(elem!1), s(s(s(s(elem!1)))))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[10076])).
% 2.03/2.28 tff(10081,plain,
% 2.03/2.28 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(elem!1), elem!1)),
% 2.03/2.28 inference(transitivity,[status(thm)],[10080, 10079])).
% 2.03/2.28 tff(10082,plain,
% 2.03/2.28 (r(s(s(s(s(elem!1)))), s(z)) <=> r(elem!1, s(z))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[10078])).
% 2.03/2.28 tff(10083,plain,
% 2.03/2.28 (r(elem!1, s(z)) <=> r(s(s(s(s(elem!1)))), s(z))),
% 2.03/2.28 inference(symmetry,[status(thm)],[10082])).
% 2.03/2.28 tff(10084,plain,
% 2.03/2.28 (r(s(s(elem!1)), s(z)) <=> r(elem!1, s(z))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[10075])).
% 2.03/2.28 tff(10085,plain,
% 2.03/2.28 (r(elem!1, s(z))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[9959, 10084])).
% 2.03/2.28 tff(10086,plain,
% 2.03/2.28 (r(s(s(s(s(elem!1)))), s(z))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[10085, 10083])).
% 2.03/2.28 tff(10087,plain,
% 2.03/2.28 (b(s(s(s(elem!1))), s(z)) <=> b(s(elem!1), s(z))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[10076])).
% 2.03/2.28 tff(10088,plain,
% 2.03/2.28 (b(s(elem!1), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 2.03/2.28 inference(symmetry,[status(thm)],[10087])).
% 2.03/2.28 tff(10089,plain,
% 2.03/2.28 ((~b(s(elem!1), s(z))) <=> (~b(s(s(s(elem!1))), s(z)))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[10088])).
% 2.03/2.28 tff(10090,plain,
% 2.03/2.28 ((s(s(s(elem!1))) = s(s(z))) <=> (s(elem!1) = s(s(z)))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[10076])).
% 2.03/2.28 tff(10091,plain,
% 2.03/2.28 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(elem!1) = s(s(z))))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[10090])).
% 2.03/2.28 tff(10092,plain,
% 2.03/2.28 (~(s(elem!1) = s(s(z)))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[283, 10091])).
% 2.03/2.28 tff(10093,plain,
% 2.03/2.28 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(elem!1))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[10076])).
% 2.03/2.28 tff(10094,plain,
% 2.03/2.28 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[10075])).
% 2.03/2.28 tff(10095,plain,
% 2.03/2.28 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(elem!1, s(elem!1))),
% 2.03/2.28 inference(transitivity,[status(thm)],[10094, 10093])).
% 2.03/2.28 tff(10096,plain,
% 2.03/2.28 ((s(s(elem!1)) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[10075])).
% 2.03/2.28 tff(10097,plain,
% 2.03/2.28 ((s(s(elem!1)) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 2.03/2.28 inference(transitivity,[status(thm)],[10096, 225])).
% 2.03/2.28 tff(10098,plain,
% 2.03/2.28 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[10097])).
% 2.03/2.28 tff(10099,plain,
% 2.03/2.28 (~(s(s(z)) = elem!1)),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[1, 10098])).
% 2.03/2.28 tff(10100,plain,
% 2.03/2.28 (b(s(s(elem!1)), z) <=> b(elem!1, z)),
% 2.03/2.28 inference(monotonicity,[status(thm)],[10075])).
% 2.03/2.28 tff(10101,plain,
% 2.03/2.28 (b(elem!1, z)),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[9951, 10100])).
% 2.03/2.28 tff(10102,plain,
% 2.03/2.28 (r(s(z), s(s(elem!1))) <=> r(s(z), elem!1)),
% 2.03/2.28 inference(monotonicity,[status(thm)],[10075])).
% 2.03/2.28 tff(10103,plain,
% 2.03/2.28 (r(s(z), elem!1)),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[9986, 10102])).
% 2.03/2.28 tff(10104,plain,
% 2.03/2.28 (~(s(s(s(elem!1))) = elem!1)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[714, 199, 9580])).
% 2.03/2.28 tff(10105,plain,
% 2.03/2.28 ((~b(s(elem!1), z)) <=> (~b(s(s(s(elem!1))), z))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[7687])).
% 2.03/2.28 tff(10106,plain,
% 2.03/2.28 (b(s(s(s(elem!1))), s(z))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[196, 394])).
% 2.03/2.28 tff(10107,plain,
% 2.03/2.28 (b(s(elem!1), s(z))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[10106, 261])).
% 2.03/2.28 tff(10108,plain,
% 2.03/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(10109,plain,
% 2.03/2.28 (((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(10110,plain,
% 2.03/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z)))))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[10109])).
% 2.03/2.28 tff(10111,plain,
% 2.03/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))),
% 2.03/2.28 inference(transitivity,[status(thm)],[10110, 10108])).
% 2.03/2.28 tff(10112,plain,
% 2.03/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))),
% 2.03/2.28 inference(quant_inst,[status(thm)],[])).
% 2.03/2.28 tff(10113,plain,
% 2.03/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z)))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[10112, 10111])).
% 2.03/2.28 tff(10114,plain,
% 2.03/2.28 (~b(s(elem!1), z)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[10113, 128, 550, 7825, 10107])).
% 2.03/2.28 tff(10115,plain,
% 2.03/2.28 (~b(s(s(s(elem!1))), z)),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[10114, 10105])).
% 2.03/2.28 tff(10116,plain,
% 2.03/2.28 (r(s(s(s(elem!1))), z)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[5301, 10115])).
% 2.03/2.28 tff(10117,plain,
% 2.03/2.28 (b(z, elem!1)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[457, 9337, 378])).
% 2.03/2.28 tff(10118,plain,
% 2.03/2.28 (r(s(elem!1), z)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[728, 21, 109, 10114])).
% 2.03/2.28 tff(10119,plain,
% 2.03/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(elem!1))))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(10120,plain,
% 2.03/2.28 (((~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(elem!1), z)) | (~r(s(s(z)), s(elem!1)))) <=> ((~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(elem!1))))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(10121,plain,
% 2.03/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(elem!1), z)) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(elem!1)))))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[10120])).
% 2.03/2.28 tff(10122,plain,
% 2.03/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(elem!1), z)) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(elem!1))))),
% 2.03/2.28 inference(transitivity,[status(thm)],[10121, 10119])).
% 2.03/2.28 tff(10123,plain,
% 2.03/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(elem!1), z)) | (~r(s(s(z)), s(elem!1))))),
% 2.03/2.28 inference(quant_inst,[status(thm)],[])).
% 2.03/2.28 tff(10124,plain,
% 2.03/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(elem!1)))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[10123, 10122])).
% 2.03/2.28 tff(10125,plain,
% 2.03/2.28 (~r(s(s(z)), s(elem!1))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[10124, 45, 28, 10118])).
% 2.03/2.28 tff(10126,plain,
% 2.03/2.28 ((s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[351, 21, 10125])).
% 2.03/2.28 tff(10127,plain,
% 2.03/2.28 (b(s(s(z)), s(elem!1))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[10126, 285])).
% 2.03/2.28 tff(10128,plain,
% 2.03/2.28 (b(s(z), s(elem!1))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[9344, 286])).
% 2.03/2.28 tff(10129,plain,
% 2.03/2.28 (((~b(s(z), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(elem!1))))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(10130,plain,
% 2.03/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(elem!1)))))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[10129])).
% 2.03/2.28 tff(10131,plain,
% 2.03/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(elem!1))))),
% 2.03/2.28 inference(transitivity,[status(thm)],[10130, 342])).
% 2.03/2.28 tff(10132,plain,
% 2.03/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(z))))),
% 2.03/2.28 inference(quant_inst,[status(thm)],[])).
% 2.03/2.28 tff(10133,plain,
% 2.03/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(z)), s(elem!1)))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[10132, 10131])).
% 2.03/2.28 tff(10134,plain,
% 2.03/2.28 (~b(s(s(z)), s(z))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[10133, 128, 10128, 10107, 10127])).
% 2.03/2.28 tff(10135,plain,
% 2.03/2.28 (r(s(s(z)), s(z))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[86, 10134])).
% 2.03/2.28 tff(10136,plain,
% 2.03/2.28 (r(elem!1, s(z))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[325, 1578])).
% 2.03/2.28 tff(10137,plain,
% 2.03/2.28 (~r(s(s(z)), elem!1)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[1573, 45, 10136, 10135])).
% 2.03/2.28 tff(10138,plain,
% 2.03/2.28 (b(s(s(z)), elem!1)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[370, 10137, 484])).
% 2.03/2.28 tff(10139,plain,
% 2.03/2.28 (~b(s(s(s(elem!1))), elem!1)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[5131, 10138, 577, 10117, 10116])).
% 2.03/2.28 tff(10140,plain,
% 2.03/2.28 (r(s(s(s(elem!1))), elem!1)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[742, 10139, 10104])).
% 2.03/2.28 tff(10141,plain,
% 2.03/2.28 (r(s(elem!1), elem!1)),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[10140, 687])).
% 2.03/2.28 tff(10142,plain,
% 2.03/2.28 (~b(s(s(s(s(z)))), elem!1)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[627, 10138, 10117, 577])).
% 2.03/2.28 tff(10143,plain,
% 2.03/2.28 (r(s(s(s(s(z)))), elem!1)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[632, 10142, 243])).
% 2.03/2.28 tff(10144,plain,
% 2.03/2.28 (~r(s(elem!1), s(s(s(s(z)))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[750, 45, 10143, 10141])).
% 2.03/2.28 tff(10145,plain,
% 2.03/2.28 (b(s(elem!1), s(s(s(s(z)))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[765, 21, 762, 10144])).
% 2.03/2.28 tff(10146,plain,
% 2.03/2.28 (~r(s(z), s(s(s(s(z)))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[672, 45, 1340, 10143])).
% 2.03/2.28 tff(10147,plain,
% 2.03/2.28 (b(s(z), s(s(s(s(z)))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[684, 21, 681, 10146])).
% 2.03/2.28 tff(10148,plain,
% 2.03/2.28 (~r(s(s(s(s(z)))), s(z))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[8293, 45, 1340, 10143])).
% 2.03/2.28 tff(10149,plain,
% 2.03/2.28 (b(s(s(s(s(z)))), s(z))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[784, 10148])).
% 2.03/2.28 tff(10150,plain,
% 2.03/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(10151,plain,
% 2.03/2.28 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(elem!1)))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(10152,plain,
% 2.03/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[10151])).
% 2.03/2.28 tff(10153,plain,
% 2.03/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.03/2.28 inference(transitivity,[status(thm)],[10152, 10150])).
% 2.03/2.28 tff(10154,plain,
% 2.03/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(elem!1))))),
% 2.03/2.28 inference(quant_inst,[status(thm)],[])).
% 2.03/2.28 tff(10155,plain,
% 2.03/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[10154, 10153])).
% 2.03/2.28 tff(10156,plain,
% 2.03/2.28 ($false),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[10155, 128, 7825, 10128, 10149, 10147, 10145])).
% 2.03/2.28 tff(10157,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~(s(s(elem!1)) = elem!1)) | (~b(elem!1, z)) | (s(s(z)) = elem!1) | (~r(s(s(z)), z)) | (~b(z, s(z))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.28 tff(10158,plain,
% 2.03/2.28 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[10157, 10103, 10075, 10101, 10099, 28, 550, 9959])).
% 2.03/2.28 tff(10159,plain,
% 2.03/2.28 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[321, 10158, 9960])).
% 2.03/2.28 tff(10160,plain,
% 2.03/2.28 (b(elem!1, s(elem!1))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[10159, 10095])).
% 2.03/2.28 tff(10161,plain,
% 2.03/2.28 ((s(s(elem!1)) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 2.03/2.28 inference(transitivity,[status(thm)],[10097, 650])).
% 2.03/2.28 tff(10162,plain,
% 2.03/2.28 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(elem!1 = s(s(z))))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[10161])).
% 2.03/2.28 tff(10163,plain,
% 2.03/2.28 (~(elem!1 = s(s(z)))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[1, 10162])).
% 2.03/2.28 tff(10164,plain,
% 2.03/2.28 (~(s(s(z)) = s(elem!1))),
% 2.03/2.28 inference(modus_ponens,[status(thm)],[759, 276])).
% 2.03/2.28 tff(10165,plain,
% 2.03/2.28 (~b(s(elem!1), z)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[10113, 128, 550, 7825, 263])).
% 2.03/2.28 tff(10166,plain,
% 2.03/2.28 (r(s(elem!1), z)),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[728, 21, 109, 10165])).
% 2.03/2.28 tff(10167,plain,
% 2.03/2.28 (~r(s(s(z)), s(elem!1))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[10124, 45, 28, 10166])).
% 2.03/2.28 tff(10168,plain,
% 2.03/2.28 ((s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[351, 21, 10167])).
% 2.03/2.28 tff(10169,plain,
% 2.03/2.28 (b(s(s(z)), s(elem!1))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[10168, 10164])).
% 2.03/2.28 tff(10170,plain,
% 2.03/2.28 (~r(s(elem!1), s(s(z)))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[7237, 45, 28, 10166])).
% 2.03/2.28 tff(10171,plain,
% 2.03/2.28 (b(s(elem!1), s(s(z)))),
% 2.03/2.28 inference(unit_resolution,[status(thm)],[473, 21, 759, 10170])).
% 2.03/2.28 tff(10172,plain,
% 2.03/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(10173,plain,
% 2.03/2.28 (((~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(z))))) <=> ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))))),
% 2.03/2.28 inference(rewrite,[status(thm)],[])).
% 2.03/2.28 tff(10174,plain,
% 2.03/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1)))))),
% 2.03/2.28 inference(monotonicity,[status(thm)],[10173])).
% 2.03/2.28 tff(10175,plain,
% 2.03/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))))),
% 2.03/2.29 inference(transitivity,[status(thm)],[10174, 10172])).
% 2.03/2.29 tff(10176,plain,
% 2.03/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(z)))))),
% 2.03/2.29 inference(quant_inst,[status(thm)],[])).
% 2.03/2.29 tff(10177,plain,
% 2.03/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1)))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[10176, 10175])).
% 2.03/2.29 tff(10178,plain,
% 2.03/2.29 (~b(elem!1, s(s(z)))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10177, 128, 577, 7825, 1830, 263, 10169])).
% 2.03/2.29 tff(10179,plain,
% 2.03/2.29 (r(elem!1, s(s(z)))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[493, 10178, 7443])).
% 2.03/2.29 tff(10180,plain,
% 2.03/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z)))))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(10181,plain,
% 2.03/2.29 (((~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z)))))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(10182,plain,
% 2.03/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z))))))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[10181])).
% 2.03/2.29 tff(10183,plain,
% 2.03/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z)))))),
% 2.03/2.29 inference(transitivity,[status(thm)],[10182, 10180])).
% 2.03/2.29 tff(10184,plain,
% 2.03/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(z))))),
% 2.03/2.29 inference(quant_inst,[status(thm)],[])).
% 2.03/2.29 tff(10185,plain,
% 2.03/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z))))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[10184, 10183])).
% 2.03/2.29 tff(10186,plain,
% 2.03/2.29 ($false),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10185, 45, 313, 7454, 634])).
% 2.03/2.29 tff(10187,plain,((~r(s(z), s(s(z)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.29 tff(10188,plain,
% 2.03/2.29 (~r(s(z), s(s(z)))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10187, 10179, 313])).
% 2.03/2.29 tff(10189,plain,
% 2.03/2.29 (b(s(z), s(s(z)))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[648, 10188])).
% 2.03/2.29 tff(10190,plain,
% 2.03/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(elem!1))))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(10191,plain,
% 2.03/2.29 (((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(elem!1))) | (~b(s(z), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(elem!1))))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(10192,plain,
% 2.03/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(elem!1))) | (~b(s(z), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(elem!1)))))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[10191])).
% 2.03/2.29 tff(10193,plain,
% 2.03/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(elem!1))) | (~b(s(z), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(elem!1))))),
% 2.03/2.29 inference(transitivity,[status(thm)],[10192, 10190])).
% 2.03/2.29 tff(10194,plain,
% 2.03/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(elem!1))) | (~b(s(z), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(z))))),
% 2.03/2.29 inference(quant_inst,[status(thm)],[])).
% 2.03/2.29 tff(10195,plain,
% 2.03/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(elem!1)))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[10194, 10193])).
% 2.03/2.29 tff(10196,plain,
% 2.03/2.29 ($false),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10195, 128, 10189, 263, 10171, 10169])).
% 2.03/2.29 tff(10197,plain,((~b(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (elem!1 = s(s(z))) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (s(elem!1) = s(s(z))) | (~r(s(s(z)), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.29 tff(10198,plain,
% 2.03/2.29 (~b(s(elem!1), s(z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10197, 10085, 10163, 10101, 10160, 10092, 28, 550])).
% 2.03/2.29 tff(10199,plain,
% 2.03/2.29 (~b(s(s(s(elem!1))), s(z))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[10198, 10089])).
% 2.03/2.29 tff(10200,plain,
% 2.03/2.29 (r(s(s(s(elem!1))), s(z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[196, 10199])).
% 2.03/2.29 tff(10201,plain,
% 2.03/2.29 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10059, 10200, 10086])).
% 2.03/2.29 tff(10202,plain,
% 2.03/2.29 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[1856, 10201, 9961])).
% 2.03/2.29 tff(10203,plain,
% 2.03/2.29 (b(s(elem!1), elem!1)),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[10202, 10081])).
% 2.03/2.29 tff(10204,plain,
% 2.03/2.29 (r(s(s(s(elem!1))), s(z)) <=> r(s(elem!1), s(z))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[10076])).
% 2.03/2.29 tff(10205,plain,
% 2.03/2.29 (r(s(elem!1), s(z))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[10200, 10204])).
% 2.03/2.29 tff(10206,plain,
% 2.03/2.29 (~r(s(elem!1), s(s(z)))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[5035, 45, 35, 5029])).
% 2.03/2.29 tff(10207,plain,
% 2.03/2.29 (b(s(elem!1), s(s(z)))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[473, 21, 759, 10206])).
% 2.03/2.29 tff(10208,plain,
% 2.03/2.29 (b(elem!1, s(s(z)))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[493, 1566, 7443])).
% 2.03/2.29 tff(10209,plain,
% 2.03/2.29 (b(s(s(z)), elem!1)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[370, 1574, 484])).
% 2.03/2.29 tff(10210,plain,
% 2.03/2.29 ($false),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[9678, 128, 10209, 10208, 4791, 10207])).
% 2.03/2.29 tff(10211,plain,((~r(s(s(z)), s(z))) | (~b(s(elem!1), elem!1)) | (s(elem!1) = s(s(z))) | (s(s(z)) = elem!1) | (elem!1 = s(s(z))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.29 tff(10212,plain,
% 2.03/2.29 (~r(s(s(z)), s(z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10211, 10203, 10092, 10099, 10163, 10085, 10205])).
% 2.03/2.29 tff(10213,plain,
% 2.03/2.29 (b(s(s(z)), s(z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[86, 10212])).
% 2.03/2.29 tff(10214,plain,
% 2.03/2.29 (~b(z, s(s(z)))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[8843, 128, 550, 7825, 10213])).
% 2.03/2.29 tff(10215,plain,
% 2.03/2.29 (r(z, s(s(z)))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[516, 10214])).
% 2.03/2.29 tff(10216,plain,
% 2.03/2.29 ((s(s(elem!1)) = z) <=> (elem!1 = z)),
% 2.03/2.29 inference(monotonicity,[status(thm)],[10075])).
% 2.03/2.29 tff(10217,plain,
% 2.03/2.29 ((s(s(elem!1)) = z) <=> (z = elem!1)),
% 2.03/2.29 inference(transitivity,[status(thm)],[10216, 247])).
% 2.03/2.29 tff(10218,plain,
% 2.03/2.29 ((~(s(s(elem!1)) = z)) <=> (~(z = elem!1))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[10217])).
% 2.03/2.29 tff(10219,plain,
% 2.03/2.29 (~(z = elem!1)),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[154, 10218])).
% 2.03/2.29 tff(10220,plain,
% 2.03/2.29 (b(s(s(s(elem!1))), elem!1) <=> b(s(elem!1), elem!1)),
% 2.03/2.29 inference(monotonicity,[status(thm)],[10076])).
% 2.03/2.29 tff(10221,plain,
% 2.03/2.29 (b(s(elem!1), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 2.03/2.29 inference(symmetry,[status(thm)],[10220])).
% 2.03/2.29 tff(10222,plain,
% 2.03/2.29 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), elem!1)),
% 2.03/2.29 inference(transitivity,[status(thm)],[10080, 10079, 10221])).
% 2.03/2.29 tff(10223,plain,
% 2.03/2.29 (b(s(s(s(elem!1))), elem!1)),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[10202, 10222])).
% 2.03/2.29 tff(10224,plain,
% 2.03/2.29 (~b(z, s(s(s(elem!1))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[7179, 498, 2659, 577])).
% 2.03/2.29 tff(10225,plain,
% 2.03/2.29 (r(z, s(s(s(elem!1))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[858, 10224])).
% 2.03/2.29 tff(10226,plain,
% 2.03/2.29 ((~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~r(z, s(s(s(elem!1)))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[8822, 7825])).
% 2.03/2.29 tff(10227,plain,
% 2.03/2.29 (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10226, 10225, 550, 385])).
% 2.03/2.29 tff(10228,plain,
% 2.03/2.29 (r(s(s(s(s(s(s(z)))))), s(elem!1)) <=> r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[354])).
% 2.03/2.29 tff(10229,plain,
% 2.03/2.29 (r(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(s(z)))))), s(elem!1))),
% 2.03/2.29 inference(symmetry,[status(thm)],[10228])).
% 2.03/2.29 tff(10230,plain,
% 2.03/2.29 ((~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(s(s(z)))))), s(elem!1)))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[10229])).
% 2.03/2.29 tff(10231,plain,
% 2.03/2.29 (~r(s(s(s(s(s(s(z)))))), s(elem!1))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[1096, 10230])).
% 2.03/2.29 tff(10232,assumption,(r(s(s(s(s(s(s(z)))))), s(elem!1))), introduced(assumption)).
% 2.03/2.29 tff(10233,plain,
% 2.03/2.29 ($false),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10232, 10231])).
% 2.03/2.29 tff(10234,plain,((~r(s(s(s(s(s(s(z)))))), s(elem!1))) | r(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.29 tff(10235,plain,
% 2.03/2.29 (~r(s(s(s(s(s(s(z)))))), s(elem!1))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10234, 10227, 199])).
% 2.03/2.29 tff(10236,plain,
% 2.03/2.29 (~(s(s(s(s(s(s(z)))))) = s(elem!1))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[9657, 199])).
% 2.03/2.29 tff(10237,plain,
% 2.03/2.29 (b(s(s(s(s(s(s(z)))))), s(elem!1))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[7815, 21, 10236, 10235])).
% 2.03/2.29 tff(10238,plain,
% 2.03/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, 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(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(10239,plain,
% 2.03/2.29 (((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(10240,plain,
% 2.03/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)))))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(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(X0, 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(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1)))))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[10239])).
% 2.03/2.29 tff(10241,plain,
% 2.03/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)))))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(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(X0, 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(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))))),
% 2.03/2.29 inference(transitivity,[status(thm)],[10240, 10238])).
% 2.03/2.29 tff(10242,plain,
% 2.03/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)))))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), s(elem!1))) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.03/2.29 inference(quant_inst,[status(thm)],[])).
% 2.03/2.29 tff(10243,plain,
% 2.03/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(elem!1)))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[10242, 10241])).
% 2.03/2.29 tff(10244,plain,
% 2.03/2.29 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10243, 128, 1830, 4791, 10237])).
% 2.03/2.29 tff(10245,plain,
% 2.03/2.29 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[1055, 10244, 246])).
% 2.03/2.29 tff(10246,plain,
% 2.03/2.29 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[7620, 10245, 313])).
% 2.03/2.29 tff(10247,plain,
% 2.03/2.29 (~b(s(elem!1), z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[5997, 128, 498, 577, 4791])).
% 2.03/2.29 tff(10248,plain,
% 2.03/2.29 (~b(s(s(s(elem!1))), z)),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[10247, 10105])).
% 2.03/2.29 tff(10249,plain,
% 2.03/2.29 (r(s(s(s(elem!1))), z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[5301, 10248])).
% 2.03/2.29 tff(10250,plain,
% 2.03/2.29 (~b(s(s(z)), elem!1)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[5131, 10249, 577, 2659, 498])).
% 2.03/2.29 tff(10251,plain,
% 2.03/2.29 (r(s(s(z)), elem!1)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[370, 10250, 484])).
% 2.03/2.29 tff(10252,plain,
% 2.03/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(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))))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(10253,plain,
% 2.03/2.29 (((~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))))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(10254,plain,
% 2.03/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(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)))))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[10253])).
% 2.03/2.29 tff(10255,plain,
% 2.03/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(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))))),
% 2.03/2.29 inference(transitivity,[status(thm)],[10254, 10252])).
% 2.03/2.29 tff(10256,plain,
% 2.03/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))))),
% 2.03/2.29 inference(quant_inst,[status(thm)],[])).
% 2.03/2.29 tff(10257,plain,
% 2.03/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z)))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[10256, 10255])).
% 2.03/2.29 tff(10258,plain,
% 2.03/2.29 (~r(s(s(z)), s(z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10257, 45, 1340, 10251])).
% 2.03/2.29 tff(10259,plain,
% 2.03/2.29 (b(s(s(z)), s(z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[86, 10258])).
% 2.03/2.29 tff(10260,plain,
% 2.03/2.29 ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z)))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[9195, 7825])).
% 2.03/2.29 tff(10261,plain,
% 2.03/2.29 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10260, 10259, 550])).
% 2.03/2.29 tff(10262,plain,
% 2.03/2.29 ($false),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[1148, 21, 10261, 10246, 8155])).
% 2.03/2.29 tff(10263,plain,((~b(z, elem!1)) | (~r(elem!1, s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~(s(s(elem!1)) = elem!1)) | (~b(z, s(z))) | (~r(s(z), elem!1)) | (s(s(z)) = elem!1) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.29 tff(10264,plain,
% 2.03/2.29 (~b(z, elem!1)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10263, 10085, 10160, 10203, 10075, 550, 10103, 10099, 10101, 10223, 10200])).
% 2.03/2.29 tff(10265,plain,
% 2.03/2.29 (r(z, elem!1)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[1549, 10264, 10219])).
% 2.03/2.29 tff(10266,plain,
% 2.03/2.29 ($false),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[1441, 45, 1416, 1103, 519])).
% 2.03/2.29 tff(10267,plain,((~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.29 tff(10268,plain,
% 2.03/2.29 (~r(s(s(z)), elem!1)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10267, 10265, 10215])).
% 2.03/2.29 tff(10269,plain,
% 2.03/2.29 (b(s(s(z)), elem!1)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[370, 10268, 10099])).
% 2.03/2.29 tff(10270,plain,
% 2.03/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(z)))))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(10271,plain,
% 2.03/2.29 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(z)))))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(10272,plain,
% 2.03/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(z))))))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[10271])).
% 2.03/2.29 tff(10273,plain,
% 2.03/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(z)))))),
% 2.03/2.29 inference(transitivity,[status(thm)],[10272, 10270])).
% 2.03/2.29 tff(10274,plain,
% 2.03/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))))),
% 2.03/2.29 inference(quant_inst,[status(thm)],[])).
% 2.03/2.29 tff(10275,plain,
% 2.03/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(z))))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[10274, 10273])).
% 2.03/2.29 tff(10276,plain,
% 2.03/2.29 (~b(s(elem!1), s(s(z)))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10275, 128, 10269, 10160, 10203])).
% 2.03/2.29 tff(10277,plain,
% 2.03/2.29 (r(s(elem!1), s(s(z)))),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[473, 21, 10092, 10276])).
% 2.03/2.29 tff(10278,plain,
% 2.03/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(z)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(z)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(z)))))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(10279,plain,
% 2.03/2.29 (((~r(z, s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(z, elem!1)) | (~r(s(elem!1), z))) <=> ((~r(z, elem!1)) | (~r(z, s(s(z)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(z)))))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(10280,plain,
% 2.03/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(z, elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(z)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(z))))))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[10279])).
% 2.03/2.29 tff(10281,plain,
% 2.03/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(z, elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(z)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(z)))))),
% 2.03/2.29 inference(transitivity,[status(thm)],[10280, 10278])).
% 2.03/2.29 tff(10282,plain,
% 2.03/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(z, elem!1)) | (~r(s(elem!1), z)))),
% 2.03/2.29 inference(quant_inst,[status(thm)],[])).
% 2.03/2.29 tff(10283,plain,
% 2.03/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(z)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(z))))),
% 2.03/2.29 inference(modus_ponens,[status(thm)],[10282, 10281])).
% 2.03/2.29 tff(10284,plain,
% 2.03/2.29 (~r(s(elem!1), z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[10283, 45, 10265, 10215, 10277])).
% 2.03/2.29 tff(10285,plain,
% 2.03/2.29 (b(s(elem!1), z)),
% 2.03/2.29 inference(unit_resolution,[status(thm)],[728, 21, 109, 10284])).
% 2.03/2.29 tff(10286,plain,
% 2.03/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(10287,plain,
% 2.03/2.29 (((~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))))),
% 2.03/2.29 inference(rewrite,[status(thm)],[])).
% 2.03/2.29 tff(10288,plain,
% 2.03/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1)))))),
% 2.03/2.29 inference(monotonicity,[status(thm)],[10287])).
% 2.03/2.29 tff(10289,plain,
% 2.03/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))))),
% 2.03/2.29 inference(transitivity,[status(thm)],[10288, 10286])).
% 2.03/2.29 tff(10290,plain,
% 2.03/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1), z)) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))))),
% 2.03/2.29 inference(quant_inst,[status(thm)],[])).
% 2.03/2.29 tff(10291,plain,
% 2.03/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1)))),
% 2.03/2.30 inference(modus_ponens,[status(thm)],[10290, 10289])).
% 2.03/2.30 tff(10292,plain,
% 2.03/2.30 ($false),
% 2.03/2.30 inference(unit_resolution,[status(thm)],[10291, 128, 10101, 550, 7825, 10160, 10285])).
% 2.03/2.30 tff(10293,plain,((s(s(elem!1)) = s(s(z))) | (~b(z, s(z))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.03/2.30 tff(10294,plain,
% 2.03/2.30 (s(s(elem!1)) = s(s(z))),
% 2.03/2.30 inference(unit_resolution,[status(thm)],[10293, 8511, 26])).
% 2.03/2.30 tff(10295,plain,
% 2.03/2.30 (z = elem!1),
% 2.03/2.30 inference(unit_resolution,[status(thm)],[4260, 10294])).
% 2.03/2.30 tff(10296,plain,
% 2.03/2.30 ((s(s(s(s(s(s(z)))))) = z) <=> (s(s(s(s(s(s(z)))))) = elem!1)),
% 2.03/2.30 inference(monotonicity,[status(thm)],[10295])).
% 2.03/2.30 tff(10297,plain,
% 2.03/2.30 ((~(s(s(s(s(s(s(z)))))) = z)) <=> (~(s(s(s(s(s(s(z)))))) = elem!1))),
% 2.03/2.30 inference(monotonicity,[status(thm)],[10296])).
% 2.03/2.30 tff(10298,plain,
% 2.03/2.30 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.03/2.30 inference(modus_ponens,[status(thm)],[1019, 10297])).
% 2.03/2.30 tff(10299,plain,
% 2.03/2.30 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.03/2.30 inference(monotonicity,[status(thm)],[10294])).
% 2.03/2.30 tff(10300,plain,
% 2.03/2.30 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.03/2.30 inference(symmetry,[status(thm)],[10299])).
% 2.03/2.30 tff(10301,plain,
% 2.03/2.30 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.03/2.30 inference(monotonicity,[status(thm)],[10300])).
% 2.03/2.30 tff(10302,plain,
% 2.03/2.30 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(z))))),
% 2.03/2.30 inference(symmetry,[status(thm)],[10301])).
% 2.03/2.30 tff(10303,plain,
% 2.03/2.30 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 2.03/2.30 inference(monotonicity,[status(thm)],[10295])).
% 2.03/2.30 tff(10304,plain,
% 2.03/2.30 ((s(s(s(elem!1))) = z) <=> (elem!1 = s(s(s(elem!1))))),
% 2.03/2.30 inference(transitivity,[status(thm)],[10303, 705])).
% 2.03/2.30 tff(10305,plain,
% 2.03/2.30 ((~(s(s(s(elem!1))) = z)) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 2.03/2.30 inference(monotonicity,[status(thm)],[10304])).
% 2.03/2.30 tff(10306,plain,
% 2.03/2.30 (~(elem!1 = s(s(s(elem!1))))),
% 2.03/2.30 inference(modus_ponens,[status(thm)],[382, 10305])).
% 2.03/2.30 tff(10307,plain,
% 2.03/2.30 (r(s(s(z)), z) <=> r(s(s(z)), elem!1)),
% 2.03/2.30 inference(monotonicity,[status(thm)],[10295])).
% 2.03/2.30 tff(10308,plain,
% 2.03/2.30 (r(s(s(z)), elem!1)),
% 2.03/2.30 inference(modus_ponens,[status(thm)],[26, 10307])).
% 2.13/2.30 tff(10309,plain,
% 2.13/2.30 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10300])).
% 2.13/2.30 tff(10310,plain,
% 2.13/2.30 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(z))))),
% 2.13/2.30 inference(symmetry,[status(thm)],[10309])).
% 2.13/2.30 tff(10311,plain,
% 2.13/2.30 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10294])).
% 2.13/2.30 tff(10312,plain,
% 2.13/2.30 (s(s(z)) = s(s(elem!1))),
% 2.13/2.30 inference(symmetry,[status(thm)],[10294])).
% 2.13/2.30 tff(10313,plain,
% 2.13/2.30 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10312])).
% 2.13/2.30 tff(10314,plain,
% 2.13/2.30 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 2.13/2.30 inference(transitivity,[status(thm)],[10313, 799])).
% 2.13/2.30 tff(10315,plain,
% 2.13/2.30 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10314])).
% 2.13/2.30 tff(10316,plain,
% 2.13/2.30 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[283, 10315])).
% 2.13/2.30 tff(10317,plain,
% 2.13/2.30 (s(s(elem!1)) = s(s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10293, 550, 28])).
% 2.13/2.30 tff(10318,plain,
% 2.13/2.30 (b(s(s(elem!1)), s(z)) <=> b(s(s(z)), s(z))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10317])).
% 2.13/2.30 tff(10319,plain,
% 2.13/2.30 (b(s(s(z)), s(z))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[30, 10318])).
% 2.13/2.30 tff(10320,plain,
% 2.13/2.30 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10260, 10319, 550])).
% 2.13/2.30 tff(10321,plain,
% 2.13/2.30 (r(s(s(s(s(s(s(z)))))), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[1148, 21, 10320, 8155])).
% 2.13/2.30 tff(10322,plain,
% 2.13/2.30 (z = elem!1),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[4260, 10317])).
% 2.13/2.30 tff(10323,plain,
% 2.13/2.30 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10322])).
% 2.13/2.30 tff(10324,plain,
% 2.13/2.30 ((~(s(s(s(s(z)))) = z)) <=> (~(s(s(s(s(z)))) = elem!1))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10323])).
% 2.13/2.30 tff(10325,plain,
% 2.13/2.30 (~(s(s(s(s(z)))) = elem!1)),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[586, 10324])).
% 2.13/2.30 tff(10326,plain,
% 2.13/2.30 (s(s(z)) = s(s(elem!1))),
% 2.13/2.30 inference(symmetry,[status(thm)],[10317])).
% 2.13/2.30 tff(10327,plain,
% 2.13/2.30 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10317])).
% 2.13/2.30 tff(10328,plain,
% 2.13/2.30 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10327])).
% 2.13/2.30 tff(10329,plain,
% 2.13/2.30 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 2.13/2.30 inference(symmetry,[status(thm)],[10328])).
% 2.13/2.30 tff(10330,plain,
% 2.13/2.30 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10329, 10326])).
% 2.13/2.30 tff(10331,plain,
% 2.13/2.30 (r(s(s(s(s(elem!1)))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(z)))),
% 2.13/2.30 inference(symmetry,[status(thm)],[10330])).
% 2.13/2.30 tff(10332,plain,
% 2.13/2.30 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10326])).
% 2.13/2.30 tff(10333,plain,
% 2.13/2.30 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10332])).
% 2.13/2.30 tff(10334,plain,
% 2.13/2.30 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[239, 10333])).
% 2.13/2.30 tff(10335,plain,
% 2.13/2.30 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10329, 10326])).
% 2.13/2.30 tff(10336,plain,
% 2.13/2.30 ((~b(s(s(s(s(z)))), s(s(z)))) <=> (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10335])).
% 2.13/2.30 tff(10337,plain,
% 2.13/2.30 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.13/2.30 inference(symmetry,[status(thm)],[10327])).
% 2.13/2.30 tff(10338,plain,
% 2.13/2.30 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10337])).
% 2.13/2.30 tff(10339,plain,
% 2.13/2.30 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(z))))),
% 2.13/2.30 inference(symmetry,[status(thm)],[10338])).
% 2.13/2.30 tff(10340,plain,
% 2.13/2.30 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10317])).
% 2.13/2.30 tff(10341,plain,
% 2.13/2.30 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10326])).
% 2.13/2.30 tff(10342,plain,
% 2.13/2.30 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 2.13/2.30 inference(transitivity,[status(thm)],[10341, 799])).
% 2.13/2.30 tff(10343,plain,
% 2.13/2.30 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10342])).
% 2.13/2.30 tff(10344,plain,
% 2.13/2.30 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[283, 10343])).
% 2.13/2.30 tff(10345,plain,
% 2.13/2.30 (~b(z, s(s(elem!1)))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[9870, 30, 550])).
% 2.13/2.30 tff(10346,plain,
% 2.13/2.30 (r(z, s(s(elem!1)))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[160, 10345])).
% 2.13/2.30 tff(10347,plain,
% 2.13/2.30 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10337])).
% 2.13/2.30 tff(10348,plain,
% 2.13/2.30 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.30 inference(symmetry,[status(thm)],[10347])).
% 2.13/2.30 tff(10349,plain,
% 2.13/2.30 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10328])).
% 2.13/2.30 tff(10350,plain,
% 2.13/2.30 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[693, 10344])).
% 2.13/2.30 tff(10351,plain,
% 2.13/2.30 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[700, 10350])).
% 2.13/2.30 tff(10352,plain,
% 2.13/2.30 (b(s(z), s(s(s(z)))) <=> b(s(z), s(s(s(elem!1))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10337])).
% 2.13/2.30 tff(10353,plain,
% 2.13/2.30 ((~b(s(z), s(s(s(z))))) <=> (~b(s(z), s(s(s(elem!1)))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10352])).
% 2.13/2.30 tff(10354,plain,
% 2.13/2.30 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10337])).
% 2.13/2.30 tff(10355,plain,
% 2.13/2.30 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), elem!1)),
% 2.13/2.30 inference(symmetry,[status(thm)],[10354])).
% 2.13/2.30 tff(10356,plain,
% 2.13/2.30 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10322])).
% 2.13/2.30 tff(10357,plain,
% 2.13/2.30 ((s(s(s(elem!1))) = z) <=> (elem!1 = s(s(s(elem!1))))),
% 2.13/2.30 inference(transitivity,[status(thm)],[10356, 705])).
% 2.13/2.30 tff(10358,plain,
% 2.13/2.30 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 2.13/2.30 inference(transitivity,[status(thm)],[10357, 982])).
% 2.13/2.30 tff(10359,plain,
% 2.13/2.30 ((~(s(s(s(elem!1))) = z)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10358])).
% 2.13/2.30 tff(10360,plain,
% 2.13/2.30 (~(s(s(s(elem!1))) = elem!1)),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[382, 10359])).
% 2.13/2.30 tff(10361,plain,
% 2.13/2.30 (r(s(s(elem!1)), elem!1) <=> r(s(s(z)), elem!1)),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10317])).
% 2.13/2.30 tff(10362,plain,
% 2.13/2.30 (r(s(s(z)), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 2.13/2.30 inference(symmetry,[status(thm)],[10361])).
% 2.13/2.30 tff(10363,plain,
% 2.13/2.30 (r(s(s(z)), z) <=> r(s(s(z)), elem!1)),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10322])).
% 2.13/2.30 tff(10364,plain,
% 2.13/2.30 (r(s(s(z)), z) <=> r(s(s(elem!1)), elem!1)),
% 2.13/2.30 inference(transitivity,[status(thm)],[10363, 10362])).
% 2.13/2.30 tff(10365,plain,
% 2.13/2.30 (r(s(s(elem!1)), elem!1)),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[28, 10364])).
% 2.13/2.30 tff(10366,plain,
% 2.13/2.30 (~r(s(s(s(elem!1))), elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[4990, 324, 10365])).
% 2.13/2.30 tff(10367,plain,
% 2.13/2.30 (b(s(s(s(elem!1))), elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[742, 10366, 10360])).
% 2.13/2.30 tff(10368,plain,
% 2.13/2.30 (b(s(s(s(z))), elem!1)),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[10367, 10355])).
% 2.13/2.30 tff(10369,plain,
% 2.13/2.30 (b(s(z), z) <=> b(s(z), elem!1)),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10322])).
% 2.13/2.30 tff(10370,plain,
% 2.13/2.30 (b(s(z), elem!1)),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[7825, 10369])).
% 2.13/2.30 tff(10371,plain,
% 2.13/2.30 (b(z, s(z)) <=> b(elem!1, s(z))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10322])).
% 2.13/2.30 tff(10372,plain,
% 2.13/2.30 (b(elem!1, s(z))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[550, 10371])).
% 2.13/2.30 tff(10373,plain,
% 2.13/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(10374,plain,
% 2.13/2.30 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(10375,plain,
% 2.13/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))) | (~b(s(s(s(z))), elem!1))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10374])).
% 2.13/2.30 tff(10376,plain,
% 2.13/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.13/2.30 inference(transitivity,[status(thm)],[10375, 10373])).
% 2.13/2.30 tff(10377,plain,
% 2.13/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 2.13/2.30 inference(quant_inst,[status(thm)],[])).
% 2.13/2.30 tff(10378,plain,
% 2.13/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[10377, 10376])).
% 2.13/2.30 tff(10379,plain,
% 2.13/2.30 (~b(s(z), s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10378, 128, 10372, 10370, 10368])).
% 2.13/2.30 tff(10380,plain,
% 2.13/2.30 (~b(s(z), s(s(s(elem!1))))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[10379, 10353])).
% 2.13/2.30 tff(10381,plain,
% 2.13/2.30 (r(s(z), s(s(s(elem!1))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[339, 10380])).
% 2.13/2.30 tff(10382,plain,
% 2.13/2.30 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[9233, 10381, 550, 273, 28])).
% 2.13/2.30 tff(10383,plain,
% 2.13/2.30 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[1772, 7944])).
% 2.13/2.30 tff(10384,plain,
% 2.13/2.30 ($false),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[1247, 10383])).
% 2.13/2.30 tff(10385,plain,((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | r(s(s(s(s(z)))), s(s(s(elem!1)))) | (~(s(s(elem!1)) = s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.30 tff(10386,plain,
% 2.13/2.30 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10385, 10382, 10317])).
% 2.13/2.30 tff(10387,plain,
% 2.13/2.30 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[1820, 10386, 10351])).
% 2.13/2.30 tff(10388,plain,
% 2.13/2.30 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[10387, 10349])).
% 2.13/2.30 tff(10389,plain,
% 2.13/2.30 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[10388, 10348])).
% 2.13/2.30 tff(10390,plain,
% 2.13/2.30 ((s(s(s(s(s(s(z)))))) = z) <=> (s(s(s(s(s(s(z)))))) = elem!1)),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10322])).
% 2.13/2.30 tff(10391,plain,
% 2.13/2.30 ((~(s(s(s(s(s(s(z)))))) = z)) <=> (~(s(s(s(s(s(s(z)))))) = elem!1))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10390])).
% 2.13/2.30 tff(10392,plain,
% 2.13/2.30 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[1019, 10391])).
% 2.13/2.30 tff(10393,plain,
% 2.13/2.30 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10337])).
% 2.13/2.30 tff(10394,plain,
% 2.13/2.30 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(z))))),
% 2.13/2.30 inference(symmetry,[status(thm)],[10393])).
% 2.13/2.30 tff(10395,plain,
% 2.13/2.30 ((~(s(s(s(elem!1))) = z)) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10357])).
% 2.13/2.30 tff(10396,plain,
% 2.13/2.30 (~(elem!1 = s(s(s(elem!1))))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[382, 10395])).
% 2.13/2.30 tff(10397,plain,
% 2.13/2.30 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10317])).
% 2.13/2.30 tff(10398,plain,
% 2.13/2.30 (r(s(s(z)), s(s(s(elem!1))))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[324, 10397])).
% 2.13/2.30 tff(10399,plain,
% 2.13/2.30 ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1)))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[8953, 7825])).
% 2.13/2.30 tff(10400,plain,
% 2.13/2.30 (~r(z, s(s(s(elem!1))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10399, 10381, 10398])).
% 2.13/2.30 tff(10401,plain,
% 2.13/2.30 (~r(elem!1, s(s(s(elem!1))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[2461, 10400, 10322])).
% 2.13/2.30 tff(10402,plain,
% 2.13/2.30 (b(elem!1, s(s(s(elem!1))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[2466, 10401, 10396])).
% 2.13/2.30 tff(10403,plain,
% 2.13/2.30 (b(elem!1, s(s(s(z))))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[10402, 10394])).
% 2.13/2.30 tff(10404,plain,
% 2.13/2.30 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[8174, 10403, 10368, 10317])).
% 2.13/2.30 tff(10405,plain,
% 2.13/2.30 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[1055, 10404, 10392])).
% 2.13/2.30 tff(10406,plain,
% 2.13/2.30 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 2.13/2.30 inference(transitivity,[status(thm)],[10342, 7930])).
% 2.13/2.30 tff(10407,plain,
% 2.13/2.30 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10406])).
% 2.13/2.30 tff(10408,plain,
% 2.13/2.30 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[283, 10407])).
% 2.13/2.30 tff(10409,plain,
% 2.13/2.30 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10317])).
% 2.13/2.30 tff(10410,plain,
% 2.13/2.30 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.13/2.30 inference(symmetry,[status(thm)],[10409])).
% 2.13/2.30 tff(10411,plain,
% 2.13/2.30 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10337])).
% 2.13/2.30 tff(10412,plain,
% 2.13/2.30 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.13/2.30 inference(transitivity,[status(thm)],[10411, 10410])).
% 2.13/2.30 tff(10413,plain,
% 2.13/2.30 ((~b(s(s(s(z))), s(s(z)))) <=> (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10412])).
% 2.13/2.30 tff(10414,plain,
% 2.13/2.30 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10328])).
% 2.13/2.30 tff(10415,plain,
% 2.13/2.30 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z))))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10414])).
% 2.13/2.30 tff(10416,plain,
% 2.13/2.30 (s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(elem!1))))))),
% 2.13/2.30 inference(symmetry,[status(thm)],[10415])).
% 2.13/2.30 tff(10417,plain,
% 2.13/2.30 ((s(s(s(z))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1)))))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10337, 10416])).
% 2.13/2.30 tff(10418,plain,
% 2.13/2.30 ((s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(z))) = s(s(s(s(s(s(z)))))))),
% 2.13/2.30 inference(symmetry,[status(thm)],[10417])).
% 2.13/2.30 tff(10419,plain,
% 2.13/2.30 ((~(s(s(s(elem!1))) = s(s(s(s(s(s(elem!1)))))))) <=> (~(s(s(s(z))) = s(s(s(s(s(s(z))))))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10418])).
% 2.13/2.30 tff(10420,plain,
% 2.13/2.30 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10317])).
% 2.13/2.30 tff(10421,plain,
% 2.13/2.30 (s(elem!1) = s(z)),
% 2.13/2.30 inference(transitivity,[status(thm)],[106, 10420, 69])).
% 2.13/2.30 tff(10422,plain,
% 2.13/2.30 ((s(elem!1) = s(s(s(s(elem!1))))) <=> (s(z) = s(s(s(s(elem!1)))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10421])).
% 2.13/2.30 tff(10423,plain,
% 2.13/2.30 ((s(elem!1) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(z))),
% 2.13/2.30 inference(transitivity,[status(thm)],[10422, 2245])).
% 2.13/2.30 tff(10424,plain,
% 2.13/2.30 ((s(s(s(s(elem!1)))) = s(z)) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 2.13/2.30 inference(symmetry,[status(thm)],[10423])).
% 2.13/2.30 tff(10425,plain,
% 2.13/2.30 ((~(s(s(s(s(elem!1)))) = s(z))) <=> (~(s(elem!1) = s(s(s(s(elem!1))))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10424])).
% 2.13/2.30 tff(10426,plain,
% 2.13/2.30 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[1723, 10425])).
% 2.13/2.30 tff(10427,plain,
% 2.13/2.30 (~(s(s(s(elem!1))) = s(s(s(s(s(s(elem!1)))))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[3236, 10426])).
% 2.13/2.30 tff(10428,plain,
% 2.13/2.30 (~(s(s(s(z))) = s(s(s(s(s(s(z)))))))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[10427, 10419])).
% 2.13/2.30 tff(10429,plain,
% 2.13/2.30 (r(s(s(s(z))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10337])).
% 2.13/2.30 tff(10430,plain,
% 2.13/2.30 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(z))), s(z))),
% 2.13/2.30 inference(symmetry,[status(thm)],[10429])).
% 2.13/2.30 tff(10431,plain,
% 2.13/2.30 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10337])).
% 2.13/2.30 tff(10432,plain,
% 2.13/2.30 ((~b(s(s(s(z))), s(z))) <=> (~b(s(s(s(elem!1))), s(z)))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10431])).
% 2.13/2.30 tff(10433,plain,
% 2.13/2.30 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[4252])).
% 2.13/2.30 tff(10434,plain,
% 2.13/2.30 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.13/2.30 inference(symmetry,[status(thm)],[10433])).
% 2.13/2.30 tff(10435,plain,
% 2.13/2.30 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[7885])).
% 2.13/2.30 tff(10436,plain,
% 2.13/2.30 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.13/2.30 inference(transitivity,[status(thm)],[10435, 10434])).
% 2.13/2.30 tff(10437,plain,
% 2.13/2.30 ((~b(s(s(z)), s(s(s(z))))) <=> (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10436])).
% 2.13/2.30 tff(10438,assumption,(b(s(s(s(z))), s(z))), introduced(assumption)).
% 2.13/2.30 tff(10439,plain,
% 2.13/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(10440,plain,
% 2.13/2.30 (((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(10441,plain,
% 2.13/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10440])).
% 2.13/2.30 tff(10442,plain,
% 2.13/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.13/2.30 inference(transitivity,[status(thm)],[10441, 10439])).
% 2.13/2.30 tff(10443,plain,
% 2.13/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.13/2.30 inference(quant_inst,[status(thm)],[])).
% 2.13/2.30 tff(10444,plain,
% 2.13/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[10443, 10442])).
% 2.13/2.30 tff(10445,plain,
% 2.13/2.30 ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10444, 128, 297, 8123, 273])).
% 2.13/2.30 tff(10446,plain,
% 2.13/2.30 (~b(s(s(z)), s(s(s(z))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10445, 10438])).
% 2.13/2.30 tff(10447,plain,
% 2.13/2.30 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[10446, 10437])).
% 2.13/2.30 tff(10448,plain,
% 2.13/2.30 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[321, 10447, 8054])).
% 2.13/2.30 tff(10449,plain,
% 2.13/2.30 ((~b(s(s(s(z))), elem!1)) <=> (~b(s(s(s(elem!1))), elem!1))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[8039])).
% 2.13/2.30 tff(10450,plain,
% 2.13/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(z))), elem!1)))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(10451,plain,
% 2.13/2.30 (((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(10452,plain,
% 2.13/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(z))), elem!1))))),
% 2.13/2.30 inference(monotonicity,[status(thm)],[10451])).
% 2.13/2.30 tff(10453,plain,
% 2.13/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(z))), elem!1)))),
% 2.13/2.30 inference(transitivity,[status(thm)],[10452, 10450])).
% 2.13/2.30 tff(10454,plain,
% 2.13/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 2.13/2.30 inference(quant_inst,[status(thm)],[])).
% 2.13/2.30 tff(10455,plain,
% 2.13/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[10454, 10453])).
% 2.13/2.30 tff(10456,plain,
% 2.13/2.30 ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10455, 128, 297, 8123])).
% 2.13/2.30 tff(10457,plain,
% 2.13/2.30 (~b(s(s(s(z))), elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10456, 10438])).
% 2.13/2.30 tff(10458,plain,
% 2.13/2.30 (~b(s(s(s(elem!1))), elem!1)),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[10457, 10449])).
% 2.13/2.30 tff(10459,plain,
% 2.13/2.30 (r(s(s(s(elem!1))), elem!1)),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[742, 10458, 8046])).
% 2.13/2.30 tff(10460,plain,
% 2.13/2.30 ($false),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[4990, 10459, 10448, 2349])).
% 2.13/2.30 tff(10461,plain,((~b(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), elem!1)) | (~(s(s(elem!1)) = s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.30 tff(10462,plain,
% 2.13/2.30 (~b(s(s(s(z))), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10461, 273, 10317, 10372, 10365])).
% 2.13/2.30 tff(10463,plain,
% 2.13/2.30 (~b(s(s(s(elem!1))), s(z))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[10462, 10432])).
% 2.13/2.30 tff(10464,plain,
% 2.13/2.30 (r(s(s(s(elem!1))), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[196, 10463])).
% 2.13/2.30 tff(10465,plain,
% 2.13/2.30 (r(s(s(s(z))), s(z))),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[10464, 10430])).
% 2.13/2.30 tff(10466,plain,
% 2.13/2.30 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10260, 273, 550])).
% 2.13/2.30 tff(10467,plain,
% 2.13/2.30 (r(s(s(s(s(s(s(z)))))), s(z))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[1148, 21, 10466, 8155])).
% 2.13/2.30 tff(10468,plain,
% 2.13/2.30 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[8170, 45, 10467, 10465])).
% 2.13/2.30 tff(10469,plain,
% 2.13/2.30 ((s(s(s(z))) = s(s(s(s(s(s(z))))))) | b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[8149, 21, 10468])).
% 2.13/2.30 tff(10470,plain,
% 2.13/2.30 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10469, 10428])).
% 2.13/2.30 tff(10471,plain,
% 2.13/2.30 (r(s(s(z)), elem!1)),
% 2.13/2.30 inference(modus_ponens,[status(thm)],[28, 10363])).
% 2.13/2.30 tff(10472,plain,
% 2.13/2.30 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[7664, 10405, 10471])).
% 2.13/2.30 tff(10473,plain,
% 2.13/2.30 ((s(s(s(s(s(s(z)))))) = s(s(z))) | b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[1134, 21, 10472])).
% 2.13/2.30 tff(10474,plain,
% 2.13/2.30 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 2.13/2.30 inference(unit_resolution,[status(thm)],[10473, 1124])).
% 2.13/2.30 tff(10475,plain,
% 2.13/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z)))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~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(X0, 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(s(s(z)))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.13/2.30 inference(rewrite,[status(thm)],[])).
% 2.13/2.30 tff(10476,plain,
% 2.13/2.30 (((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(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(s(s(z))))))))) <=> ((~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(10477,plain,
% 2.13/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(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(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z)))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[10476])).
% 2.13/2.31 tff(10478,plain,
% 2.13/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(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(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z)))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.13/2.31 inference(transitivity,[status(thm)],[10477, 10475])).
% 2.13/2.31 tff(10479,plain,
% 2.13/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(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(s(s(z)))))))))),
% 2.13/2.31 inference(quant_inst,[status(thm)],[])).
% 2.13/2.31 tff(10480,plain,
% 2.13/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z)))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[10479, 10478])).
% 2.13/2.31 tff(10481,plain,
% 2.13/2.31 ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10480, 128, 10370, 273, 10368, 10474])).
% 2.13/2.31 tff(10482,plain,
% 2.13/2.31 (~b(s(s(s(z))), s(s(z)))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10481, 10470])).
% 2.13/2.31 tff(10483,plain,
% 2.13/2.31 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[10482, 10413])).
% 2.13/2.31 tff(10484,plain,
% 2.13/2.31 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[889, 10483, 10408])).
% 2.13/2.31 tff(10485,plain,
% 2.13/2.31 (~b(s(s(s(s(elem!1)))), z)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[4546, 10387, 88, 10484])).
% 2.13/2.31 tff(10486,plain,
% 2.13/2.31 (~b(s(s(s(s(z)))), elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[2402, 10485, 10322])).
% 2.13/2.31 tff(10487,plain,
% 2.13/2.31 (r(s(s(s(s(z)))), elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[632, 10486, 10325])).
% 2.13/2.31 tff(10488,plain,
% 2.13/2.31 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[2986, 45, 10487, 10405])).
% 2.13/2.31 tff(10489,plain,
% 2.13/2.31 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[1215, 21, 1212, 10488])).
% 2.13/2.31 tff(10490,plain,
% 2.13/2.31 ((s(s(s(s(s(s(z)))))) = s(s(s(z)))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[10416, 10337])).
% 2.13/2.31 tff(10491,plain,
% 2.13/2.31 ((s(s(s(s(s(s(z)))))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1)))))))),
% 2.13/2.31 inference(transitivity,[status(thm)],[10490, 3226])).
% 2.13/2.31 tff(10492,plain,
% 2.13/2.31 ((s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(z)))))) = s(s(s(z))))),
% 2.13/2.31 inference(symmetry,[status(thm)],[10491])).
% 2.13/2.31 tff(10493,plain,
% 2.13/2.31 ((~(s(s(s(elem!1))) = s(s(s(s(s(s(elem!1)))))))) <=> (~(s(s(s(s(s(s(z)))))) = s(s(s(z)))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[10492])).
% 2.13/2.31 tff(10494,plain,
% 2.13/2.31 (~(s(s(s(s(s(s(z)))))) = s(s(s(z))))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[10427, 10493])).
% 2.13/2.31 tff(10495,plain,
% 2.13/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), 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(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(10496,plain,
% 2.13/2.31 (((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(10497,plain,
% 2.13/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), 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(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[10496])).
% 2.13/2.31 tff(10498,plain,
% 2.13/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), 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(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.13/2.31 inference(transitivity,[status(thm)],[10497, 10495])).
% 2.13/2.31 tff(10499,plain,
% 2.13/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.13/2.31 inference(quant_inst,[status(thm)],[])).
% 2.13/2.31 tff(10500,plain,
% 2.13/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[10499, 10498])).
% 2.13/2.31 tff(10501,plain,
% 2.13/2.31 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10500, 45, 10467, 10465])).
% 2.13/2.31 tff(10502,plain,
% 2.13/2.31 ((s(s(s(s(s(s(z)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[8090, 21, 10501])).
% 2.13/2.31 tff(10503,plain,
% 2.13/2.31 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10502, 10494])).
% 2.13/2.31 tff(10504,plain,
% 2.13/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(10505,plain,
% 2.13/2.31 (((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), 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(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(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(s(z)))))), s(s(s(z))))))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(10506,plain,
% 2.13/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z)))))), 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(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[10505])).
% 2.13/2.31 tff(10507,plain,
% 2.13/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z)))))), 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(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.13/2.31 inference(transitivity,[status(thm)],[10506, 10504])).
% 2.13/2.31 tff(10508,plain,
% 2.13/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z)))))), 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(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.13/2.31 inference(quant_inst,[status(thm)],[])).
% 2.13/2.31 tff(10509,plain,
% 2.13/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[10508, 10507])).
% 2.13/2.31 tff(10510,plain,
% 2.13/2.31 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10509, 128, 10403, 10368, 10503])).
% 2.13/2.31 tff(10511,plain,
% 2.13/2.31 ($false),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10510, 10489, 10389])).
% 2.13/2.31 tff(10512,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.31 tff(10513,plain,
% 2.13/2.31 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10512, 10346, 10319, 550, 28])).
% 2.13/2.31 tff(10514,plain,
% 2.13/2.31 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[321, 10513, 10344])).
% 2.13/2.31 tff(10515,plain,
% 2.13/2.31 (b(s(s(z)), s(s(s(elem!1))))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[10514, 10340])).
% 2.13/2.31 tff(10516,plain,
% 2.13/2.31 (b(s(s(z)), s(s(s(z))))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[10515, 10339])).
% 2.13/2.31 tff(10517,plain,
% 2.13/2.31 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[10337, 10329])).
% 2.13/2.31 tff(10518,plain,
% 2.13/2.31 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 2.13/2.31 inference(symmetry,[status(thm)],[10517])).
% 2.13/2.31 tff(10519,plain,
% 2.13/2.31 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.13/2.31 inference(transitivity,[status(thm)],[10332, 3209])).
% 2.13/2.31 tff(10520,plain,
% 2.13/2.31 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[10519])).
% 2.13/2.31 tff(10521,plain,
% 2.13/2.31 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[239, 10520])).
% 2.13/2.31 tff(10522,plain,
% 2.13/2.31 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[8524, 30, 550, 10521])).
% 2.13/2.31 tff(10523,plain,
% 2.13/2.31 (r(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[1828, 10522])).
% 2.13/2.31 tff(10524,plain,
% 2.13/2.31 (~b(s(s(s(z))), s(z))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10461, 10319, 10317, 10372, 10365])).
% 2.13/2.31 tff(10525,plain,
% 2.13/2.31 (~b(s(s(s(elem!1))), s(z))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[10524, 10432])).
% 2.13/2.31 tff(10526,plain,
% 2.13/2.31 (r(s(s(s(elem!1))), s(z))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[196, 10525])).
% 2.13/2.31 tff(10527,plain,
% 2.13/2.31 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10059, 10526, 10523])).
% 2.13/2.31 tff(10528,plain,
% 2.13/2.31 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[1856, 10527, 10350])).
% 2.13/2.31 tff(10529,plain,
% 2.13/2.31 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[10528, 10518])).
% 2.13/2.31 tff(10530,plain,
% 2.13/2.31 (~b(s(z), s(s(s(elem!1))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[7941, 10513, 30, 10334])).
% 2.13/2.31 tff(10531,plain,
% 2.13/2.31 (r(s(z), s(s(s(elem!1))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[339, 10530])).
% 2.13/2.31 tff(10532,plain,
% 2.13/2.31 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[9233, 10531, 550, 10319, 28])).
% 2.13/2.31 tff(10533,plain,
% 2.13/2.31 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10385, 10532, 10317])).
% 2.13/2.31 tff(10534,plain,
% 2.13/2.31 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[1820, 10533, 10351])).
% 2.13/2.31 tff(10535,plain,
% 2.13/2.31 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[10534, 10349])).
% 2.13/2.31 tff(10536,plain,
% 2.13/2.31 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[10535, 10348])).
% 2.13/2.31 tff(10537,plain,
% 2.13/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(10538,plain,
% 2.13/2.31 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), s(s(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(z))))))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(10539,plain,
% 2.13/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(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(X0, 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(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[10538])).
% 2.13/2.31 tff(10540,plain,
% 2.13/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(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(X0, 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(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.13/2.31 inference(transitivity,[status(thm)],[10539, 10537])).
% 2.13/2.31 tff(10541,plain,
% 2.13/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.13/2.31 inference(quant_inst,[status(thm)],[])).
% 2.13/2.31 tff(10542,plain,
% 2.13/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[10541, 10540])).
% 2.13/2.31 tff(10543,plain,
% 2.13/2.31 ((~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)))))) | (~b(s(s(z)), s(s(s(z)))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10542, 128])).
% 2.13/2.31 tff(10544,plain,
% 2.13/2.31 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10543, 10536, 10529, 10516])).
% 2.13/2.31 tff(10545,plain,
% 2.13/2.31 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[10544, 10336])).
% 2.13/2.31 tff(10546,plain,
% 2.13/2.31 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[1897, 10545, 10334])).
% 2.13/2.31 tff(10547,plain,
% 2.13/2.31 (r(s(s(s(s(z)))), s(s(z)))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[10546, 10331])).
% 2.13/2.31 tff(10548,plain,
% 2.13/2.31 (r(z, s(s(z))) <=> r(elem!1, s(s(z)))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[10322])).
% 2.13/2.31 tff(10549,plain,
% 2.13/2.31 (r(z, s(s(elem!1))) <=> r(z, s(s(z)))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[10317])).
% 2.13/2.31 tff(10550,plain,
% 2.13/2.31 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(z)))),
% 2.13/2.31 inference(transitivity,[status(thm)],[10549, 10548])).
% 2.13/2.31 tff(10551,plain,
% 2.13/2.31 (r(elem!1, s(s(z)))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[10346, 10550])).
% 2.13/2.31 tff(10552,plain,
% 2.13/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(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(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(10553,plain,
% 2.13/2.31 (((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(10554,plain,
% 2.13/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[10553])).
% 2.13/2.31 tff(10555,plain,
% 2.13/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.13/2.31 inference(transitivity,[status(thm)],[10554, 10552])).
% 2.13/2.31 tff(10556,plain,
% 2.13/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.13/2.31 inference(quant_inst,[status(thm)],[])).
% 2.13/2.31 tff(10557,plain,
% 2.13/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z))))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[10556, 10555])).
% 2.13/2.31 tff(10558,plain,
% 2.13/2.31 (~r(s(s(s(s(z)))), elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10557, 45, 10551, 10547])).
% 2.13/2.31 tff(10559,plain,
% 2.13/2.31 (b(s(s(s(s(z)))), elem!1)),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[632, 10558, 10325])).
% 2.13/2.31 tff(10560,plain,
% 2.13/2.31 (~b(s(s(s(s(z)))), s(z))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[2802, 128, 10372, 10370, 10559])).
% 2.13/2.31 tff(10561,plain,
% 2.13/2.31 (r(s(s(s(s(z)))), s(z))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[784, 10560])).
% 2.13/2.31 tff(10562,plain,
% 2.13/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $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(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(10563,plain,
% 2.13/2.31 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.13/2.31 inference(rewrite,[status(thm)],[])).
% 2.13/2.31 tff(10564,plain,
% 2.13/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[10563])).
% 2.13/2.31 tff(10565,plain,
% 2.13/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.13/2.31 inference(transitivity,[status(thm)],[10564, 10562])).
% 2.13/2.31 tff(10566,plain,
% 2.13/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.13/2.31 inference(quant_inst,[status(thm)],[])).
% 2.13/2.31 tff(10567,plain,
% 2.13/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 2.13/2.31 inference(modus_ponens,[status(thm)],[10566, 10565])).
% 2.13/2.31 tff(10568,plain,
% 2.13/2.31 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[10567, 45, 10561, 10321])).
% 2.13/2.31 tff(10569,plain,
% 2.13/2.31 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.13/2.31 inference(unit_resolution,[status(thm)],[1215, 21, 1212, 10568])).
% 2.13/2.31 tff(10570,plain,
% 2.13/2.31 (r(s(s(s(z))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 2.13/2.31 inference(monotonicity,[status(thm)],[10337])).
% 2.13/2.31 tff(10571,plain,
% 2.13/2.31 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(z))), elem!1)),
% 2.13/2.31 inference(symmetry,[status(thm)],[10570])).
% 2.13/2.31 tff(10572,plain,
% 2.13/2.31 ((~b(s(s(s(z))), elem!1)) <=> (~b(s(s(s(elem!1))), elem!1))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[10354])).
% 2.13/2.31 tff(10573,plain,
% 2.13/2.31 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 2.13/2.31 inference(monotonicity,[status(thm)],[10329])).
% 2.13/2.31 tff(10574,plain,
% 2.13/2.31 (b(elem!1, s(s(s(s(elem!1))))) <=> b(elem!1, s(s(s(s(z)))))),
% 2.13/2.31 inference(symmetry,[status(thm)],[10573])).
% 2.13/2.31 tff(10575,plain,
% 2.13/2.31 (elem!1 = z),
% 2.13/2.32 inference(symmetry,[status(thm)],[10322])).
% 2.13/2.32 tff(10576,plain,
% 2.13/2.32 ((elem!1 = s(s(s(s(elem!1))))) <=> (z = s(s(s(s(elem!1)))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[10575])).
% 2.13/2.32 tff(10577,plain,
% 2.13/2.32 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = z)),
% 2.13/2.32 inference(transitivity,[status(thm)],[10576, 1694])).
% 2.13/2.32 tff(10578,plain,
% 2.13/2.32 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 2.13/2.32 inference(symmetry,[status(thm)],[10577])).
% 2.13/2.32 tff(10579,plain,
% 2.13/2.32 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[10578])).
% 2.13/2.32 tff(10580,plain,
% 2.13/2.32 (~(elem!1 = s(s(s(s(elem!1)))))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[176, 10579])).
% 2.13/2.32 tff(10581,plain,
% 2.13/2.32 (r(elem!1, s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[10329])).
% 2.13/2.32 tff(10582,plain,
% 2.13/2.32 ((~r(elem!1, s(s(s(s(z)))))) <=> (~r(elem!1, s(s(s(s(elem!1))))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[10581])).
% 2.13/2.32 tff(10583,plain,
% 2.13/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), 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(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(10584,plain,
% 2.13/2.32 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(10585,plain,
% 2.13/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), 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(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(s(s(z))))))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[10584])).
% 2.13/2.32 tff(10586,plain,
% 2.13/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), 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(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.13/2.32 inference(transitivity,[status(thm)],[10585, 10583])).
% 2.13/2.32 tff(10587,plain,
% 2.13/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.13/2.32 inference(quant_inst,[status(thm)],[])).
% 2.13/2.32 tff(10588,plain,
% 2.13/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(elem!1, s(s(s(s(z))))))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[10587, 10586])).
% 2.13/2.32 tff(10589,plain,
% 2.13/2.32 (~r(elem!1, s(s(s(s(z)))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[10588, 45, 10551, 10547])).
% 2.13/2.32 tff(10590,plain,
% 2.13/2.32 (~r(elem!1, s(s(s(s(elem!1)))))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[10589, 10582])).
% 2.13/2.32 tff(10591,plain,
% 2.13/2.32 (b(elem!1, s(s(s(s(elem!1)))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[1766, 10590, 10580])).
% 2.13/2.32 tff(10592,plain,
% 2.13/2.32 (b(elem!1, s(s(s(s(z)))))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[10591, 10574])).
% 2.13/2.32 tff(10593,plain,
% 2.13/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(10594,plain,
% 2.13/2.32 (((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(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(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(10595,plain,
% 2.13/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[10594])).
% 2.13/2.32 tff(10596,plain,
% 2.13/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))),
% 2.13/2.32 inference(transitivity,[status(thm)],[10595, 10593])).
% 2.13/2.32 tff(10597,plain,
% 2.13/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)))),
% 2.13/2.32 inference(quant_inst,[status(thm)],[])).
% 2.13/2.32 tff(10598,plain,
% 2.13/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[10597, 10596])).
% 2.13/2.32 tff(10599,plain,
% 2.13/2.32 (~b(s(s(s(z))), elem!1)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[10598, 128, 10559, 10529, 10592])).
% 2.13/2.32 tff(10600,plain,
% 2.13/2.32 (~b(s(s(s(elem!1))), elem!1)),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[10599, 10572])).
% 2.13/2.32 tff(10601,plain,
% 2.13/2.32 (r(s(s(s(elem!1))), elem!1)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[742, 10600, 10360])).
% 2.13/2.32 tff(10602,plain,
% 2.13/2.32 (r(s(s(s(z))), elem!1)),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[10601, 10571])).
% 2.13/2.32 tff(10603,plain,
% 2.13/2.32 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[1477, 128, 297, 922, 576, 1010])).
% 2.13/2.32 tff(10604,plain,
% 2.13/2.32 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[1215, 21, 1212, 10603])).
% 2.13/2.32 tff(10605,assumption,(~b(s(s(s(s(s(s(z)))))), s(z))), introduced(assumption)).
% 2.13/2.32 tff(10606,plain,
% 2.13/2.32 (r(s(s(s(s(s(s(z)))))), s(z))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[1148, 21, 10605, 8155])).
% 2.13/2.32 tff(10607,plain,
% 2.13/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(10608,plain,
% 2.13/2.32 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(10609,plain,
% 2.13/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[10608])).
% 2.13/2.32 tff(10610,plain,
% 2.13/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.13/2.32 inference(transitivity,[status(thm)],[10609, 10607])).
% 2.13/2.32 tff(10611,plain,
% 2.13/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 2.13/2.32 inference(quant_inst,[status(thm)],[])).
% 2.13/2.32 tff(10612,plain,
% 2.13/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[10611, 10610])).
% 2.13/2.32 tff(10613,plain,
% 2.13/2.32 ($false),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[10612, 45, 930, 10606, 2968, 10604])).
% 2.13/2.32 tff(10614,plain,((~b(s(s(s(s(s(s(z)))))), elem!1)) | b(s(s(s(s(s(s(z)))))), s(z)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.32 tff(10615,plain,
% 2.13/2.32 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[10614, 10320, 10372, 10370, 10559])).
% 2.13/2.32 tff(10616,plain,
% 2.13/2.32 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[1055, 10615, 10392])).
% 2.13/2.32 tff(10617,plain,
% 2.13/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~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)))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(10618,plain,
% 2.13/2.32 (((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(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(s(z)))))))))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(10619,plain,
% 2.13/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~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)))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[10618])).
% 2.13/2.32 tff(10620,plain,
% 2.13/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~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)))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.13/2.32 inference(transitivity,[status(thm)],[10619, 10617])).
% 2.13/2.32 tff(10621,plain,
% 2.13/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.13/2.32 inference(quant_inst,[status(thm)],[])).
% 2.13/2.32 tff(10622,plain,
% 2.13/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[10621, 10620])).
% 2.13/2.32 tff(10623,plain,
% 2.13/2.32 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[10622, 45, 10616, 10602])).
% 2.13/2.32 tff(10624,plain,
% 2.13/2.32 ((s(s(s(z))) = s(s(s(s(s(s(z))))))) | b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[8149, 21, 10623])).
% 2.13/2.32 tff(10625,plain,
% 2.13/2.32 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[10624, 10428])).
% 2.13/2.32 tff(10626,plain,
% 2.13/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(10627,plain,
% 2.13/2.32 (((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.13/2.32 inference(rewrite,[status(thm)],[])).
% 2.13/2.32 tff(10628,plain,
% 2.13/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[10627])).
% 2.13/2.32 tff(10629,plain,
% 2.13/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.13/2.32 inference(transitivity,[status(thm)],[10628, 10626])).
% 2.13/2.32 tff(10630,plain,
% 2.13/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.13/2.32 inference(quant_inst,[status(thm)],[])).
% 2.13/2.32 tff(10631,plain,
% 2.13/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[10630, 10629])).
% 2.13/2.32 tff(10632,plain,
% 2.13/2.32 ($false),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[10631, 128, 10559, 10529, 10592, 10625, 10569])).
% 2.13/2.32 tff(10633,plain,((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.32 tff(10634,plain,
% 2.13/2.32 (~b(s(s(elem!1)), s(z))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[10633, 8511, 26])).
% 2.13/2.32 tff(10635,plain,
% 2.13/2.32 (r(s(s(elem!1)), s(z))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[292, 10634])).
% 2.13/2.32 tff(10636,plain,
% 2.13/2.32 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[10312])).
% 2.13/2.32 tff(10637,plain,
% 2.13/2.32 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.13/2.32 inference(transitivity,[status(thm)],[10636, 3209])).
% 2.13/2.32 tff(10638,plain,
% 2.13/2.32 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[10637])).
% 2.13/2.32 tff(10639,plain,
% 2.13/2.32 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[239, 10638])).
% 2.13/2.32 tff(10640,plain,
% 2.13/2.32 (~b(s(s(s(elem!1))), s(z))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[9973, 10635, 10639, 8511, 26])).
% 2.13/2.32 tff(10641,plain,
% 2.13/2.32 (r(s(s(s(elem!1))), s(z))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[196, 10640])).
% 2.13/2.32 tff(10642,plain,
% 2.13/2.32 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[393, 10641, 10635])).
% 2.13/2.32 tff(10643,plain,
% 2.13/2.32 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[321, 10642, 10316])).
% 2.13/2.32 tff(10644,plain,
% 2.13/2.32 (b(s(s(z)), s(s(s(elem!1))))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[10643, 10311])).
% 2.13/2.32 tff(10645,plain,
% 2.13/2.32 (b(s(s(z)), s(s(s(z))))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[10644, 10310])).
% 2.13/2.32 tff(10646,plain,
% 2.13/2.32 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[10300])).
% 2.13/2.32 tff(10647,plain,
% 2.13/2.32 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(z))), s(s(z)))),
% 2.13/2.32 inference(symmetry,[status(thm)],[10646])).
% 2.13/2.32 tff(10648,plain,
% 2.13/2.32 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[10294])).
% 2.13/2.32 tff(10649,plain,
% 2.13/2.32 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 2.13/2.32 inference(transitivity,[status(thm)],[10314, 7930])).
% 2.13/2.32 tff(10650,plain,
% 2.13/2.32 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[10649])).
% 2.13/2.32 tff(10651,plain,
% 2.13/2.32 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[283, 10650])).
% 2.13/2.32 tff(10652,plain,
% 2.13/2.32 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[10294])).
% 2.13/2.32 tff(10653,plain,
% 2.13/2.32 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.13/2.32 inference(symmetry,[status(thm)],[10652])).
% 2.13/2.32 tff(10654,plain,
% 2.13/2.32 ((~r(s(s(s(elem!1))), s(s(z)))) <=> (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[10653])).
% 2.13/2.32 tff(10655,plain,
% 2.13/2.32 (r(s(s(elem!1)), s(z)) <=> r(s(s(z)), s(z))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[10294])).
% 2.13/2.32 tff(10656,plain,
% 2.13/2.32 (r(s(s(z)), s(z))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[10635, 10655])).
% 2.13/2.32 tff(10657,plain,
% 2.13/2.32 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[6248, 10656, 10641])).
% 2.13/2.32 tff(10658,plain,
% 2.13/2.32 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[10657, 10654])).
% 2.13/2.32 tff(10659,plain,
% 2.13/2.32 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[889, 10658, 10651])).
% 2.13/2.32 tff(10660,plain,
% 2.13/2.32 (b(s(s(s(elem!1))), s(s(z)))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[10659, 10648])).
% 2.13/2.32 tff(10661,plain,
% 2.13/2.32 (b(s(s(s(z))), s(s(z)))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[10660, 10647])).
% 2.13/2.32 tff(10662,plain,
% 2.13/2.32 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[693, 10316])).
% 2.13/2.32 tff(10663,plain,
% 2.13/2.32 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[10299])).
% 2.13/2.32 tff(10664,plain,
% 2.13/2.32 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 2.13/2.32 inference(symmetry,[status(thm)],[10663])).
% 2.13/2.32 tff(10665,plain,
% 2.13/2.32 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[10300, 10664])).
% 2.13/2.32 tff(10666,plain,
% 2.13/2.32 ((~b(s(s(s(z))), s(s(s(s(z)))))) <=> (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[10665])).
% 2.13/2.32 tff(10667,plain,
% 2.13/2.32 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[10664, 10312])).
% 2.13/2.32 tff(10668,plain,
% 2.13/2.32 (b(s(s(s(s(elem!1)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 2.13/2.32 inference(symmetry,[status(thm)],[10667])).
% 2.13/2.32 tff(10669,plain,
% 2.13/2.32 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[10636])).
% 2.13/2.32 tff(10670,plain,
% 2.13/2.32 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[239, 10669])).
% 2.13/2.32 tff(10671,plain,
% 2.13/2.32 (r(z, s(s(elem!1))) <=> r(z, s(s(z)))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[10294])).
% 2.13/2.32 tff(10672,plain,
% 2.13/2.32 (r(z, s(s(z))) <=> r(z, s(s(elem!1)))),
% 2.13/2.32 inference(symmetry,[status(thm)],[10671])).
% 2.13/2.32 tff(10673,plain,
% 2.13/2.32 (r(z, s(s(z))) <=> r(elem!1, s(s(z)))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[10295])).
% 2.13/2.32 tff(10674,plain,
% 2.13/2.32 (r(elem!1, s(s(z))) <=> r(z, s(s(z)))),
% 2.13/2.32 inference(symmetry,[status(thm)],[10673])).
% 2.13/2.32 tff(10675,plain,
% 2.13/2.32 (r(elem!1, s(s(z))) <=> r(z, s(s(elem!1)))),
% 2.13/2.32 inference(transitivity,[status(thm)],[10674, 10672])).
% 2.13/2.32 tff(10676,plain,
% 2.13/2.32 ((s(s(z)) = z) <=> (s(s(z)) = elem!1)),
% 2.13/2.32 inference(monotonicity,[status(thm)],[10295])).
% 2.13/2.32 tff(10677,plain,
% 2.13/2.32 ((s(s(z)) = z) <=> (elem!1 = s(s(z)))),
% 2.13/2.32 inference(transitivity,[status(thm)],[10676, 650])).
% 2.13/2.32 tff(10678,plain,
% 2.13/2.32 ((~(s(s(z)) = z)) <=> (~(elem!1 = s(s(z))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[10677])).
% 2.13/2.32 tff(10679,plain,
% 2.13/2.32 (~(elem!1 = s(s(z)))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[11, 10678])).
% 2.13/2.32 tff(10680,plain,
% 2.13/2.32 (r(s(s(s(z))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[10300])).
% 2.13/2.32 tff(10681,plain,
% 2.13/2.32 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(z))), s(z))),
% 2.13/2.32 inference(symmetry,[status(thm)],[10680])).
% 2.13/2.32 tff(10682,plain,
% 2.13/2.32 (r(s(s(s(z))), s(z))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[10641, 10681])).
% 2.13/2.32 tff(10683,plain,
% 2.13/2.32 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[7885])).
% 2.13/2.32 tff(10684,plain,
% 2.13/2.32 (r(s(s(s(s(z)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.32 inference(symmetry,[status(thm)],[10683])).
% 2.13/2.32 tff(10685,plain,
% 2.13/2.32 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[693, 8054])).
% 2.13/2.32 tff(10686,plain,
% 2.13/2.32 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.13/2.32 inference(unit_resolution,[status(thm)],[700, 10685])).
% 2.13/2.32 tff(10687,plain,
% 2.13/2.32 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 2.13/2.32 inference(transitivity,[status(thm)],[8052, 7930])).
% 2.13/2.32 tff(10688,plain,
% 2.13/2.32 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 2.13/2.32 inference(monotonicity,[status(thm)],[10687])).
% 2.13/2.32 tff(10689,plain,
% 2.13/2.32 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.13/2.32 inference(modus_ponens,[status(thm)],[283, 10688])).
% 2.13/2.32 tff(10690,plain,
% 2.13/2.32 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(z))))),
% 2.13/2.33 inference(symmetry,[status(thm)],[10435])).
% 2.13/2.33 tff(10691,plain,
% 2.13/2.33 (b(s(s(z)), s(s(s(elem!1))))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[8055, 10433])).
% 2.13/2.33 tff(10692,plain,
% 2.13/2.33 (b(s(s(z)), s(s(s(z))))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[10691, 10690])).
% 2.13/2.33 tff(10693,assumption,(b(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 2.13/2.33 tff(10694,plain,
% 2.13/2.33 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[8041])).
% 2.13/2.33 tff(10695,plain,
% 2.13/2.33 (b(elem!1, s(s(s(elem!1)))) <=> b(z, s(s(s(elem!1))))),
% 2.13/2.33 inference(symmetry,[status(thm)],[10694])).
% 2.13/2.33 tff(10696,plain,
% 2.13/2.33 (b(elem!1, s(s(s(z)))) <=> b(z, s(s(s(elem!1))))),
% 2.13/2.33 inference(transitivity,[status(thm)],[8073, 10695])).
% 2.13/2.33 tff(10697,plain,
% 2.13/2.33 ((~b(elem!1, s(s(s(z))))) <=> (~b(z, s(s(s(elem!1)))))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[10696])).
% 2.13/2.33 tff(10698,plain,
% 2.13/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(10699,plain,
% 2.13/2.33 (((~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(10700,plain,
% 2.13/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[10699])).
% 2.13/2.33 tff(10701,plain,
% 2.13/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 2.13/2.33 inference(transitivity,[status(thm)],[10700, 10698])).
% 2.13/2.33 tff(10702,plain,
% 2.13/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(z))))))),
% 2.13/2.33 inference(quant_inst,[status(thm)],[])).
% 2.13/2.33 tff(10703,plain,
% 2.13/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[10702, 10701])).
% 2.13/2.33 tff(10704,plain,
% 2.13/2.33 (~b(elem!1, s(s(s(z))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[10703, 128, 8861, 10693, 10692])).
% 2.13/2.33 tff(10705,plain,
% 2.13/2.33 (~b(z, s(s(s(elem!1))))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[10704, 10697])).
% 2.13/2.33 tff(10706,plain,
% 2.13/2.33 (r(z, s(s(s(elem!1))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[858, 10705])).
% 2.13/2.33 tff(10707,plain,
% 2.13/2.33 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[7885])).
% 2.13/2.33 tff(10708,plain,
% 2.13/2.33 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.33 inference(symmetry,[status(thm)],[10707])).
% 2.13/2.33 tff(10709,plain,
% 2.13/2.33 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[7886])).
% 2.13/2.33 tff(10710,plain,
% 2.13/2.33 (b(z, s(z)) <=> b(elem!1, s(z))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[8041])).
% 2.13/2.33 tff(10711,plain,
% 2.13/2.33 (b(elem!1, s(z))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[550, 10710])).
% 2.13/2.33 tff(10712,plain,
% 2.13/2.33 (b(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[1828, 1823])).
% 2.13/2.33 tff(10713,plain,
% 2.13/2.33 (~b(s(z), s(s(s(elem!1))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[2060, 10712, 550, 10685, 10711, 8123, 424])).
% 2.13/2.33 tff(10714,plain,
% 2.13/2.33 (r(s(z), s(s(s(elem!1))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[339, 10713])).
% 2.13/2.33 tff(10715,plain,
% 2.13/2.33 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[8684, 10714, 550, 424])).
% 2.13/2.33 tff(10716,plain,
% 2.13/2.33 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[10385, 10715, 4252])).
% 2.13/2.33 tff(10717,plain,
% 2.13/2.33 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[1820, 10716, 10686])).
% 2.13/2.33 tff(10718,plain,
% 2.13/2.33 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[10717, 10709])).
% 2.13/2.33 tff(10719,plain,
% 2.13/2.33 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[10718, 10708])).
% 2.13/2.33 tff(10720,assumption,(b(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 2.13/2.33 tff(10721,plain,
% 2.13/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z)), s(s(s(z))))))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(10722,plain,
% 2.13/2.33 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(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(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(10723,plain,
% 2.13/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, 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(z)), s(s(s(z)))))))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[10722])).
% 2.13/2.33 tff(10724,plain,
% 2.13/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, 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(z)), s(s(s(z))))))),
% 2.13/2.33 inference(transitivity,[status(thm)],[10723, 10721])).
% 2.13/2.33 tff(10725,plain,
% 2.13/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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)))))))),
% 2.13/2.33 inference(quant_inst,[status(thm)],[])).
% 2.13/2.33 tff(10726,plain,
% 2.13/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z)), s(s(s(z)))))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[10725, 10724])).
% 2.13/2.33 tff(10727,plain,
% 2.13/2.33 ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[10726, 128, 10693, 10720])).
% 2.13/2.33 tff(10728,plain,
% 2.13/2.33 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[10727, 10719])).
% 2.13/2.33 tff(10729,plain,
% 2.13/2.33 (r(s(s(z)), s(s(s(s(z)))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[610, 21, 607, 10728])).
% 2.13/2.33 tff(10730,plain,
% 2.13/2.33 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 2.13/2.33 inference(monotonicity,[status(thm)],[8041])).
% 2.13/2.33 tff(10731,plain,
% 2.13/2.33 ((~(s(s(s(s(z)))) = z)) <=> (~(s(s(s(s(z)))) = elem!1))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[10730])).
% 2.13/2.33 tff(10732,plain,
% 2.13/2.33 (~(s(s(s(s(z)))) = elem!1)),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[586, 10731])).
% 2.13/2.33 tff(10733,plain,
% 2.13/2.33 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 2.13/2.33 inference(symmetry,[status(thm)],[7886])).
% 2.13/2.33 tff(10734,plain,
% 2.13/2.33 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[10733])).
% 2.13/2.33 tff(10735,plain,
% 2.13/2.33 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 2.13/2.33 inference(symmetry,[status(thm)],[10734])).
% 2.13/2.33 tff(10736,plain,
% 2.13/2.33 ((~r(s(s(s(s(elem!1)))), s(z))) <=> (~r(s(s(s(s(z)))), s(z)))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[10735])).
% 2.13/2.33 tff(10737,plain,
% 2.13/2.33 (~r(s(s(s(s(z)))), s(z))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[1823, 10736])).
% 2.13/2.33 tff(10738,plain,
% 2.13/2.33 (b(s(s(s(s(z)))), s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[782, 21, 779, 10737])).
% 2.13/2.33 tff(10739,plain,
% 2.13/2.33 (((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(10740,plain,
% 2.13/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(z)))), s(z)))))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[10739])).
% 2.13/2.33 tff(10741,plain,
% 2.13/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(z)))), s(z))))),
% 2.13/2.33 inference(transitivity,[status(thm)],[10740, 2797])).
% 2.13/2.33 tff(10742,plain,
% 2.13/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.13/2.33 inference(quant_inst,[status(thm)],[])).
% 2.13/2.33 tff(10743,plain,
% 2.13/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[10742, 10741])).
% 2.13/2.33 tff(10744,plain,
% 2.13/2.33 (~b(s(s(s(s(z)))), elem!1)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[10743, 128, 10711, 8123, 10738])).
% 2.13/2.33 tff(10745,plain,
% 2.13/2.33 (r(s(s(s(s(z)))), elem!1)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[632, 10744, 10732])).
% 2.13/2.33 tff(10746,plain,
% 2.13/2.33 ($false),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[979, 45, 1103, 10745, 10729])).
% 2.13/2.33 tff(10747,plain,(r(s(s(s(s(elem!1)))), s(z)) | (~r(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~(s(s(elem!1)) = s(s(z)))) | (~b(z, s(z))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.33 tff(10748,plain,
% 2.13/2.33 (r(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[10747, 10706, 10693, 10692, 4252, 550, 1103])).
% 2.13/2.33 tff(10749,plain,
% 2.13/2.33 (~r(s(z), s(s(s(elem!1))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[10030, 10748, 7947, 10686, 10689, 325, 8055])).
% 2.13/2.33 tff(10750,plain,
% 2.13/2.33 (b(s(z), s(s(s(elem!1))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[339, 10749])).
% 2.13/2.33 tff(10751,plain,
% 2.13/2.33 (~b(s(s(elem!1)), s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[7940, 549, 7908, 3527, 2023])).
% 2.13/2.33 tff(10752,plain,
% 2.13/2.33 (r(s(s(elem!1)), s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[292, 10751])).
% 2.13/2.33 tff(10753,plain,
% 2.13/2.33 (~b(s(s(s(elem!1))), s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[9463, 10752, 550, 1069, 7950, 3527, 1842])).
% 2.13/2.33 tff(10754,plain,
% 2.13/2.33 (r(s(s(s(elem!1))), s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[196, 10753])).
% 2.13/2.33 tff(10755,plain,
% 2.13/2.33 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[7275, 45, 10752, 10754])).
% 2.13/2.33 tff(10756,plain,
% 2.13/2.33 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[889, 10755, 2025])).
% 2.13/2.33 tff(10757,plain,
% 2.13/2.33 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(10758,plain,
% 2.13/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[10757])).
% 2.13/2.33 tff(10759,plain,
% 2.13/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.13/2.33 inference(transitivity,[status(thm)],[10758, 9390])).
% 2.13/2.33 tff(10760,plain,
% 2.13/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.13/2.33 inference(quant_inst,[status(thm)],[])).
% 2.13/2.33 tff(10761,plain,
% 2.13/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[10760, 10759])).
% 2.13/2.33 tff(10762,plain,
% 2.13/2.33 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[10761, 128, 7950, 10756, 1842])).
% 2.13/2.33 tff(10763,plain,
% 2.13/2.33 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[1897, 10762, 2023])).
% 2.13/2.33 tff(10764,plain,
% 2.13/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(10765,plain,
% 2.13/2.33 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z)))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(10766,plain,
% 2.13/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[10765])).
% 2.13/2.33 tff(10767,plain,
% 2.13/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.13/2.33 inference(transitivity,[status(thm)],[10766, 10764])).
% 2.13/2.33 tff(10768,plain,
% 2.13/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.13/2.33 inference(quant_inst,[status(thm)],[])).
% 2.13/2.33 tff(10769,plain,
% 2.13/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[10768, 10767])).
% 2.13/2.33 tff(10770,plain,
% 2.13/2.33 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[10769, 128, 7950, 549, 10756, 1842])).
% 2.13/2.33 tff(10771,plain,
% 2.13/2.33 (r(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[1828, 10770])).
% 2.13/2.33 tff(10772,plain,
% 2.13/2.33 ($false),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[2141, 10771, 10763, 10752])).
% 2.13/2.33 tff(10773,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(z))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~b(s(z), z)) | r(s(s(elem!1)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.33 tff(10774,plain,
% 2.13/2.33 ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(z))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[10773, 7825])).
% 2.13/2.33 tff(10775,plain,
% 2.13/2.33 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[10774, 10750, 7947, 7908, 550])).
% 2.13/2.33 tff(10776,plain,
% 2.13/2.33 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[1820, 10775, 10686])).
% 2.13/2.33 tff(10777,plain,
% 2.13/2.33 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[10385, 10776, 4252])).
% 2.13/2.33 tff(10778,plain,
% 2.13/2.33 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[10777, 10684])).
% 2.13/2.33 tff(10779,plain,
% 2.13/2.33 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(z))), elem!1)),
% 2.13/2.33 inference(symmetry,[status(thm)],[8047])).
% 2.13/2.33 tff(10780,plain,
% 2.13/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(10781,plain,
% 2.13/2.33 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(10782,plain,
% 2.13/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[10781])).
% 2.13/2.33 tff(10783,plain,
% 2.13/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.13/2.33 inference(transitivity,[status(thm)],[10782, 10780])).
% 2.13/2.33 tff(10784,plain,
% 2.13/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)))),
% 2.13/2.33 inference(quant_inst,[status(thm)],[])).
% 2.13/2.33 tff(10785,plain,
% 2.13/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[10784, 10783])).
% 2.13/2.33 tff(10786,plain,
% 2.13/2.33 (~b(s(s(s(z))), elem!1)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[10785, 128, 8861, 10693, 10692])).
% 2.13/2.33 tff(10787,plain,
% 2.13/2.33 (~b(s(s(s(elem!1))), elem!1)),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[10786, 10449])).
% 2.13/2.33 tff(10788,plain,
% 2.13/2.33 (r(s(s(s(elem!1))), elem!1)),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[742, 10787, 8046])).
% 2.13/2.33 tff(10789,plain,
% 2.13/2.33 (r(s(s(s(z))), elem!1)),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[10788, 10779])).
% 2.13/2.33 tff(10790,assumption,(r(s(s(s(z))), s(z))), introduced(assumption)).
% 2.13/2.33 tff(10791,plain,
% 2.13/2.33 (r(s(s(s(s(z)))), s(z))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[10748, 10735])).
% 2.13/2.33 tff(10792,plain,
% 2.13/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(10793,plain,
% 2.13/2.33 (((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 2.13/2.33 inference(rewrite,[status(thm)],[])).
% 2.13/2.33 tff(10794,plain,
% 2.13/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1))))),
% 2.13/2.33 inference(monotonicity,[status(thm)],[10793])).
% 2.13/2.33 tff(10795,plain,
% 2.13/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 2.13/2.33 inference(transitivity,[status(thm)],[10794, 10792])).
% 2.13/2.33 tff(10796,plain,
% 2.13/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.13/2.33 inference(quant_inst,[status(thm)],[])).
% 2.13/2.33 tff(10797,plain,
% 2.13/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1))),
% 2.13/2.33 inference(modus_ponens,[status(thm)],[10796, 10795])).
% 2.13/2.33 tff(10798,plain,
% 2.13/2.33 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[10797, 45, 10791, 10790, 10789])).
% 2.13/2.33 tff(10799,plain,
% 2.13/2.33 ($false),
% 2.13/2.33 inference(unit_resolution,[status(thm)],[10798, 10778])).
% 2.13/2.33 tff(10800,plain,((~b(elem!1, s(s(z)))) | (~(s(s(elem!1)) = s(s(z)))) | (~r(s(s(s(z))), s(z))) | r(s(s(elem!1)), s(s(s(elem!1)))) | (~b(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.34 tff(10801,plain,
% 2.13/2.34 (~b(elem!1, s(s(z)))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[10800, 10294, 10682, 10642, 8511, 10635, 10661, 10308])).
% 2.13/2.34 tff(10802,plain,
% 2.13/2.34 (r(elem!1, s(s(z)))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[493, 10801, 10679])).
% 2.13/2.34 tff(10803,plain,
% 2.13/2.34 (r(z, s(s(elem!1)))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[10802, 10675])).
% 2.13/2.34 tff(10804,plain,
% 2.13/2.34 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[9036, 10803, 10635])).
% 2.13/2.34 tff(10805,plain,
% 2.13/2.34 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[1897, 10804, 10670])).
% 2.13/2.34 tff(10806,plain,
% 2.13/2.34 (b(s(s(s(s(z)))), s(s(z)))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[10805, 10668])).
% 2.13/2.34 tff(10807,plain,
% 2.13/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(10808,plain,
% 2.13/2.34 (((~b(s(s(s(z))), s(s(z)))) | (~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(s(s(z)))), 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(z))))))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(10809,plain,
% 2.13/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, 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(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[10808])).
% 2.13/2.34 tff(10810,plain,
% 2.13/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, 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(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.13/2.34 inference(transitivity,[status(thm)],[10809, 10807])).
% 2.13/2.34 tff(10811,plain,
% 2.13/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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)))))))),
% 2.13/2.34 inference(quant_inst,[status(thm)],[])).
% 2.13/2.34 tff(10812,plain,
% 2.13/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[10811, 10810])).
% 2.13/2.34 tff(10813,plain,
% 2.13/2.34 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[10812, 128, 10661, 10645, 10806])).
% 2.13/2.34 tff(10814,plain,
% 2.13/2.34 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[10813, 10666])).
% 2.13/2.34 tff(10815,plain,
% 2.13/2.34 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[1856, 10814, 10662])).
% 2.13/2.34 tff(10816,plain,
% 2.13/2.34 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[10059, 10815, 10641])).
% 2.13/2.34 tff(10817,plain,
% 2.13/2.34 (~r(z, s(s(s(elem!1))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[10747, 10816, 10661, 10645, 10294, 8511, 10308])).
% 2.13/2.34 tff(10818,plain,
% 2.13/2.34 (~r(elem!1, s(s(s(elem!1))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[2461, 10817, 10295])).
% 2.13/2.34 tff(10819,plain,
% 2.13/2.34 (b(elem!1, s(s(s(elem!1))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[2466, 10818, 10306])).
% 2.13/2.34 tff(10820,plain,
% 2.13/2.34 (b(elem!1, s(s(s(z))))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[10819, 10302])).
% 2.13/2.34 tff(10821,plain,
% 2.13/2.34 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 2.13/2.34 inference(monotonicity,[status(thm)],[10300])).
% 2.13/2.34 tff(10822,plain,
% 2.13/2.34 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), elem!1)),
% 2.13/2.34 inference(symmetry,[status(thm)],[10821])).
% 2.13/2.34 tff(10823,plain,
% 2.13/2.34 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 2.13/2.34 inference(transitivity,[status(thm)],[10304, 982])).
% 2.13/2.34 tff(10824,plain,
% 2.13/2.34 ((~(s(s(s(elem!1))) = z)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[10823])).
% 2.13/2.34 tff(10825,plain,
% 2.13/2.34 (~(s(s(s(elem!1))) = elem!1)),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[382, 10824])).
% 2.13/2.34 tff(10826,plain,
% 2.13/2.34 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[700, 10662])).
% 2.13/2.34 tff(10827,plain,
% 2.13/2.34 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[10663])).
% 2.13/2.34 tff(10828,plain,
% 2.13/2.34 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.13/2.34 inference(symmetry,[status(thm)],[10827])).
% 2.13/2.34 tff(10829,plain,
% 2.13/2.34 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[10300])).
% 2.13/2.34 tff(10830,plain,
% 2.13/2.34 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.13/2.34 inference(transitivity,[status(thm)],[10829, 10828])).
% 2.13/2.34 tff(10831,plain,
% 2.13/2.34 ((~b(s(s(s(s(z)))), s(s(s(z))))) <=> (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[10830])).
% 2.13/2.34 tff(10832,plain,
% 2.13/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(10833,plain,
% 2.13/2.34 (((~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(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(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(10834,plain,
% 2.13/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, 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(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[10833])).
% 2.13/2.34 tff(10835,plain,
% 2.13/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, 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(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.13/2.34 inference(transitivity,[status(thm)],[10834, 10832])).
% 2.13/2.34 tff(10836,plain,
% 2.13/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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))))))),
% 2.13/2.34 inference(quant_inst,[status(thm)],[])).
% 2.13/2.34 tff(10837,plain,
% 2.13/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[10836, 10835])).
% 2.13/2.34 tff(10838,plain,
% 2.13/2.34 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[10837, 128, 10661, 10645, 10806])).
% 2.13/2.34 tff(10839,plain,
% 2.13/2.34 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[10838, 10831])).
% 2.13/2.34 tff(10840,plain,
% 2.13/2.34 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[1820, 10839, 10826])).
% 2.13/2.34 tff(10841,plain,
% 2.13/2.34 (r(s(s(s(s(elem!1)))), z) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 2.13/2.34 inference(monotonicity,[status(thm)],[10295])).
% 2.13/2.34 tff(10842,plain,
% 2.13/2.34 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(elem!1)))), z)),
% 2.13/2.34 inference(symmetry,[status(thm)],[10841])).
% 2.13/2.34 tff(10843,plain,
% 2.13/2.34 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 2.13/2.34 inference(monotonicity,[status(thm)],[10663])).
% 2.13/2.34 tff(10844,plain,
% 2.13/2.34 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 2.13/2.34 inference(symmetry,[status(thm)],[10843])).
% 2.13/2.34 tff(10845,plain,
% 2.13/2.34 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(elem!1)))), z)),
% 2.13/2.34 inference(transitivity,[status(thm)],[10844, 10842])).
% 2.13/2.34 tff(10846,plain,
% 2.13/2.34 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 2.13/2.34 inference(monotonicity,[status(thm)],[10295])).
% 2.13/2.34 tff(10847,plain,
% 2.13/2.34 ((~(s(s(s(s(z)))) = z)) <=> (~(s(s(s(s(z)))) = elem!1))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[10846])).
% 2.13/2.34 tff(10848,plain,
% 2.13/2.34 (~(s(s(s(s(z)))) = elem!1)),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[586, 10847])).
% 2.13/2.34 tff(10849,plain,
% 2.13/2.34 (r(s(z), s(s(s(z)))) <=> r(s(z), s(s(s(elem!1))))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[10300])).
% 2.13/2.34 tff(10850,plain,
% 2.13/2.34 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(s(s(z))))),
% 2.13/2.34 inference(symmetry,[status(thm)],[10849])).
% 2.13/2.34 tff(10851,plain,
% 2.13/2.34 (b(z, s(z)) <=> b(elem!1, s(z))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[10295])).
% 2.13/2.34 tff(10852,plain,
% 2.13/2.34 (b(elem!1, s(z))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[8511, 10851])).
% 2.13/2.34 tff(10853,plain,
% 2.13/2.34 (b(s(z), s(s(s(z)))) <=> b(s(z), s(s(s(elem!1))))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[7885])).
% 2.13/2.34 tff(10854,plain,
% 2.13/2.34 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(s(s(z))))),
% 2.13/2.34 inference(symmetry,[status(thm)],[10853])).
% 2.13/2.34 tff(10855,plain,
% 2.13/2.34 (b(s(z), s(s(s(z))))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[549, 10854])).
% 2.13/2.34 tff(10856,plain,
% 2.13/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, 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(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, 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(elem!1, s(s(s(z))))))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(10857,plain,
% 2.13/2.34 (((~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(10858,plain,
% 2.13/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, 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(elem!1, s(s(s(z)))))))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[10857])).
% 2.13/2.34 tff(10859,plain,
% 2.13/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, 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(elem!1, s(s(s(z))))))),
% 2.13/2.34 inference(transitivity,[status(thm)],[10858, 10856])).
% 2.13/2.34 tff(10860,plain,
% 2.13/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(z))))),
% 2.13/2.34 inference(quant_inst,[status(thm)],[])).
% 2.13/2.34 tff(10861,plain,
% 2.13/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[10860, 10859])).
% 2.13/2.34 tff(10862,plain,
% 2.13/2.34 (~b(s(z), s(s(s(z))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[10861, 128, 297, 8120, 10693, 10720])).
% 2.13/2.34 tff(10863,plain,
% 2.13/2.34 ($false),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[10862, 10855])).
% 2.13/2.34 tff(10864,plain,((~b(s(z), s(s(s(elem!1))))) | (~(s(s(elem!1)) = s(s(z)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.34 tff(10865,plain,
% 2.13/2.34 (~b(s(z), s(s(s(elem!1))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[10864, 10294, 10852, 10820, 10661, 10645])).
% 2.13/2.34 tff(10866,plain,
% 2.13/2.34 (r(s(z), s(s(s(elem!1))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[339, 10865])).
% 2.13/2.34 tff(10867,plain,
% 2.13/2.34 (r(s(z), s(s(s(z))))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[10866, 10850])).
% 2.13/2.34 tff(10868,plain,
% 2.13/2.34 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[10300])).
% 2.13/2.34 tff(10869,plain,
% 2.13/2.34 (r(s(s(s(s(z)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.34 inference(symmetry,[status(thm)],[10868])).
% 2.13/2.34 tff(10870,plain,
% 2.13/2.34 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[10385, 10840, 10294])).
% 2.13/2.34 tff(10871,plain,
% 2.13/2.34 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[10870, 10869])).
% 2.13/2.34 tff(10872,plain,
% 2.13/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(10873,plain,
% 2.13/2.34 (((~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(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(10874,plain,
% 2.13/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(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(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[10873])).
% 2.13/2.34 tff(10875,plain,
% 2.13/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(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(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 2.13/2.34 inference(transitivity,[status(thm)],[10874, 10872])).
% 2.13/2.34 tff(10876,plain,
% 2.13/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(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))))),
% 2.13/2.34 inference(quant_inst,[status(thm)],[])).
% 2.13/2.34 tff(10877,plain,
% 2.13/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[10876, 10875])).
% 2.13/2.34 tff(10878,plain,
% 2.13/2.34 ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(z)))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[10877, 45, 10871])).
% 2.13/2.34 tff(10879,plain,
% 2.13/2.34 (~r(s(s(s(s(z)))), s(z))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[10878, 10867])).
% 2.13/2.34 tff(10880,plain,
% 2.13/2.34 (b(s(s(s(s(z)))), s(z))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[784, 10879])).
% 2.13/2.34 tff(10881,plain,
% 2.13/2.34 (b(s(z), z) <=> b(s(z), elem!1)),
% 2.13/2.34 inference(monotonicity,[status(thm)],[10295])).
% 2.13/2.34 tff(10882,plain,
% 2.13/2.34 (b(s(z), elem!1)),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[7825, 10881])).
% 2.13/2.34 tff(10883,plain,
% 2.13/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z))))))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(10884,plain,
% 2.13/2.34 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~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(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z))))))),
% 2.13/2.34 inference(rewrite,[status(thm)],[])).
% 2.13/2.34 tff(10885,plain,
% 2.13/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z)))))))),
% 2.13/2.34 inference(monotonicity,[status(thm)],[10884])).
% 2.13/2.34 tff(10886,plain,
% 2.13/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z))))))),
% 2.13/2.34 inference(transitivity,[status(thm)],[10885, 10883])).
% 2.13/2.34 tff(10887,plain,
% 2.13/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.13/2.34 inference(quant_inst,[status(thm)],[])).
% 2.13/2.34 tff(10888,plain,
% 2.13/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z)))))),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[10887, 10886])).
% 2.13/2.34 tff(10889,plain,
% 2.13/2.34 ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[10888, 128, 10882, 10820, 10661, 10806])).
% 2.13/2.34 tff(10890,plain,
% 2.13/2.34 (~b(s(s(s(s(z)))), elem!1)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[10889, 10880])).
% 2.13/2.34 tff(10891,plain,
% 2.13/2.34 (r(s(s(s(s(z)))), elem!1)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[632, 10890, 10848])).
% 2.13/2.34 tff(10892,plain,
% 2.13/2.34 (r(s(s(s(s(elem!1)))), z)),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[10891, 10845])).
% 2.13/2.34 tff(10893,plain,
% 2.13/2.34 (~r(s(s(s(elem!1))), z)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[1780, 10892, 10840])).
% 2.13/2.34 tff(10894,plain,
% 2.13/2.34 (~r(s(s(s(elem!1))), elem!1)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[2453, 10893, 10295])).
% 2.13/2.34 tff(10895,plain,
% 2.13/2.34 (b(s(s(s(elem!1))), elem!1)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[742, 10894, 10825])).
% 2.13/2.34 tff(10896,plain,
% 2.13/2.34 (b(s(s(s(z))), elem!1)),
% 2.13/2.34 inference(modus_ponens,[status(thm)],[10895, 10822])).
% 2.13/2.34 tff(10897,plain,
% 2.13/2.34 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[8174, 10896, 10820, 10294])).
% 2.13/2.34 tff(10898,plain,
% 2.13/2.34 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[1055, 10897, 10298])).
% 2.13/2.34 tff(10899,plain,
% 2.13/2.34 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[2986, 45, 10891, 10898])).
% 2.13/2.34 tff(10900,plain,
% 2.13/2.34 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[1215, 21, 1212, 10899])).
% 2.13/2.34 tff(10901,plain,
% 2.13/2.34 (~r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[1172, 45, 10308, 10898])).
% 2.13/2.34 tff(10902,plain,
% 2.13/2.34 (b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[1176, 21, 1123, 10901])).
% 2.13/2.34 tff(10903,plain,
% 2.13/2.34 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[979, 45, 10308, 10891])).
% 2.13/2.34 tff(10904,plain,
% 2.13/2.34 (b(s(s(z)), s(s(s(s(z)))))),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[610, 21, 607, 10903])).
% 2.13/2.34 tff(10905,plain,
% 2.13/2.34 ($false),
% 2.13/2.34 inference(unit_resolution,[status(thm)],[3087, 128, 10806, 10904, 10902, 10900])).
% 2.13/2.34 tff(10906,plain,(b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 2.13/2.34 tff(10907,plain,
% 2.13/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(10908,plain,
% 2.13/2.35 (((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z))))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(10909,plain,
% 2.13/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z))))))),
% 2.13/2.35 inference(monotonicity,[status(thm)],[10908])).
% 2.13/2.35 tff(10910,plain,
% 2.13/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.13/2.35 inference(transitivity,[status(thm)],[10909, 10907])).
% 2.13/2.35 tff(10911,plain,
% 2.13/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.13/2.35 inference(quant_inst,[status(thm)],[])).
% 2.13/2.35 tff(10912,plain,
% 2.13/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z))))),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[10911, 10910])).
% 2.13/2.35 tff(10913,plain,
% 2.13/2.35 ($false),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[10912, 128, 550, 7825, 2006, 2993, 8522])).
% 2.13/2.35 tff(10914,plain,((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.35 tff(10915,plain,
% 2.13/2.35 (~b(z, s(z))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[10914, 8522, 2993, 2006])).
% 2.13/2.35 tff(10916,plain,
% 2.13/2.35 (r(z, s(z))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[415, 10915])).
% 2.13/2.35 tff(10917,plain,
% 2.13/2.35 (~r(z, s(s(elem!1)))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[405, 10916, 325])).
% 2.13/2.35 tff(10918,plain,
% 2.13/2.35 (b(z, s(s(elem!1)))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[160, 10917])).
% 2.13/2.35 tff(10919,plain,
% 2.13/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z)), z)) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z)), z)) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(10920,plain,
% 2.13/2.35 (((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z))))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(10921,plain,
% 2.13/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z)), z)) | (~b(s(s(elem!1)), s(s(z))))))),
% 2.13/2.35 inference(monotonicity,[status(thm)],[10920])).
% 2.13/2.35 tff(10922,plain,
% 2.13/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z)), z)) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.13/2.35 inference(transitivity,[status(thm)],[10921, 10919])).
% 2.13/2.35 tff(10923,plain,
% 2.13/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.13/2.35 inference(quant_inst,[status(thm)],[])).
% 2.13/2.35 tff(10924,plain,
% 2.13/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z))))),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[10923, 10922])).
% 2.13/2.35 tff(10925,plain,
% 2.13/2.35 ($false),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[10924, 128, 10918, 2006, 2993, 8522])).
% 2.13/2.35 tff(10926,plain,((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.35 tff(10927,plain,
% 2.13/2.35 ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z)))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[10926, 10906])).
% 2.13/2.35 tff(10928,plain,
% 2.13/2.35 (~b(s(s(elem!1)), s(s(z)))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[10927, 8198, 325])).
% 2.13/2.35 tff(10929,plain,
% 2.13/2.35 (r(s(s(elem!1)), s(s(z)))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[4339, 21, 1, 10928])).
% 2.13/2.35 tff(10930,plain,
% 2.13/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z)), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z)), z)) | (~b(s(z), s(s(z)))))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(10931,plain,
% 2.13/2.35 (((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(10932,plain,
% 2.13/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(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(X0, 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(z)), z)) | (~b(s(z), s(s(z))))))),
% 2.13/2.35 inference(monotonicity,[status(thm)],[10931])).
% 2.13/2.35 tff(10933,plain,
% 2.13/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(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(X0, 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(z)), z)) | (~b(s(z), s(s(z)))))),
% 2.13/2.35 inference(transitivity,[status(thm)],[10932, 10930])).
% 2.13/2.35 tff(10934,plain,
% 2.13/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))),
% 2.13/2.35 inference(quant_inst,[status(thm)],[])).
% 2.13/2.35 tff(10935,plain,
% 2.13/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z)), z)) | (~b(s(z), s(s(z))))),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[10934, 10933])).
% 2.13/2.35 tff(10936,plain,
% 2.13/2.35 (~b(s(z), s(s(z)))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[10935, 128, 8194, 7825, 8198, 10906])).
% 2.13/2.35 tff(10937,plain,
% 2.13/2.35 (r(s(z), s(s(z)))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[648, 10936])).
% 2.13/2.35 tff(10938,plain,
% 2.13/2.35 (~b(s(z), s(s(elem!1)))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[7990, 128, 8194, 7825, 8198])).
% 2.13/2.35 tff(10939,plain,
% 2.13/2.35 (r(s(z), s(s(elem!1)))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[117, 10938])).
% 2.13/2.35 tff(10940,plain,
% 2.13/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(10941,plain,
% 2.13/2.35 (((~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(10942,plain,
% 2.13/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z))))))),
% 2.13/2.35 inference(monotonicity,[status(thm)],[10941])).
% 2.13/2.35 tff(10943,plain,
% 2.13/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.13/2.35 inference(transitivity,[status(thm)],[10942, 10940])).
% 2.13/2.35 tff(10944,plain,
% 2.13/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))))),
% 2.13/2.35 inference(quant_inst,[status(thm)],[])).
% 2.13/2.35 tff(10945,plain,
% 2.13/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z))))),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[10944, 10943])).
% 2.13/2.35 tff(10946,plain,
% 2.13/2.35 ($false),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[10945, 45, 325, 10939, 10937, 10929])).
% 2.13/2.35 tff(10947,plain,((~r(s(s(elem!1)), s(z))) | (s(s(elem!1)) = s(s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.35 tff(10948,plain,
% 2.13/2.35 (~r(s(s(elem!1)), s(z))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[10947, 1, 27])).
% 2.13/2.35 tff(10949,plain,
% 2.13/2.35 (b(s(s(elem!1)), s(z))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[292, 10948])).
% 2.13/2.35 tff(10950,plain,
% 2.13/2.35 (~b(z, s(s(elem!1)))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[7826, 1063, 10949])).
% 2.13/2.35 tff(10951,plain,
% 2.13/2.35 (r(z, s(s(elem!1)))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[160, 10950])).
% 2.13/2.35 tff(10952,plain,
% 2.13/2.35 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[5217, 128, 30, 118, 2718])).
% 2.13/2.35 tff(10953,plain,
% 2.13/2.35 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[889, 10952, 1691])).
% 2.13/2.35 tff(10954,plain,
% 2.13/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(10955,plain,
% 2.13/2.35 (((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(10956,plain,
% 2.13/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1))))))),
% 2.13/2.35 inference(monotonicity,[status(thm)],[10955])).
% 2.13/2.35 tff(10957,plain,
% 2.13/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.13/2.35 inference(transitivity,[status(thm)],[10956, 10954])).
% 2.13/2.35 tff(10958,plain,
% 2.13/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), z)))),
% 2.13/2.35 inference(quant_inst,[status(thm)],[])).
% 2.13/2.35 tff(10959,plain,
% 2.13/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[10958, 10957])).
% 2.13/2.35 tff(10960,plain,
% 2.13/2.35 (~r(s(s(s(elem!1))), z)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[10959, 45, 27, 88, 10953])).
% 2.13/2.35 tff(10961,plain,
% 2.13/2.35 (b(s(s(s(elem!1))), z)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[5301, 10960])).
% 2.13/2.35 tff(10962,plain,
% 2.13/2.35 (~r(z, s(s(s(elem!1))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[4402, 45, 88, 10953])).
% 2.13/2.35 tff(10963,plain,
% 2.13/2.35 (b(z, s(s(s(elem!1))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[858, 10962])).
% 2.13/2.35 tff(10964,plain,
% 2.13/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(10965,plain,
% 2.13/2.35 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(10966,plain,
% 2.13/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1)))))))),
% 2.13/2.35 inference(monotonicity,[status(thm)],[10965])).
% 2.13/2.35 tff(10967,plain,
% 2.13/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))))),
% 2.13/2.35 inference(transitivity,[status(thm)],[10966, 10964])).
% 2.13/2.35 tff(10968,plain,
% 2.13/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 2.13/2.35 inference(quant_inst,[status(thm)],[])).
% 2.13/2.35 tff(10969,plain,
% 2.13/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1)))))),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[10968, 10967])).
% 2.13/2.35 tff(10970,plain,
% 2.13/2.35 ($false),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[10969, 128, 7825, 2718, 10963, 10961])).
% 2.13/2.35 tff(10971,plain,((~b(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.35 tff(10972,plain,
% 2.13/2.35 (~b(s(s(s(elem!1))), s(z))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[10971, 10951, 27, 1679, 10949])).
% 2.13/2.35 tff(10973,plain,
% 2.13/2.35 (r(s(s(s(elem!1))), s(z))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[196, 10972])).
% 2.13/2.35 tff(10974,plain,
% 2.13/2.35 (~r(s(s(s(elem!1))), z)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[3935, 45, 27, 10973])).
% 2.13/2.35 tff(10975,plain,
% 2.13/2.35 (b(s(s(s(elem!1))), z)),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[5301, 10974])).
% 2.13/2.35 tff(10976,plain,
% 2.13/2.35 (~r(z, s(s(s(elem!1))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[3611, 45, 27, 10973])).
% 2.13/2.35 tff(10977,plain,
% 2.13/2.35 (b(z, s(s(s(elem!1))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[858, 10976])).
% 2.13/2.35 tff(10978,plain,
% 2.13/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(10979,plain,
% 2.13/2.35 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.13/2.35 inference(rewrite,[status(thm)],[])).
% 2.13/2.35 tff(10980,plain,
% 2.13/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 2.13/2.35 inference(monotonicity,[status(thm)],[10979])).
% 2.13/2.35 tff(10981,plain,
% 2.13/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.13/2.35 inference(transitivity,[status(thm)],[10980, 10978])).
% 2.13/2.35 tff(10982,plain,
% 2.13/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.13/2.35 inference(quant_inst,[status(thm)],[])).
% 2.13/2.35 tff(10983,plain,
% 2.13/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z))))),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[10982, 10981])).
% 2.13/2.35 tff(10984,plain,
% 2.13/2.35 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[10983, 128, 10977, 10975, 10906])).
% 2.13/2.35 tff(10985,plain,
% 2.13/2.35 (~r(s(z), s(s(elem!1)))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[97, 10951, 27])).
% 2.13/2.35 tff(10986,plain,
% 2.13/2.35 (b(s(z), s(s(elem!1)))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[117, 10985])).
% 2.13/2.35 tff(10987,plain,
% 2.13/2.35 ((z = elem!1) <=> (z = s(s(s(elem!1))))),
% 2.13/2.35 inference(monotonicity,[status(thm)],[1101])).
% 2.13/2.35 tff(10988,plain,
% 2.13/2.35 ((z = elem!1) <=> (s(s(s(elem!1))) = z)),
% 2.13/2.35 inference(transitivity,[status(thm)],[10987, 540])).
% 2.13/2.35 tff(10989,plain,
% 2.13/2.35 ((s(s(s(elem!1))) = z) <=> (z = elem!1)),
% 2.13/2.35 inference(symmetry,[status(thm)],[10988])).
% 2.13/2.35 tff(10990,plain,
% 2.13/2.35 ((~(s(s(s(elem!1))) = z)) <=> (~(z = elem!1))),
% 2.13/2.35 inference(monotonicity,[status(thm)],[10989])).
% 2.13/2.35 tff(10991,plain,
% 2.13/2.35 (~(z = elem!1)),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[382, 10990])).
% 2.13/2.35 tff(10992,plain,
% 2.13/2.35 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.13/2.35 inference(transitivity,[status(thm)],[1060, 308])).
% 2.13/2.35 tff(10993,plain,
% 2.13/2.35 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.13/2.35 inference(monotonicity,[status(thm)],[10992])).
% 2.13/2.35 tff(10994,plain,
% 2.13/2.35 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.13/2.35 inference(symmetry,[status(thm)],[10993])).
% 2.13/2.35 tff(10995,plain,
% 2.13/2.35 ((~r(s(s(elem!1)), s(s(s(elem!1))))) <=> (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 2.13/2.35 inference(monotonicity,[status(thm)],[10994])).
% 2.13/2.35 tff(10996,plain,
% 2.13/2.35 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[7908, 10995])).
% 2.13/2.35 tff(10997,plain,
% 2.13/2.35 (~(elem!1 = z)),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[1608, 1979])).
% 2.13/2.35 tff(10998,plain,
% 2.13/2.35 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[8033, 27, 3527, 7948, 7908])).
% 2.13/2.35 tff(10999,plain,
% 2.13/2.35 (s(s(elem!1)) = elem!1),
% 2.13/2.35 inference(unit_resolution,[status(thm)],[1089, 10998])).
% 2.13/2.35 tff(11000,plain,
% 2.13/2.35 ((s(s(elem!1)) = s(z)) <=> (elem!1 = s(z))),
% 2.13/2.35 inference(monotonicity,[status(thm)],[10999])).
% 2.13/2.35 tff(11001,plain,
% 2.13/2.35 ((~(s(s(elem!1)) = s(z))) <=> (~(elem!1 = s(z)))),
% 2.13/2.35 inference(monotonicity,[status(thm)],[11000])).
% 2.13/2.35 tff(11002,plain,
% 2.13/2.35 (~(elem!1 = s(z))),
% 2.13/2.35 inference(modus_ponens,[status(thm)],[111, 11001])).
% 2.13/2.35 tff(11003,plain,
% 2.13/2.35 (r(z, s(s(elem!1))) <=> r(z, elem!1)),
% 2.13/2.35 inference(monotonicity,[status(thm)],[10999])).
% 2.13/2.35 tff(11004,plain,
% 2.13/2.36 (s(s(s(elem!1))) = s(elem!1)),
% 2.13/2.36 inference(monotonicity,[status(thm)],[10999])).
% 2.13/2.36 tff(11005,plain,
% 2.13/2.36 (s(elem!1) = s(s(s(elem!1)))),
% 2.13/2.36 inference(symmetry,[status(thm)],[11004])).
% 2.13/2.36 tff(11006,plain,
% 2.13/2.36 (r(z, s(elem!1)) <=> r(z, s(s(s(elem!1))))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[11005])).
% 2.13/2.36 tff(11007,plain,
% 2.13/2.36 ((~r(z, s(elem!1))) <=> (~r(z, s(s(s(elem!1)))))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[11006])).
% 2.13/2.36 tff(11008,plain,
% 2.13/2.36 (r(s(s(s(elem!1))), s(z)) <=> r(s(elem!1), s(z))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[11004])).
% 2.13/2.36 tff(11009,plain,
% 2.13/2.36 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[321, 691, 7908])).
% 2.13/2.36 tff(11010,plain,
% 2.13/2.36 (b(z, elem!1)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[5905, 2718, 2106, 199, 27, 1608])).
% 2.13/2.36 tff(11011,plain,
% 2.13/2.36 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(elem!1))))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[354])).
% 2.13/2.36 tff(11012,plain,
% 2.13/2.36 ((~b(s(z), s(elem!1))) <=> (~b(s(z), s(s(s(elem!1)))))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[11011])).
% 2.13/2.36 tff(11013,plain,
% 2.13/2.36 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(elem!1, s(elem!1))),
% 2.13/2.36 inference(transitivity,[status(thm)],[266, 264])).
% 2.13/2.36 tff(11014,plain,
% 2.13/2.36 (b(elem!1, s(elem!1))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[2106, 11013])).
% 2.13/2.36 tff(11015,plain,
% 2.13/2.36 ((s(s(elem!1)) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[199])).
% 2.13/2.36 tff(11016,plain,
% 2.13/2.36 ((s(s(elem!1)) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 2.13/2.36 inference(transitivity,[status(thm)],[11015, 225])).
% 2.13/2.36 tff(11017,plain,
% 2.13/2.36 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[11016])).
% 2.13/2.36 tff(11018,plain,
% 2.13/2.36 (~(s(s(elem!1)) = s(s(z)))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[4260, 1608])).
% 2.13/2.36 tff(11019,plain,
% 2.13/2.36 (~(s(s(z)) = elem!1)),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[11018, 11017])).
% 2.13/2.36 tff(11020,plain,
% 2.13/2.36 (b(s(elem!1), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[354])).
% 2.13/2.36 tff(11021,plain,
% 2.13/2.36 (b(s(s(s(elem!1))), s(z)) <=> b(s(elem!1), s(z))),
% 2.13/2.36 inference(symmetry,[status(thm)],[11020])).
% 2.13/2.36 tff(11022,plain,
% 2.13/2.36 (b(s(elem!1), s(z))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[2718, 11021])).
% 2.13/2.36 tff(11023,plain,
% 2.13/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(11024,plain,
% 2.13/2.36 (((~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(11025,plain,
% 2.13/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1)))))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[11024])).
% 2.13/2.36 tff(11026,plain,
% 2.13/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 2.13/2.36 inference(transitivity,[status(thm)],[11025, 11023])).
% 2.13/2.36 tff(11027,plain,
% 2.13/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))))),
% 2.13/2.36 inference(quant_inst,[status(thm)],[])).
% 2.13/2.36 tff(11028,plain,
% 2.13/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1)))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[11027, 11026])).
% 2.13/2.36 tff(11029,plain,
% 2.13/2.36 (~b(elem!1, s(z))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[11028, 128, 1830, 263, 813])).
% 2.13/2.36 tff(11030,plain,
% 2.13/2.36 (r(elem!1, s(z))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[305, 11029, 1642])).
% 2.13/2.36 tff(11031,plain,
% 2.13/2.36 (~r(z, elem!1)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[4896, 11030, 27])).
% 2.13/2.36 tff(11032,plain,
% 2.13/2.36 (b(z, elem!1)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[1549, 11031, 1608])).
% 2.13/2.36 tff(11033,plain,
% 2.13/2.36 (~r(elem!1, z)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[569, 45, 11030, 27])).
% 2.13/2.36 tff(11034,plain,
% 2.13/2.36 (b(elem!1, z)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[574, 11033, 10997])).
% 2.13/2.36 tff(11035,plain,
% 2.13/2.36 (~b(s(z), elem!1)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[5940, 128, 1830, 263, 813])).
% 2.13/2.36 tff(11036,plain,
% 2.13/2.36 (r(s(z), elem!1)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[665, 11035, 1610])).
% 2.13/2.36 tff(11037,plain,
% 2.13/2.36 (~b(s(s(z)), elem!1)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[8324, 11034, 3527, 27, 11032, 11036, 2953])).
% 2.13/2.36 tff(11038,plain,
% 2.13/2.36 (r(s(s(z)), elem!1)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[370, 11037, 484])).
% 2.13/2.36 tff(11039,plain,
% 2.13/2.36 (~r(s(z), s(s(z)))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[8333, 45, 11036, 11038])).
% 2.13/2.36 tff(11040,plain,
% 2.13/2.36 (b(s(z), s(s(z)))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[648, 11039])).
% 2.13/2.36 tff(11041,plain,
% 2.13/2.36 (~b(s(s(s(s(z)))), elem!1)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[8372, 11040, 3527, 27, 11034, 11032])).
% 2.13/2.36 tff(11042,plain,
% 2.13/2.36 (r(s(s(s(s(z)))), elem!1)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[632, 11041, 2953])).
% 2.13/2.36 tff(11043,plain,
% 2.13/2.36 (~r(s(s(s(s(z)))), s(z))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[8293, 45, 11036, 11042])).
% 2.13/2.36 tff(11044,plain,
% 2.13/2.36 (b(s(s(s(s(z)))), s(z))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[782, 21, 779, 11043])).
% 2.13/2.36 tff(11045,plain,
% 2.13/2.36 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[979, 45, 11038, 11042])).
% 2.13/2.36 tff(11046,plain,
% 2.13/2.36 (b(s(s(z)), s(s(s(s(z)))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[610, 21, 607, 11045])).
% 2.13/2.36 tff(11047,plain,
% 2.13/2.36 (~r(s(z), s(s(s(s(z)))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[672, 45, 11036, 11042])).
% 2.13/2.36 tff(11048,plain,
% 2.13/2.36 (b(s(z), s(s(s(s(z)))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[684, 21, 681, 11047])).
% 2.13/2.36 tff(11049,plain,
% 2.13/2.36 (~r(s(s(z)), s(z))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[10257, 45, 11036, 11038])).
% 2.13/2.36 tff(11050,plain,
% 2.13/2.36 (b(s(s(z)), s(z))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[86, 11049])).
% 2.13/2.36 tff(11051,plain,
% 2.13/2.36 ($false),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[1289, 128, 11050, 11048, 11046, 11044])).
% 2.13/2.36 tff(11052,plain,((~b(s(z), s(elem!1))) | (s(s(s(s(z)))) = elem!1) | (~b(s(z), z)) | (~r(z, s(z))) | (s(s(z)) = elem!1) | (z = elem!1) | (s(z) = elem!1) | (elem!1 = s(z)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.36 tff(11053,plain,
% 2.13/2.36 (~b(s(z), s(elem!1))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[11052, 11022, 3527, 27, 11019, 1608, 257, 295, 11014, 243])).
% 2.13/2.36 tff(11054,plain,
% 2.13/2.36 (~b(s(z), s(s(s(elem!1))))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[11053, 11012])).
% 2.13/2.36 tff(11055,plain,
% 2.13/2.36 (r(s(z), s(s(s(elem!1))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[339, 11054])).
% 2.13/2.36 tff(11056,plain,
% 2.13/2.36 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(elem!1), elem!1)),
% 2.13/2.36 inference(transitivity,[status(thm)],[5893, 716])).
% 2.13/2.36 tff(11057,plain,
% 2.13/2.36 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[1802, 7954, 323])).
% 2.13/2.36 tff(11058,plain,
% 2.13/2.36 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[889, 11057, 1691])).
% 2.13/2.36 tff(11059,plain,
% 2.13/2.36 (b(s(elem!1), elem!1)),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[11058, 11056])).
% 2.13/2.36 tff(11060,plain,
% 2.13/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(11061,plain,
% 2.13/2.36 (((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(11062,plain,
% 2.13/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), s(z)))))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[11061])).
% 2.13/2.36 tff(11063,plain,
% 2.13/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 2.13/2.36 inference(transitivity,[status(thm)],[11062, 11060])).
% 2.13/2.36 tff(11064,plain,
% 2.13/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), elem!1)))),
% 2.13/2.36 inference(quant_inst,[status(thm)],[])).
% 2.13/2.36 tff(11065,plain,
% 2.13/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(elem!1), s(z)))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[11064, 11063])).
% 2.13/2.36 tff(11066,plain,
% 2.13/2.36 ($false),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[11065, 128, 498, 807, 3527, 11059, 11022])).
% 2.13/2.36 tff(11067,plain,((~b(s(s(elem!1)), s(z))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~(s(s(elem!1)) = elem!1)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.36 tff(11068,plain,
% 2.13/2.36 (~b(s(s(elem!1)), s(z))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[11067, 11010, 3527, 199, 1691, 11055, 2106, 2718])).
% 2.13/2.36 tff(11069,plain,
% 2.13/2.36 (~b(elem!1, s(z))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[300, 11068, 199])).
% 2.13/2.36 tff(11070,plain,
% 2.13/2.36 (r(elem!1, s(z))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[305, 11069, 295])).
% 2.13/2.36 tff(11071,plain,
% 2.13/2.36 (~r(elem!1, z)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[569, 45, 11070, 27])).
% 2.13/2.36 tff(11072,plain,
% 2.13/2.36 (b(elem!1, z)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[574, 11071, 10997])).
% 2.13/2.36 tff(11073,plain,
% 2.13/2.36 (~b(s(z), elem!1)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[8486, 128, 11010, 11072, 3527])).
% 2.13/2.36 tff(11074,plain,
% 2.13/2.36 (r(s(z), elem!1)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[665, 11073, 257])).
% 2.13/2.36 tff(11075,plain,
% 2.13/2.36 (~b(s(s(z)), elem!1)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[8324, 11074, 3527, 27, 11010, 11072, 243])).
% 2.13/2.36 tff(11076,plain,
% 2.13/2.36 (r(s(s(z)), elem!1)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[370, 11075, 11019])).
% 2.13/2.36 tff(11077,plain,
% 2.13/2.36 (~r(s(z), s(s(z)))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[8333, 45, 11074, 11076])).
% 2.13/2.36 tff(11078,plain,
% 2.13/2.36 (b(s(z), s(s(z)))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[648, 11077])).
% 2.13/2.36 tff(11079,plain,
% 2.13/2.36 (~b(s(s(s(s(z)))), elem!1)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[8372, 11078, 3527, 27, 11072, 11010])).
% 2.13/2.36 tff(11080,plain,
% 2.13/2.36 (r(s(s(s(s(z)))), elem!1)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[632, 11079, 243])).
% 2.13/2.36 tff(11081,plain,
% 2.13/2.36 (~r(s(s(s(s(z)))), s(z))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[8293, 45, 11074, 11080])).
% 2.13/2.36 tff(11082,plain,
% 2.13/2.36 (b(s(s(s(s(z)))), s(z))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[782, 21, 779, 11081])).
% 2.13/2.36 tff(11083,plain,
% 2.13/2.36 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[979, 45, 11076, 11080])).
% 2.13/2.36 tff(11084,plain,
% 2.13/2.36 (b(s(s(z)), s(s(s(s(z)))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[610, 21, 607, 11083])).
% 2.13/2.36 tff(11085,plain,
% 2.13/2.36 (~r(s(z), s(s(s(s(z)))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[672, 45, 11074, 11080])).
% 2.13/2.36 tff(11086,plain,
% 2.13/2.36 (b(s(z), s(s(s(s(z)))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[684, 21, 681, 11085])).
% 2.13/2.36 tff(11087,plain,
% 2.13/2.36 ((s(s(elem!1)) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 2.13/2.36 inference(transitivity,[status(thm)],[11016, 650])).
% 2.13/2.36 tff(11088,plain,
% 2.13/2.36 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(elem!1 = s(s(z))))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[11087])).
% 2.13/2.36 tff(11089,plain,
% 2.13/2.36 (~(elem!1 = s(s(z)))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[11018, 11088])).
% 2.13/2.36 tff(11090,plain,
% 2.13/2.36 (~b(s(s(elem!1)), s(z))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[11067, 498, 3527, 199, 1691, 323, 2106, 2718])).
% 2.13/2.36 tff(11091,plain,
% 2.13/2.36 (~b(elem!1, s(z))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[300, 11090, 199])).
% 2.13/2.36 tff(11092,plain,
% 2.13/2.36 (r(elem!1, s(z))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[305, 11091, 295])).
% 2.13/2.36 tff(11093,plain,
% 2.13/2.36 (~r(elem!1, z)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[569, 45, 11092, 27])).
% 2.13/2.36 tff(11094,plain,
% 2.13/2.36 (b(elem!1, z)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[574, 11093, 5065])).
% 2.13/2.36 tff(11095,plain,
% 2.13/2.36 (~r(elem!1, s(s(z)))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[1565, 45, 11092, 35])).
% 2.13/2.36 tff(11096,plain,
% 2.13/2.36 (b(elem!1, s(s(z)))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[493, 11095, 7443])).
% 2.13/2.36 tff(11097,plain,
% 2.13/2.36 (~r(s(s(z)), z)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[51, 45, 27, 35])).
% 2.13/2.36 tff(11098,plain,
% 2.13/2.36 (b(s(s(z)), z)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[25, 11097])).
% 2.13/2.36 tff(11099,plain,
% 2.13/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1))))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(11100,plain,
% 2.13/2.36 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1))))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(11101,plain,
% 2.13/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1)))))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[11100])).
% 2.13/2.36 tff(11102,plain,
% 2.13/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1))))),
% 2.13/2.36 inference(transitivity,[status(thm)],[11101, 11099])).
% 2.13/2.36 tff(11103,plain,
% 2.13/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))))),
% 2.13/2.36 inference(quant_inst,[status(thm)],[])).
% 2.13/2.36 tff(11104,plain,
% 2.13/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1)))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[11103, 11102])).
% 2.13/2.36 tff(11105,plain,
% 2.13/2.36 ((~b(elem!1, z)) | (~b(elem!1, s(s(z))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[11104, 128, 498, 11098, 11014])).
% 2.13/2.36 tff(11106,plain,
% 2.13/2.36 ($false),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[11105, 11096, 11094])).
% 2.13/2.36 tff(11107,plain,((~b(z, elem!1)) | (elem!1 = s(s(z))) | (elem!1 = z) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~(s(s(elem!1)) = elem!1)) | (~b(s(z), z)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.36 tff(11108,plain,
% 2.13/2.36 (~r(s(s(z)), s(z))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[11107, 11010, 10997, 11089, 27, 199, 3527, 1691, 11055, 2106, 2718])).
% 2.13/2.36 tff(11109,plain,
% 2.13/2.36 (b(s(s(z)), s(z))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[86, 11108])).
% 2.13/2.36 tff(11110,plain,
% 2.13/2.36 ($false),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[1289, 128, 11109, 11086, 11084, 11082])).
% 2.13/2.36 tff(11111,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~r(z, s(z))) | (~(s(s(elem!1)) = elem!1)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.13/2.36 tff(11112,plain,
% 2.13/2.36 (~b(s(s(s(elem!1))), s(z))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[11111, 804, 27, 10999, 3527, 11009, 1608])).
% 2.13/2.36 tff(11113,plain,
% 2.13/2.36 (r(s(s(s(elem!1))), s(z))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[196, 11112])).
% 2.13/2.36 tff(11114,plain,
% 2.13/2.36 (r(s(elem!1), s(z))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[11113, 11008])).
% 2.13/2.36 tff(11115,plain,
% 2.13/2.36 (~r(z, s(elem!1))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[7704, 45, 27, 11114])).
% 2.13/2.36 tff(11116,plain,
% 2.13/2.36 (~r(z, s(s(s(elem!1))))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[11115, 11007])).
% 2.13/2.36 tff(11117,plain,
% 2.13/2.36 (b(z, s(s(s(elem!1))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[858, 11116])).
% 2.13/2.36 tff(11118,plain,
% 2.13/2.36 (b(s(elem!1), z) <=> b(s(s(s(elem!1))), z)),
% 2.13/2.36 inference(monotonicity,[status(thm)],[11005])).
% 2.13/2.36 tff(11119,plain,
% 2.13/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(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(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(11120,plain,
% 2.13/2.36 (((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), z))) <=> ((~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(11121,plain,
% 2.13/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z)))))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[11120])).
% 2.13/2.36 tff(11122,plain,
% 2.13/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))),
% 2.13/2.36 inference(transitivity,[status(thm)],[11121, 11119])).
% 2.13/2.36 tff(11123,plain,
% 2.13/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), z)))),
% 2.13/2.36 inference(quant_inst,[status(thm)],[])).
% 2.13/2.36 tff(11124,plain,
% 2.13/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z)))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[11123, 11122])).
% 2.13/2.36 tff(11125,plain,
% 2.13/2.36 (~r(s(elem!1), z)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[11124, 45, 27, 11114])).
% 2.13/2.36 tff(11126,plain,
% 2.13/2.36 (b(s(elem!1), z)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[728, 21, 109, 11125])).
% 2.13/2.36 tff(11127,plain,
% 2.13/2.36 (b(s(s(s(elem!1))), z)),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[11126, 11118])).
% 2.13/2.36 tff(11128,plain,
% 2.13/2.36 (~b(z, s(s(elem!1)))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[3460, 11127, 11009, 11117])).
% 2.13/2.36 tff(11129,plain,
% 2.13/2.36 (r(z, s(s(elem!1)))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[160, 11128])).
% 2.13/2.36 tff(11130,plain,
% 2.13/2.36 (r(z, elem!1)),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[11129, 11003])).
% 2.13/2.36 tff(11131,plain,
% 2.13/2.36 (~r(s(s(elem!1)), s(z))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[405, 11129, 27])).
% 2.13/2.36 tff(11132,plain,
% 2.13/2.36 (b(s(s(elem!1)), s(z))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[292, 11131])).
% 2.13/2.36 tff(11133,plain,
% 2.13/2.36 (~(s(elem!1) = s(s(z)))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[5015, 11002])).
% 2.13/2.36 tff(11134,plain,
% 2.13/2.36 (b(s(s(elem!1)), elem!1) <=> b(elem!1, elem!1)),
% 2.13/2.36 inference(monotonicity,[status(thm)],[10999])).
% 2.13/2.36 tff(11135,plain,
% 2.13/2.36 (b(elem!1, elem!1) <=> b(s(s(elem!1)), elem!1)),
% 2.13/2.36 inference(symmetry,[status(thm)],[11134])).
% 2.13/2.36 tff(11136,plain,
% 2.13/2.36 ((~b(elem!1, elem!1)) <=> (~b(s(s(elem!1)), elem!1))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[11135])).
% 2.13/2.36 tff(11137,plain,
% 2.13/2.36 (~b(s(s(elem!1)), elem!1)),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[4243, 11136])).
% 2.13/2.36 tff(11138,plain,
% 2.13/2.36 (~(s(s(s(elem!1))) = elem!1)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[5268, 11009, 11137])).
% 2.13/2.36 tff(11139,plain,
% 2.13/2.36 (~r(s(z), s(s(elem!1)))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[97, 11129, 27])).
% 2.13/2.36 tff(11140,plain,
% 2.13/2.36 (b(s(z), s(s(elem!1)))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[117, 11139])).
% 2.13/2.36 tff(11141,plain,
% 2.13/2.36 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[1820, 809, 7948])).
% 2.13/2.36 tff(11142,plain,
% 2.13/2.36 (b(s(z), s(s(elem!1))) <=> b(s(z), elem!1)),
% 2.13/2.36 inference(monotonicity,[status(thm)],[10999])).
% 2.13/2.36 tff(11143,plain,
% 2.13/2.36 (b(s(z), elem!1)),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[11140, 11142])).
% 2.13/2.36 tff(11144,plain,
% 2.13/2.36 (b(s(s(elem!1)), s(z)) <=> b(elem!1, s(z))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[10999])).
% 2.13/2.36 tff(11145,plain,
% 2.13/2.36 (b(elem!1, s(z))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[11132, 11144])).
% 2.13/2.36 tff(11146,plain,
% 2.13/2.36 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(elem!1))), elem!1)),
% 2.13/2.36 inference(monotonicity,[status(thm)],[354, 199])).
% 2.13/2.36 tff(11147,plain,
% 2.13/2.36 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(elem!1)))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[202])).
% 2.13/2.36 tff(11148,plain,
% 2.13/2.36 (b(s(elem!1), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 2.13/2.36 inference(transitivity,[status(thm)],[11147, 11146])).
% 2.13/2.36 tff(11149,plain,
% 2.13/2.36 ((~b(s(elem!1), elem!1)) <=> (~b(s(s(s(elem!1))), elem!1))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[11148])).
% 2.13/2.36 tff(11150,plain,
% 2.13/2.36 (~(s(elem!1) = s(s(s(s(z)))))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[761, 759, 199])).
% 2.13/2.36 tff(11151,plain,
% 2.13/2.36 (r(s(elem!1), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[354])).
% 2.13/2.36 tff(11152,plain,
% 2.13/2.36 (r(s(s(s(elem!1))), s(z)) <=> r(s(elem!1), s(z))),
% 2.13/2.36 inference(symmetry,[status(thm)],[11151])).
% 2.13/2.36 tff(11153,plain,
% 2.13/2.36 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.13/2.36 inference(symmetry,[status(thm)],[266])).
% 2.13/2.36 tff(11154,plain,
% 2.13/2.36 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(elem!1))))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[354])).
% 2.13/2.36 tff(11155,plain,
% 2.13/2.36 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.13/2.36 inference(transitivity,[status(thm)],[5233, 5228, 11154, 11153])).
% 2.13/2.36 tff(11156,plain,
% 2.13/2.36 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[1842, 11155])).
% 2.13/2.36 tff(11157,plain,
% 2.13/2.36 (~b(s(s(s(elem!1))), s(z))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[2726, 11156, 30, 876])).
% 2.13/2.36 tff(11158,plain,
% 2.13/2.36 (r(s(s(s(elem!1))), s(z))),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[196, 11157])).
% 2.13/2.36 tff(11159,plain,
% 2.13/2.36 (r(s(elem!1), s(z))),
% 2.13/2.36 inference(modus_ponens,[status(thm)],[11158, 11152])).
% 2.13/2.36 tff(11160,plain,
% 2.13/2.36 (~b(s(s(z)), elem!1)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[5037, 4791, 759, 297, 922, 5029])).
% 2.13/2.36 tff(11161,plain,
% 2.13/2.36 (r(s(s(z)), elem!1)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[370, 11160, 484])).
% 2.13/2.36 tff(11162,plain,
% 2.13/2.36 (~r(s(s(s(s(z)))), elem!1)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[1469, 11161, 1416])).
% 2.13/2.36 tff(11163,plain,
% 2.13/2.36 (b(s(s(s(s(z)))), elem!1)),
% 2.13/2.36 inference(unit_resolution,[status(thm)],[632, 11162, 2953])).
% 2.13/2.36 tff(11164,plain,
% 2.13/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z)))), 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(X0, 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(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(11165,plain,
% 2.13/2.36 (((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, 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(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.13/2.36 inference(rewrite,[status(thm)],[])).
% 2.13/2.36 tff(11166,plain,
% 2.13/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(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(X0, 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(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 2.13/2.36 inference(monotonicity,[status(thm)],[11165])).
% 2.13/2.36 tff(11167,plain,
% 2.13/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(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(X0, 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(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.13/2.37 inference(transitivity,[status(thm)],[11166, 11164])).
% 2.13/2.37 tff(11168,plain,
% 2.13/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.13/2.37 inference(quant_inst,[status(thm)],[])).
% 2.13/2.37 tff(11169,plain,
% 2.13/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z))))))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[11168, 11167])).
% 2.13/2.37 tff(11170,plain,
% 2.13/2.37 (~b(s(elem!1), s(s(s(s(z)))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[11169, 128, 297, 922, 11163, 4791])).
% 2.13/2.37 tff(11171,assumption,(~(s(elem!1) = s(s(s(s(z)))))), introduced(assumption)).
% 2.13/2.37 tff(11172,plain,
% 2.13/2.37 (r(s(elem!1), s(s(s(s(z)))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[765, 21, 11171, 11170])).
% 2.13/2.37 tff(11173,plain,
% 2.13/2.37 (~b(s(z), s(s(s(s(z)))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[928, 128, 297, 922, 11163])).
% 2.13/2.37 tff(11174,plain,
% 2.13/2.37 (r(s(z), s(s(s(s(z)))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[684, 21, 681, 11173])).
% 2.13/2.37 tff(11175,plain,
% 2.13/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(elem!1), 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(z), s(s(s(s(z)))))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.13/2.37 inference(rewrite,[status(thm)],[])).
% 2.13/2.37 tff(11176,plain,
% 2.13/2.37 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(elem!1), s(z)))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.13/2.37 inference(rewrite,[status(thm)],[])).
% 2.13/2.37 tff(11177,plain,
% 2.13/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(z), 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(z), s(s(s(s(z)))))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[11176])).
% 2.13/2.37 tff(11178,plain,
% 2.13/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(z), 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(z), s(s(s(s(z)))))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.13/2.37 inference(transitivity,[status(thm)],[11177, 11175])).
% 2.13/2.37 tff(11179,plain,
% 2.13/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(elem!1), s(z))))),
% 2.13/2.37 inference(quant_inst,[status(thm)],[])).
% 2.13/2.37 tff(11180,plain,
% 2.13/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(s(z))))))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[11179, 11178])).
% 2.13/2.37 tff(11181,plain,
% 2.13/2.37 ($false),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[11180, 45, 5029, 11174, 11172])).
% 2.13/2.37 tff(11182,plain,((~b(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (s(elem!1) = s(s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (s(s(s(s(z)))) = elem!1) | (~r(z, elem!1)) | (s(s(z)) = elem!1) | (s(elem!1) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.37 tff(11183,plain,
% 2.13/2.37 (~b(s(elem!1), elem!1)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[11182, 11159, 11150, 297, 922, 243, 1416, 240, 759])).
% 2.13/2.37 tff(11184,plain,
% 2.13/2.37 (~b(s(s(s(elem!1))), elem!1)),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[11183, 11149])).
% 2.13/2.37 tff(11185,plain,
% 2.13/2.37 (r(s(s(s(elem!1))), elem!1)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[742, 11184, 817])).
% 2.13/2.37 tff(11186,plain,
% 2.13/2.37 (r(s(elem!1), elem!1)),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[11185, 687])).
% 2.13/2.37 tff(11187,plain,
% 2.13/2.37 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(elem!1, s(elem!1))),
% 2.13/2.37 inference(transitivity,[status(thm)],[5233, 5228])).
% 2.13/2.37 tff(11188,plain,
% 2.13/2.37 (b(elem!1, s(elem!1))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[1842, 11187])).
% 2.13/2.37 tff(11189,plain,
% 2.13/2.37 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(z)))))),
% 2.13/2.37 inference(commutativity,[status(thm)],[])).
% 2.13/2.37 tff(11190,plain,
% 2.13/2.37 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 2.13/2.37 inference(symmetry,[status(thm)],[11189])).
% 2.13/2.37 tff(11191,plain,
% 2.13/2.37 ((~(s(elem!1) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[11190])).
% 2.13/2.37 tff(11192,plain,
% 2.13/2.37 (~(s(s(s(s(z)))) = s(elem!1))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[11171, 11191])).
% 2.13/2.37 tff(11193,plain,
% 2.13/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), 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(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.13/2.37 inference(rewrite,[status(thm)],[])).
% 2.13/2.37 tff(11194,plain,
% 2.13/2.37 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.13/2.37 inference(rewrite,[status(thm)],[])).
% 2.13/2.37 tff(11195,plain,
% 2.13/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[11194])).
% 2.13/2.37 tff(11196,plain,
% 2.13/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.13/2.37 inference(transitivity,[status(thm)],[11195, 11193])).
% 2.13/2.37 tff(11197,plain,
% 2.13/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.13/2.37 inference(quant_inst,[status(thm)],[])).
% 2.13/2.37 tff(11198,plain,
% 2.13/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(s(z))))))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[11197, 11196])).
% 2.13/2.37 tff(11199,plain,
% 2.13/2.37 (~r(s(elem!1), s(s(s(s(z)))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[11198, 45, 5029, 2804])).
% 2.13/2.37 tff(11200,plain,
% 2.13/2.37 (b(s(elem!1), s(s(s(s(z)))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[765, 21, 11171, 11199])).
% 2.13/2.37 tff(11201,plain,
% 2.13/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(X0, 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(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 2.13/2.37 inference(rewrite,[status(thm)],[])).
% 2.13/2.37 tff(11202,plain,
% 2.13/2.37 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), 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(s(s(s(z)))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 2.13/2.37 inference(rewrite,[status(thm)],[])).
% 2.13/2.37 tff(11203,plain,
% 2.13/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), 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(X0, 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(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[11202])).
% 2.13/2.37 tff(11204,plain,
% 2.13/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), 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(X0, 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(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 2.13/2.37 inference(transitivity,[status(thm)],[11203, 11201])).
% 2.13/2.37 tff(11205,plain,
% 2.13/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)))), 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)))),
% 2.13/2.37 inference(quant_inst,[status(thm)],[])).
% 2.13/2.37 tff(11206,plain,
% 2.13/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[11205, 11204])).
% 2.13/2.37 tff(11207,plain,
% 2.13/2.37 (~b(s(s(s(s(z)))), s(elem!1))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[11206, 128, 576, 1830, 11200])).
% 2.13/2.37 tff(11208,plain,
% 2.13/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 2.13/2.37 inference(rewrite,[status(thm)],[])).
% 2.13/2.37 tff(11209,plain,
% 2.13/2.37 (((~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 2.13/2.37 inference(rewrite,[status(thm)],[])).
% 2.13/2.37 tff(11210,plain,
% 2.13/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~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(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(elem!1)))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[11209])).
% 2.13/2.37 tff(11211,plain,
% 2.13/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~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(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 2.13/2.37 inference(transitivity,[status(thm)],[11210, 11208])).
% 2.13/2.37 tff(11212,plain,
% 2.13/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 2.13/2.37 inference(quant_inst,[status(thm)],[])).
% 2.13/2.37 tff(11213,plain,
% 2.13/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[11212, 11211])).
% 2.13/2.37 tff(11214,plain,
% 2.13/2.37 (~r(s(s(s(s(z)))), s(elem!1))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[11213, 45, 5029, 3397, 2804])).
% 2.13/2.37 tff(11215,plain,
% 2.13/2.37 (((~![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)))),
% 2.13/2.37 inference(rewrite,[status(thm)],[])).
% 2.13/2.37 tff(11216,plain,
% 2.13/2.37 ((~![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)))),
% 2.13/2.37 inference(quant_inst,[status(thm)],[])).
% 2.13/2.37 tff(11217,plain,
% 2.13/2.37 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1)) | r(s(s(s(s(z)))), s(elem!1))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[11216, 11215])).
% 2.13/2.37 tff(11218,plain,
% 2.13/2.37 ((s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[11217, 21, 11214])).
% 2.13/2.37 tff(11219,plain,
% 2.13/2.37 ($false),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[11218, 11207, 11192])).
% 2.13/2.37 tff(11220,plain,((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(elem!1))) | (s(elem!1) = s(s(s(s(z))))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.37 tff(11221,plain,
% 2.13/2.37 (~b(s(s(s(s(z)))), elem!1)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[11220, 11188, 11150, 11159, 11186, 297, 922])).
% 2.13/2.37 tff(11222,plain,
% 2.13/2.37 (r(s(s(s(s(z)))), elem!1)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[632, 11221, 243])).
% 2.13/2.37 tff(11223,plain,
% 2.13/2.37 (~r(s(s(s(s(z)))), z)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[1459, 45, 1416, 11222])).
% 2.13/2.37 tff(11224,plain,
% 2.13/2.37 (b(s(s(s(s(z)))), z)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[589, 21, 586, 11223])).
% 2.13/2.37 tff(11225,plain,
% 2.13/2.37 (~r(s(elem!1), s(s(s(s(z)))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[750, 45, 11222, 11186])).
% 2.13/2.37 tff(11226,plain,
% 2.13/2.37 (b(s(elem!1), s(s(s(s(z)))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[765, 21, 11150, 11225])).
% 2.13/2.37 tff(11227,plain,
% 2.13/2.37 (~r(s(elem!1), z)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[5337, 45, 1416, 11186])).
% 2.13/2.37 tff(11228,plain,
% 2.13/2.37 (b(s(elem!1), z)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[728, 21, 109, 11227])).
% 2.13/2.37 tff(11229,plain,
% 2.13/2.37 (b(z, s(elem!1)) <=> b(z, s(s(s(elem!1))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[354])).
% 2.13/2.37 tff(11230,plain,
% 2.13/2.37 (b(z, s(s(s(elem!1)))) <=> b(z, s(elem!1))),
% 2.13/2.37 inference(symmetry,[status(thm)],[11229])).
% 2.13/2.37 tff(11231,plain,
% 2.13/2.37 (b(z, s(elem!1))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[874, 11230])).
% 2.13/2.37 tff(11232,plain,
% 2.13/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.13/2.37 inference(rewrite,[status(thm)],[])).
% 2.13/2.37 tff(11233,plain,
% 2.13/2.37 (((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z))))))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.13/2.37 inference(rewrite,[status(thm)],[])).
% 2.13/2.37 tff(11234,plain,
% 2.13/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[11233])).
% 2.13/2.37 tff(11235,plain,
% 2.13/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.13/2.37 inference(transitivity,[status(thm)],[11234, 11232])).
% 2.13/2.37 tff(11236,plain,
% 2.13/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.13/2.37 inference(quant_inst,[status(thm)],[])).
% 2.13/2.37 tff(11237,plain,
% 2.13/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z))))))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[11236, 11235])).
% 2.13/2.37 tff(11238,plain,
% 2.13/2.37 ($false),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[11237, 128, 11231, 11228, 11226, 11224])).
% 2.13/2.37 tff(11239,plain,((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~(s(s(elem!1)) = elem!1)) | (s(s(s(elem!1))) = elem!1) | (s(elem!1) = s(s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.37 tff(11240,plain,
% 2.13/2.37 ($false),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[11239, 11145, 11143, 11141, 11140, 11117, 10999, 11138, 11133, 11132, 11130])).
% 2.13/2.37 tff(11241,plain,((s(s(elem!1)) = s(s(s(elem!1)))) | (~r(z, s(z))) | (~b(s(z), z)) | (z = elem!1) | r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.37 tff(11242,plain,
% 2.13/2.37 (s(s(elem!1)) = s(s(s(elem!1)))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[11241, 27, 3527, 1608, 7948, 7908])).
% 2.13/2.37 tff(11243,plain,
% 2.13/2.37 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), elem!1)),
% 2.13/2.37 inference(monotonicity,[status(thm)],[986])).
% 2.13/2.37 tff(11244,plain,
% 2.13/2.37 (r(s(s(s(s(elem!1)))), s(z))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[313, 7593])).
% 2.13/2.37 tff(11245,plain,
% 2.13/2.37 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[953])).
% 2.13/2.37 tff(11246,plain,
% 2.13/2.37 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.13/2.37 inference(symmetry,[status(thm)],[11245])).
% 2.13/2.37 tff(11247,plain,
% 2.13/2.37 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[955])).
% 2.13/2.37 tff(11248,plain,
% 2.13/2.37 (b(elem!1, s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.13/2.37 inference(symmetry,[status(thm)],[11247])).
% 2.13/2.37 tff(11249,plain,
% 2.13/2.37 (b(elem!1, s(elem!1)) <=> b(elem!1, elem!1)),
% 2.13/2.37 inference(monotonicity,[status(thm)],[310])).
% 2.13/2.37 tff(11250,plain,
% 2.13/2.37 (b(elem!1, elem!1) <=> b(elem!1, s(elem!1))),
% 2.13/2.37 inference(symmetry,[status(thm)],[11249])).
% 2.13/2.37 tff(11251,plain,
% 2.13/2.37 (b(elem!1, elem!1) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.13/2.37 inference(transitivity,[status(thm)],[11250, 11248, 11246])).
% 2.13/2.37 tff(11252,plain,
% 2.13/2.37 ((~b(elem!1, elem!1)) <=> (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[11251])).
% 2.13/2.37 tff(11253,plain,
% 2.13/2.37 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[4243, 11252])).
% 2.13/2.37 tff(11254,plain,
% 2.13/2.37 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[2176, 325, 27, 1737])).
% 2.13/2.37 tff(11255,plain,
% 2.13/2.37 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[1073, 11254])).
% 2.13/2.37 tff(11256,plain,
% 2.13/2.37 (s(s(elem!1)) = elem!1),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[1089, 11255])).
% 2.13/2.37 tff(11257,plain,
% 2.13/2.37 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[11256])).
% 2.13/2.37 tff(11258,plain,
% 2.13/2.37 ((~r(s(s(elem!1)), s(s(s(elem!1))))) <=> (~r(elem!1, s(s(s(elem!1)))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[11257])).
% 2.13/2.37 tff(11259,plain,
% 2.13/2.37 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[333, 325, 323])).
% 2.13/2.37 tff(11260,plain,
% 2.13/2.37 (~r(elem!1, s(s(s(elem!1))))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[11259, 11258])).
% 2.13/2.37 tff(11261,plain,
% 2.13/2.37 (elem!1 = s(s(elem!1))),
% 2.13/2.37 inference(symmetry,[status(thm)],[11256])).
% 2.13/2.37 tff(11262,plain,
% 2.13/2.37 (s(elem!1) = s(s(s(elem!1)))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[11261])).
% 2.13/2.37 tff(11263,plain,
% 2.13/2.37 (s(s(s(elem!1))) = s(elem!1)),
% 2.13/2.37 inference(symmetry,[status(thm)],[11262])).
% 2.13/2.37 tff(11264,plain,
% 2.13/2.37 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[11263])).
% 2.13/2.37 tff(11265,plain,
% 2.13/2.37 (s(s(s(s(elem!1)))) = elem!1),
% 2.13/2.37 inference(transitivity,[status(thm)],[11264, 11256])).
% 2.13/2.37 tff(11266,plain,
% 2.13/2.37 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(elem!1, s(s(s(elem!1))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[11265, 11262])).
% 2.13/2.37 tff(11267,plain,
% 2.13/2.37 ((~b(s(s(s(s(elem!1)))), s(elem!1))) <=> (~b(elem!1, s(s(s(elem!1)))))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[11266])).
% 2.13/2.37 tff(11268,plain,
% 2.13/2.37 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[11263])).
% 2.13/2.37 tff(11269,plain,
% 2.13/2.37 ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) <=> (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[11268])).
% 2.13/2.37 tff(11270,plain,
% 2.13/2.37 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[4264, 11269])).
% 2.13/2.37 tff(11271,plain,
% 2.13/2.37 (~b(elem!1, s(s(s(elem!1))))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[11270, 11267])).
% 2.13/2.37 tff(11272,plain,
% 2.13/2.37 (elem!1 = s(s(s(elem!1)))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[2466, 11271, 11260])).
% 2.13/2.37 tff(11273,plain,
% 2.13/2.37 ((~(elem!1 = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[225])).
% 2.13/2.37 tff(11274,plain,
% 2.13/2.37 (s(s(z)) = elem!1),
% 2.13/2.37 inference(symmetry,[status(thm)],[485])).
% 2.13/2.37 tff(11275,plain,
% 2.13/2.37 (s(s(z)) = s(s(elem!1))),
% 2.13/2.37 inference(transitivity,[status(thm)],[11274, 202])).
% 2.13/2.37 tff(11276,plain,
% 2.13/2.37 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[11275])).
% 2.13/2.37 tff(11277,plain,
% 2.13/2.37 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 2.13/2.37 inference(symmetry,[status(thm)],[11276])).
% 2.13/2.37 tff(11278,assumption,(elem!1 = s(s(s(elem!1)))), introduced(assumption)).
% 2.13/2.37 tff(11279,plain,
% 2.13/2.37 (elem!1 = s(z)),
% 2.13/2.37 inference(transitivity,[status(thm)],[11278, 953, 106, 11277, 69])).
% 2.13/2.37 tff(11280,plain,
% 2.13/2.37 ($false),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[295, 11279])).
% 2.13/2.37 tff(11281,plain,((~(elem!1 = s(s(z)))) | (~(elem!1 = s(s(s(elem!1))))) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.37 tff(11282,plain,
% 2.13/2.37 (~(elem!1 = s(s(z)))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[11281, 11272, 11256])).
% 2.13/2.37 tff(11283,plain,
% 2.13/2.37 (~(s(s(z)) = elem!1)),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[11282, 11273])).
% 2.13/2.37 tff(11284,plain,
% 2.13/2.37 (s(s(s(elem!1))) = elem!1),
% 2.13/2.37 inference(symmetry,[status(thm)],[11278])).
% 2.13/2.37 tff(11285,plain,
% 2.13/2.37 (s(s(s(z))) = s(s(elem!1))),
% 2.13/2.37 inference(transitivity,[status(thm)],[218, 215, 105, 309, 11284, 202])).
% 2.13/2.37 tff(11286,plain,
% 2.13/2.37 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[11285])).
% 2.13/2.37 tff(11287,plain,
% 2.13/2.37 (s(s(z)) = elem!1),
% 2.13/2.37 inference(transitivity,[status(thm)],[223, 11286, 105, 309, 11284])).
% 2.13/2.37 tff(11288,plain,
% 2.13/2.37 ($false),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[484, 11287])).
% 2.13/2.37 tff(11289,plain,((~(s(s(s(s(z)))) = elem!1)) | (s(s(z)) = elem!1) | (~(elem!1 = s(s(s(elem!1))))) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.37 tff(11290,plain,
% 2.13/2.37 (~(s(s(s(s(z)))) = elem!1)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[11289, 11283, 11272, 11256])).
% 2.13/2.37 tff(11291,plain,
% 2.13/2.37 (b(z, s(s(elem!1))) <=> b(z, elem!1)),
% 2.13/2.37 inference(monotonicity,[status(thm)],[11256])).
% 2.13/2.37 tff(11292,plain,
% 2.13/2.37 (b(z, elem!1)),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[8194, 11291])).
% 2.13/2.37 tff(11293,plain,
% 2.13/2.37 (s(s(s(elem!1))) = elem!1),
% 2.13/2.37 inference(symmetry,[status(thm)],[11272])).
% 2.13/2.37 tff(11294,plain,
% 2.13/2.37 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), elem!1)),
% 2.13/2.37 inference(monotonicity,[status(thm)],[11293])).
% 2.13/2.37 tff(11295,plain,
% 2.13/2.37 (r(s(z), elem!1)),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[323, 11294])).
% 2.13/2.37 tff(11296,plain,
% 2.13/2.37 ((s(s(elem!1)) = z) <=> (elem!1 = z)),
% 2.13/2.37 inference(monotonicity,[status(thm)],[11256])).
% 2.13/2.37 tff(11297,plain,
% 2.13/2.37 ((s(s(elem!1)) = z) <=> (z = elem!1)),
% 2.13/2.37 inference(transitivity,[status(thm)],[11296, 247])).
% 2.13/2.37 tff(11298,plain,
% 2.13/2.37 ((s(s(elem!1)) = z) <=> (elem!1 = z)),
% 2.13/2.37 inference(transitivity,[status(thm)],[11297, 459])).
% 2.13/2.37 tff(11299,plain,
% 2.13/2.37 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = z))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[11298])).
% 2.13/2.37 tff(11300,plain,
% 2.13/2.37 (~(elem!1 = z)),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[154, 11299])).
% 2.13/2.37 tff(11301,plain,
% 2.13/2.37 (r(s(s(elem!1)), s(z)) <=> r(elem!1, s(z))),
% 2.13/2.37 inference(monotonicity,[status(thm)],[11256])).
% 2.13/2.37 tff(11302,plain,
% 2.13/2.37 (r(elem!1, s(z))),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[325, 11301])).
% 2.13/2.37 tff(11303,plain,
% 2.13/2.37 (~r(elem!1, z)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[569, 45, 11302, 27])).
% 2.13/2.37 tff(11304,plain,
% 2.13/2.37 (b(elem!1, z)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[574, 11303, 11300])).
% 2.13/2.37 tff(11305,plain,
% 2.13/2.37 (~b(s(s(z)), elem!1)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[8324, 11292, 11304, 3527, 27, 11295, 11290])).
% 2.13/2.37 tff(11306,plain,
% 2.13/2.37 (r(s(s(z)), elem!1)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[370, 11305, 11283])).
% 2.13/2.37 tff(11307,plain,
% 2.13/2.37 (~r(s(z), s(s(z)))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[8333, 45, 11295, 11306])).
% 2.13/2.37 tff(11308,plain,
% 2.13/2.37 (b(s(z), s(s(z)))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[648, 11307])).
% 2.13/2.37 tff(11309,plain,
% 2.13/2.37 (~b(s(s(s(s(z)))), elem!1)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[8372, 11304, 27, 3527, 11308, 11292])).
% 2.13/2.37 tff(11310,plain,
% 2.13/2.37 (r(s(s(s(s(z)))), elem!1)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[632, 11309, 11290])).
% 2.13/2.37 tff(11311,plain,
% 2.13/2.37 (~r(s(s(s(s(z)))), s(z))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[8293, 45, 11295, 11310])).
% 2.13/2.37 tff(11312,plain,
% 2.13/2.37 (b(s(s(s(s(z)))), s(z))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[782, 21, 779, 11311])).
% 2.13/2.37 tff(11313,plain,
% 2.13/2.37 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[979, 45, 11306, 11310])).
% 2.13/2.37 tff(11314,plain,
% 2.13/2.37 (b(s(s(z)), s(s(s(s(z)))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[610, 21, 607, 11313])).
% 2.13/2.37 tff(11315,plain,
% 2.13/2.37 (~r(s(z), s(s(s(s(z)))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[672, 45, 11295, 11310])).
% 2.13/2.37 tff(11316,plain,
% 2.13/2.37 (b(s(z), s(s(s(s(z)))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[684, 21, 681, 11315])).
% 2.13/2.37 tff(11317,plain,
% 2.13/2.37 (~r(s(s(z)), s(z))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[10257, 45, 11295, 11306])).
% 2.13/2.37 tff(11318,plain,
% 2.13/2.37 (b(s(s(z)), s(z))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[86, 11317])).
% 2.13/2.37 tff(11319,plain,
% 2.13/2.37 ($false),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[1289, 128, 11318, 11316, 11314, 11312])).
% 2.13/2.37 tff(11320,plain,((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~b(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.37 tff(11321,plain,
% 2.13/2.37 (~r(s(z), s(s(s(elem!1))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[11320, 1580, 3527, 27, 11253, 11244])).
% 2.13/2.37 tff(11322,plain,
% 2.13/2.37 (b(s(z), s(s(s(elem!1))))),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[339, 11321])).
% 2.13/2.37 tff(11323,plain,
% 2.13/2.37 (b(s(z), elem!1)),
% 2.13/2.37 inference(modus_ponens,[status(thm)],[11322, 11243])).
% 2.13/2.37 tff(11324,plain,
% 2.13/2.37 (b(elem!1, z)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[574, 5594, 10997])).
% 2.13/2.37 tff(11325,plain,
% 2.13/2.37 (~r(z, elem!1)),
% 2.13/2.37 inference(unit_resolution,[status(thm)],[4896, 313, 27])).
% 2.13/2.37 tff(11326,plain,
% 2.13/2.37 (b(z, elem!1)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[1549, 11325, 1608])).
% 2.13/2.38 tff(11327,plain,
% 2.13/2.38 ($false),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[8486, 128, 11326, 11324, 3527, 11323])).
% 2.13/2.38 tff(11328,plain,((~r(elem!1, s(z))) | (~b(s(z), z)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~(s(s(elem!1)) = elem!1)) | (~r(z, s(z))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.13/2.38 tff(11329,plain,
% 2.13/2.38 (~r(elem!1, s(z))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[11328, 11242, 3527, 10999, 27, 1608])).
% 2.13/2.38 tff(11330,plain,
% 2.13/2.38 (b(elem!1, s(z))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[305, 11329, 11002])).
% 2.13/2.38 tff(11331,plain,
% 2.13/2.38 (elem!1 = s(s(elem!1))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[377, 10999])).
% 2.13/2.38 tff(11332,plain,
% 2.13/2.38 (r(s(z), s(s(elem!1))) <=> r(s(z), elem!1)),
% 2.13/2.38 inference(monotonicity,[status(thm)],[10999])).
% 2.13/2.38 tff(11333,plain,
% 2.13/2.38 (r(s(z), elem!1) <=> r(s(z), s(s(elem!1)))),
% 2.13/2.38 inference(symmetry,[status(thm)],[11332])).
% 2.13/2.38 tff(11334,plain,
% 2.13/2.38 ((s(s(elem!1)) = s(z)) <=> (s(z) = elem!1)),
% 2.13/2.38 inference(transitivity,[status(thm)],[11000, 253])).
% 2.13/2.38 tff(11335,plain,
% 2.13/2.38 ((~(s(s(elem!1)) = s(z))) <=> (~(s(z) = elem!1))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[11334])).
% 2.13/2.38 tff(11336,plain,
% 2.13/2.38 (~(s(z) = elem!1)),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[111, 11335])).
% 2.13/2.38 tff(11337,plain,
% 2.13/2.38 ((s(s(elem!1)) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[10999])).
% 2.13/2.38 tff(11338,plain,
% 2.13/2.38 ((s(s(elem!1)) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 2.13/2.38 inference(transitivity,[status(thm)],[11337, 225])).
% 2.13/2.38 tff(11339,plain,
% 2.13/2.38 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[11338])).
% 2.13/2.38 tff(11340,plain,
% 2.13/2.38 (~(s(s(z)) = elem!1)),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[11018, 11339])).
% 2.13/2.38 tff(11341,plain,
% 2.13/2.38 (~(s(s(s(s(z)))) = elem!1)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[242, 10999])).
% 2.13/2.38 tff(11342,plain,
% 2.13/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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), z)))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(11343,plain,
% 2.13/2.38 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), z)))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(11344,plain,
% 2.13/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~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(X0, 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), z))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[11343])).
% 2.13/2.38 tff(11345,plain,
% 2.13/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~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(X0, 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), z)))),
% 2.13/2.38 inference(transitivity,[status(thm)],[11344, 11342])).
% 2.13/2.38 tff(11346,plain,
% 2.13/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 2.13/2.38 inference(quant_inst,[status(thm)],[])).
% 2.13/2.38 tff(11347,plain,
% 2.13/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), z))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[11346, 11345])).
% 2.13/2.38 tff(11348,plain,
% 2.13/2.38 ($false),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[11347, 128, 498, 297, 3527, 922])).
% 2.13/2.38 tff(11349,plain,((~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.38 tff(11350,plain,
% 2.13/2.38 (~b(z, elem!1)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[11349, 922, 3527, 297])).
% 2.13/2.38 tff(11351,plain,
% 2.13/2.38 (r(z, elem!1)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[1549, 11350, 1608])).
% 2.13/2.38 tff(11352,plain,
% 2.13/2.38 (r(s(s(z)), elem!1)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[370, 960, 484])).
% 2.13/2.38 tff(11353,plain,
% 2.13/2.38 (~r(s(s(z)), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[1433, 45, 1416, 11352])).
% 2.13/2.38 tff(11354,plain,
% 2.13/2.38 (b(s(s(z)), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[25, 11353])).
% 2.13/2.38 tff(11355,plain,
% 2.13/2.38 (~r(z, s(s(z)))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[1441, 45, 1416, 11352])).
% 2.13/2.38 tff(11356,plain,
% 2.13/2.38 (b(z, s(s(z)))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[516, 11355])).
% 2.13/2.38 tff(11357,plain,
% 2.13/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(11358,plain,
% 2.13/2.38 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(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(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(11359,plain,
% 2.13/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z))))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[11358])).
% 2.13/2.38 tff(11360,plain,
% 2.13/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))))),
% 2.13/2.38 inference(transitivity,[status(thm)],[11359, 11357])).
% 2.13/2.38 tff(11361,plain,
% 2.13/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 2.13/2.38 inference(quant_inst,[status(thm)],[])).
% 2.13/2.38 tff(11362,plain,
% 2.13/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z))))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[11361, 11360])).
% 2.13/2.38 tff(11363,plain,
% 2.13/2.38 ($false),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[11362, 128, 3527, 11356, 273, 11354])).
% 2.13/2.38 tff(11364,plain,((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~r(z, elem!1)) | (s(s(z)) = elem!1) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.38 tff(11365,plain,
% 2.13/2.38 (~b(s(s(z)), s(z))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[11364, 11351, 3527, 484, 297, 922])).
% 2.13/2.38 tff(11366,plain,
% 2.13/2.38 (r(s(s(z)), s(z))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[86, 11365])).
% 2.13/2.38 tff(11367,plain,
% 2.13/2.38 (~r(s(s(s(s(z)))), s(z))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[2950, 11351, 27, 11366])).
% 2.13/2.38 tff(11368,plain,
% 2.13/2.38 (b(s(s(s(s(z)))), s(z))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[782, 21, 779, 11367])).
% 2.13/2.38 tff(11369,plain,
% 2.13/2.38 (~b(s(s(s(s(z)))), elem!1)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[10743, 128, 297, 922, 11368])).
% 2.13/2.38 tff(11370,plain,
% 2.13/2.38 (r(s(s(s(s(z)))), elem!1)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[632, 11369, 2953])).
% 2.13/2.38 tff(11371,plain,
% 2.13/2.38 (~r(s(s(s(s(z)))), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[1459, 45, 11351, 11370])).
% 2.13/2.38 tff(11372,plain,
% 2.13/2.38 (b(s(s(s(s(z)))), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[589, 21, 586, 11371])).
% 2.13/2.38 tff(11373,plain,
% 2.13/2.38 (~r(s(s(z)), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[2936, 45, 11351, 27, 11366])).
% 2.13/2.38 tff(11374,plain,
% 2.13/2.38 (b(s(s(z)), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[25, 11373])).
% 2.13/2.38 tff(11375,plain,
% 2.13/2.38 (~r(z, s(s(z)))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[2946, 11366, 27])).
% 2.13/2.38 tff(11376,plain,
% 2.13/2.38 (b(z, s(s(z)))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[516, 11375])).
% 2.13/2.38 tff(11377,plain,
% 2.13/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(11378,plain,
% 2.13/2.38 (((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(11379,plain,
% 2.13/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[11378])).
% 2.13/2.38 tff(11380,plain,
% 2.13/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.13/2.38 inference(transitivity,[status(thm)],[11379, 11377])).
% 2.13/2.38 tff(11381,plain,
% 2.13/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.13/2.38 inference(quant_inst,[status(thm)],[])).
% 2.13/2.38 tff(11382,plain,
% 2.13/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[11381, 11380])).
% 2.13/2.38 tff(11383,plain,
% 2.13/2.38 ($false),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[11382, 128, 3527, 11376, 11374, 11368, 11372])).
% 2.13/2.38 tff(11384,plain,((~b(s(z), elem!1)) | (~b(s(z), z)) | (s(s(s(s(z)))) = elem!1) | (~b(elem!1, s(z))) | (~r(z, s(z))) | (s(s(z)) = elem!1) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.13/2.38 tff(11385,plain,
% 2.13/2.38 (~b(s(z), elem!1)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[11384, 11341, 3527, 11330, 27, 11340, 1608])).
% 2.13/2.38 tff(11386,plain,
% 2.13/2.38 (r(s(z), elem!1)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[665, 11385, 11336])).
% 2.13/2.38 tff(11387,plain,
% 2.13/2.38 (r(s(z), s(s(elem!1)))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[11386, 11333])).
% 2.13/2.38 tff(11388,plain,
% 2.13/2.38 (~r(z, s(s(elem!1)))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[97, 11387, 27])).
% 2.13/2.38 tff(11389,plain,
% 2.13/2.38 (b(z, s(s(elem!1)))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[160, 11388])).
% 2.13/2.38 tff(11390,plain,
% 2.13/2.38 (b(z, elem!1)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[457, 11389, 11331])).
% 2.13/2.38 tff(11391,plain,
% 2.13/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(11392,plain,
% 2.13/2.38 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(11393,plain,
% 2.13/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[11392])).
% 2.13/2.38 tff(11394,plain,
% 2.13/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)))),
% 2.13/2.38 inference(transitivity,[status(thm)],[11393, 11391])).
% 2.13/2.38 tff(11395,plain,
% 2.13/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))),
% 2.13/2.38 inference(quant_inst,[status(thm)],[])).
% 2.13/2.38 tff(11396,plain,
% 2.13/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[11395, 11394])).
% 2.13/2.38 tff(11397,plain,
% 2.13/2.38 (~b(elem!1, z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[11396, 128, 11390, 11330, 3527])).
% 2.13/2.38 tff(11398,plain,
% 2.13/2.38 (r(elem!1, z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[574, 11397, 10997])).
% 2.13/2.38 tff(11399,plain,
% 2.13/2.38 (~b(s(s(z)), s(z))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[7869, 11390, 11330, 3527, 11340, 11398])).
% 2.13/2.38 tff(11400,plain,
% 2.13/2.38 (r(s(s(z)), s(z))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[86, 11399])).
% 2.13/2.38 tff(11401,plain,
% 2.13/2.38 (~r(s(s(z)), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[51, 45, 27, 11400])).
% 2.13/2.38 tff(11402,plain,
% 2.13/2.38 (b(s(s(z)), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[25, 11401])).
% 2.13/2.38 tff(11403,plain,
% 2.13/2.38 ((s(s(elem!1)) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 2.13/2.38 inference(transitivity,[status(thm)],[11338, 650])).
% 2.13/2.38 tff(11404,plain,
% 2.13/2.38 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(elem!1 = s(s(z))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[11403])).
% 2.13/2.38 tff(11405,plain,
% 2.13/2.38 (~(elem!1 = s(s(z)))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[11018, 11404])).
% 2.13/2.38 tff(11406,plain,
% 2.13/2.38 (s(s(s(elem!1))) = s(s(elem!1))),
% 2.13/2.38 inference(symmetry,[status(thm)],[11242])).
% 2.13/2.38 tff(11407,plain,
% 2.13/2.38 (s(s(s(elem!1))) = elem!1),
% 2.13/2.38 inference(transitivity,[status(thm)],[11406, 10999])).
% 2.13/2.38 tff(11408,plain,
% 2.13/2.38 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), elem!1)),
% 2.13/2.38 inference(monotonicity,[status(thm)],[11407])).
% 2.13/2.38 tff(11409,plain,
% 2.13/2.38 (r(s(z), elem!1) <=> r(s(z), s(s(s(elem!1))))),
% 2.13/2.38 inference(symmetry,[status(thm)],[11408])).
% 2.13/2.38 tff(11410,plain,
% 2.13/2.38 (r(s(z), s(s(s(elem!1))))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[11386, 11409])).
% 2.13/2.38 tff(11411,plain,
% 2.13/2.38 (~r(z, s(s(z)))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[2946, 11400, 27])).
% 2.13/2.38 tff(11412,plain,
% 2.13/2.38 (b(z, s(s(z)))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[516, 11411])).
% 2.13/2.38 tff(11413,plain,
% 2.13/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(11414,plain,
% 2.13/2.38 (((~b(s(s(z)), z)) | (~b(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(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(11415,plain,
% 2.13/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z))))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[11414])).
% 2.13/2.38 tff(11416,plain,
% 2.13/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))),
% 2.13/2.38 inference(transitivity,[status(thm)],[11415, 11413])).
% 2.13/2.38 tff(11417,plain,
% 2.13/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))),
% 2.13/2.38 inference(quant_inst,[status(thm)],[])).
% 2.13/2.38 tff(11418,plain,
% 2.13/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z))))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[11417, 11416])).
% 2.13/2.38 tff(11419,plain,
% 2.13/2.38 (~b(s(z), s(s(z)))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[11418, 128, 3527, 11412, 11402])).
% 2.13/2.38 tff(11420,plain,
% 2.13/2.38 (r(s(z), s(s(z)))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[648, 11419])).
% 2.13/2.38 tff(11421,plain,
% 2.13/2.38 (~r(elem!1, s(s(z)))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[7464, 11420, 11242, 11410])).
% 2.13/2.38 tff(11422,plain,
% 2.13/2.38 (b(elem!1, s(s(z)))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[493, 11421, 11405])).
% 2.13/2.38 tff(11423,plain,
% 2.13/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, s(s(z)))))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(11424,plain,
% 2.13/2.38 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(11425,plain,
% 2.13/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, s(s(z))))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[11424])).
% 2.13/2.38 tff(11426,plain,
% 2.13/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1, s(s(z)))))),
% 2.13/2.38 inference(transitivity,[status(thm)],[11425, 11423])).
% 2.13/2.38 tff(11427,plain,
% 2.13/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, elem!1)))),
% 2.13/2.38 inference(quant_inst,[status(thm)],[])).
% 2.13/2.38 tff(11428,plain,
% 2.13/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(z))))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[11427, 11426])).
% 2.13/2.38 tff(11429,plain,
% 2.13/2.38 ($false),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[11428, 128, 11390, 11412, 11422, 11402])).
% 2.13/2.38 tff(11430,plain,((~r(z, s(z))) | (~b(s(z), z)) | (z = elem!1) | r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.38 tff(11431,plain,
% 2.13/2.38 ((~r(z, s(z))) | (z = elem!1) | r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[11430, 7825])).
% 2.13/2.38 tff(11432,plain,
% 2.13/2.38 ($false),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[11431, 10996, 10991, 27, 7908])).
% 2.13/2.38 tff(11433,plain,((~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(z, s(z))) | r(s(s(elem!1)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.38 tff(11434,plain,
% 2.13/2.38 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[11433, 7908, 27])).
% 2.13/2.38 tff(11435,plain,
% 2.13/2.38 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[321, 11434, 7908])).
% 2.13/2.38 tff(11436,plain,
% 2.13/2.38 (~b(s(s(s(elem!1))), s(z))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[8056, 30, 27, 2106, 1063])).
% 2.13/2.38 tff(11437,plain,
% 2.13/2.38 (r(s(s(s(elem!1))), s(z))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[196, 11436])).
% 2.13/2.38 tff(11438,plain,
% 2.13/2.38 (~b(z, s(s(elem!1)))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[7826, 30, 1063])).
% 2.13/2.38 tff(11439,plain,
% 2.13/2.38 (r(z, s(s(elem!1)))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[160, 11438])).
% 2.13/2.38 tff(11440,plain,
% 2.13/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(11441,plain,
% 2.13/2.38 (((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 2.13/2.38 inference(rewrite,[status(thm)],[])).
% 2.13/2.38 tff(11442,plain,
% 2.13/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z)))))),
% 2.13/2.38 inference(monotonicity,[status(thm)],[11441])).
% 2.13/2.38 tff(11443,plain,
% 2.13/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 2.13/2.38 inference(transitivity,[status(thm)],[11442, 11440])).
% 2.13/2.38 tff(11444,plain,
% 2.13/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))),
% 2.13/2.38 inference(quant_inst,[status(thm)],[])).
% 2.13/2.38 tff(11445,plain,
% 2.13/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z)))),
% 2.13/2.38 inference(modus_ponens,[status(thm)],[11444, 11443])).
% 2.13/2.38 tff(11446,plain,
% 2.13/2.38 (~r(s(s(s(elem!1))), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[11445, 45, 27, 11439, 11437])).
% 2.13/2.38 tff(11447,plain,
% 2.13/2.38 (b(s(s(s(elem!1))), z)),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[5301, 11446])).
% 2.13/2.38 tff(11448,plain,
% 2.13/2.38 (~r(z, s(s(s(elem!1))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[3611, 45, 27, 11437])).
% 2.13/2.38 tff(11449,plain,
% 2.13/2.38 (b(z, s(s(s(elem!1))))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[858, 11448])).
% 2.13/2.38 tff(11450,plain,
% 2.13/2.38 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.13/2.38 inference(unit_resolution,[status(thm)],[10983, 128, 11449, 11447, 10906])).
% 2.13/2.38 tff(11451,plain,
% 2.13/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 2.13/2.39 inference(rewrite,[status(thm)],[])).
% 2.13/2.39 tff(11452,plain,
% 2.13/2.39 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 2.13/2.39 inference(rewrite,[status(thm)],[])).
% 2.13/2.39 tff(11453,plain,
% 2.13/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11452])).
% 2.13/2.39 tff(11454,plain,
% 2.13/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 2.13/2.39 inference(transitivity,[status(thm)],[11453, 11451])).
% 2.13/2.39 tff(11455,plain,
% 2.13/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 2.13/2.39 inference(quant_inst,[status(thm)],[])).
% 2.13/2.39 tff(11456,plain,
% 2.13/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[11455, 11454])).
% 2.13/2.39 tff(11457,plain,
% 2.13/2.39 (~b(s(s(z)), s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11456, 128, 7825, 11449, 11447, 10906])).
% 2.13/2.39 tff(11458,plain,
% 2.13/2.39 (r(s(s(z)), s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[86, 11457])).
% 2.13/2.39 tff(11459,plain,
% 2.13/2.39 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[6248, 11458, 11437])).
% 2.13/2.39 tff(11460,plain,
% 2.13/2.39 ($false),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[4350, 21, 11459, 11450, 283])).
% 2.13/2.39 tff(11461,plain,((~b(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.39 tff(11462,plain,
% 2.13/2.39 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11461, 11435, 30, 27])).
% 2.13/2.39 tff(11463,plain,
% 2.13/2.39 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[1073, 11462])).
% 2.13/2.39 tff(11464,plain,
% 2.13/2.39 (s(s(elem!1)) = elem!1),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[1089, 11463])).
% 2.13/2.39 tff(11465,plain,
% 2.13/2.39 ((s(s(elem!1)) = z) <=> (elem!1 = z)),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11464])).
% 2.13/2.39 tff(11466,plain,
% 2.13/2.39 ((s(s(elem!1)) = z) <=> (z = elem!1)),
% 2.13/2.39 inference(transitivity,[status(thm)],[11465, 247])).
% 2.13/2.39 tff(11467,plain,
% 2.13/2.39 ((~(s(s(elem!1)) = z)) <=> (~(z = elem!1))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11466])).
% 2.13/2.39 tff(11468,plain,
% 2.13/2.39 (~(z = elem!1)),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[154, 11467])).
% 2.13/2.39 tff(11469,plain,
% 2.13/2.39 (s(s(s(elem!1))) = s(elem!1)),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11464])).
% 2.13/2.39 tff(11470,plain,
% 2.13/2.39 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11469])).
% 2.13/2.39 tff(11471,plain,
% 2.13/2.39 (r(s(s(s(s(elem!1)))), s(elem!1)) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.13/2.39 inference(symmetry,[status(thm)],[11470])).
% 2.13/2.39 tff(11472,plain,
% 2.13/2.39 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11469])).
% 2.13/2.39 tff(11473,plain,
% 2.13/2.39 (s(s(s(s(elem!1)))) = elem!1),
% 2.13/2.39 inference(transitivity,[status(thm)],[11472, 11464])).
% 2.13/2.39 tff(11474,plain,
% 2.13/2.39 (r(s(s(s(s(elem!1)))), s(elem!1)) <=> r(elem!1, s(elem!1))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11473])).
% 2.13/2.39 tff(11475,plain,
% 2.13/2.39 (r(elem!1, s(elem!1)) <=> r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.13/2.39 inference(symmetry,[status(thm)],[11474])).
% 2.13/2.39 tff(11476,plain,
% 2.13/2.39 (r(elem!1, s(elem!1)) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.13/2.39 inference(transitivity,[status(thm)],[11475, 11471])).
% 2.13/2.39 tff(11477,plain,
% 2.13/2.39 ((~r(elem!1, s(elem!1))) <=> (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11476])).
% 2.13/2.39 tff(11478,plain,
% 2.13/2.39 (s(elem!1) = s(s(s(elem!1)))),
% 2.13/2.39 inference(symmetry,[status(thm)],[11469])).
% 2.13/2.39 tff(11479,plain,
% 2.13/2.39 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(elem!1))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11478])).
% 2.13/2.39 tff(11480,plain,
% 2.13/2.39 (r(elem!1, s(s(s(elem!1)))) <=> r(elem!1, s(elem!1))),
% 2.13/2.39 inference(symmetry,[status(thm)],[11479])).
% 2.13/2.39 tff(11481,plain,
% 2.13/2.39 ((~r(elem!1, s(s(s(elem!1))))) <=> (~r(elem!1, s(elem!1)))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11480])).
% 2.13/2.39 tff(11482,plain,
% 2.13/2.39 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11464])).
% 2.13/2.39 tff(11483,plain,
% 2.13/2.39 ((~r(s(s(elem!1)), s(s(s(elem!1))))) <=> (~r(elem!1, s(s(s(elem!1)))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11482])).
% 2.13/2.39 tff(11484,plain,
% 2.13/2.39 (~r(elem!1, s(s(s(elem!1))))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[7908, 11483])).
% 2.13/2.39 tff(11485,plain,
% 2.13/2.39 (~r(elem!1, s(elem!1))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[11484, 11481])).
% 2.13/2.39 tff(11486,plain,
% 2.13/2.39 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[11485, 11477])).
% 2.13/2.39 tff(11487,plain,
% 2.13/2.39 ($false),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11431, 11486, 11468, 27, 7908])).
% 2.13/2.39 tff(11488,plain,(r(s(s(elem!1)), s(s(s(elem!1)))) | (~r(z, s(z))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.39 tff(11489,plain,
% 2.13/2.39 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11488, 10949, 27])).
% 2.13/2.39 tff(11490,plain,
% 2.13/2.39 (~b(s(s(z)), s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[6843, 10975, 27, 1, 11489, 10951, 10949, 10986])).
% 2.13/2.39 tff(11491,plain,
% 2.13/2.39 (r(s(s(z)), s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[86, 11490])).
% 2.13/2.39 tff(11492,plain,
% 2.13/2.39 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[6248, 11491, 10973])).
% 2.13/2.39 tff(11493,plain,
% 2.13/2.39 ($false),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[4350, 21, 11492, 10984, 283])).
% 2.13/2.39 tff(11494,plain,((s(s(s(s(elem!1)))) = s(s(elem!1))) | (~r(z, s(z))) | (s(s(elem!1)) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.39 tff(11495,plain,
% 2.13/2.39 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11494, 1, 27])).
% 2.13/2.39 tff(11496,plain,
% 2.13/2.39 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[1073, 11495])).
% 2.13/2.39 tff(11497,plain,
% 2.13/2.39 (s(s(elem!1)) = elem!1),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[1089, 11496])).
% 2.13/2.39 tff(11498,plain,
% 2.13/2.39 (elem!1 = s(s(elem!1))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[377, 11497])).
% 2.13/2.39 tff(11499,plain,
% 2.13/2.39 (r(s(z), s(s(elem!1))) <=> r(s(z), elem!1)),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11497])).
% 2.13/2.39 tff(11500,plain,
% 2.13/2.39 (r(s(z), elem!1) <=> r(s(z), s(s(elem!1)))),
% 2.13/2.39 inference(symmetry,[status(thm)],[11499])).
% 2.13/2.39 tff(11501,plain,
% 2.13/2.39 ((s(s(elem!1)) = s(z)) <=> (elem!1 = s(z))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11497])).
% 2.13/2.39 tff(11502,plain,
% 2.13/2.39 ((s(s(elem!1)) = s(z)) <=> (s(z) = elem!1)),
% 2.13/2.39 inference(transitivity,[status(thm)],[11501, 253])).
% 2.13/2.39 tff(11503,plain,
% 2.13/2.39 ((~(s(s(elem!1)) = s(z))) <=> (~(s(z) = elem!1))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11502])).
% 2.13/2.39 tff(11504,plain,
% 2.13/2.39 (~(s(z) = elem!1)),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[111, 11503])).
% 2.13/2.39 tff(11505,plain,
% 2.13/2.39 ((s(s(elem!1)) = z) <=> (elem!1 = z)),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11497])).
% 2.13/2.39 tff(11506,plain,
% 2.13/2.39 ((s(s(elem!1)) = z) <=> (z = elem!1)),
% 2.13/2.39 inference(transitivity,[status(thm)],[11505, 247])).
% 2.13/2.39 tff(11507,plain,
% 2.13/2.39 ((~(s(s(elem!1)) = z)) <=> (~(z = elem!1))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11506])).
% 2.13/2.39 tff(11508,plain,
% 2.13/2.39 (~(z = elem!1)),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[154, 11507])).
% 2.13/2.39 tff(11509,plain,
% 2.13/2.39 ((s(s(elem!1)) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11497])).
% 2.13/2.39 tff(11510,plain,
% 2.13/2.39 ((s(s(elem!1)) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 2.13/2.39 inference(transitivity,[status(thm)],[11509, 225])).
% 2.13/2.39 tff(11511,plain,
% 2.13/2.39 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11510])).
% 2.13/2.39 tff(11512,plain,
% 2.13/2.39 (~(s(s(z)) = elem!1)),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[1, 11511])).
% 2.13/2.39 tff(11513,plain,
% 2.13/2.39 (~(s(s(s(s(z)))) = elem!1)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[242, 11497])).
% 2.13/2.39 tff(11514,plain,
% 2.13/2.39 (b(s(s(elem!1)), s(z)) <=> b(elem!1, s(z))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11497])).
% 2.13/2.39 tff(11515,plain,
% 2.13/2.39 (b(elem!1, s(z))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[10949, 11514])).
% 2.13/2.39 tff(11516,plain,
% 2.13/2.39 ((~b(s(z), elem!1)) | (s(s(s(s(z)))) = elem!1) | (~b(elem!1, s(z))) | (~r(z, s(z))) | (s(s(z)) = elem!1) | (z = elem!1)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11384, 7825])).
% 2.13/2.39 tff(11517,plain,
% 2.13/2.39 (~b(s(z), elem!1)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11516, 11515, 27, 11513, 11512, 11508])).
% 2.13/2.39 tff(11518,plain,
% 2.13/2.39 (r(s(z), elem!1)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[665, 11517, 11504])).
% 2.13/2.39 tff(11519,plain,
% 2.13/2.39 (r(s(z), s(s(elem!1)))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[11518, 11500])).
% 2.13/2.39 tff(11520,plain,
% 2.13/2.39 (~r(z, s(s(elem!1)))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[97, 11519, 27])).
% 2.13/2.39 tff(11521,plain,
% 2.13/2.39 (b(z, s(s(elem!1)))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[160, 11520])).
% 2.13/2.39 tff(11522,plain,
% 2.13/2.39 (b(z, elem!1)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[457, 11521, 11498])).
% 2.13/2.39 tff(11523,plain,
% 2.13/2.39 ((s(s(elem!1)) = z) <=> (elem!1 = z)),
% 2.13/2.39 inference(transitivity,[status(thm)],[11506, 459])).
% 2.13/2.39 tff(11524,plain,
% 2.13/2.39 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = z))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11523])).
% 2.13/2.39 tff(11525,plain,
% 2.13/2.39 (~(elem!1 = z)),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[154, 11524])).
% 2.13/2.39 tff(11526,plain,
% 2.13/2.39 (~b(elem!1, z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11396, 128, 11522, 11515, 7825])).
% 2.13/2.39 tff(11527,plain,
% 2.13/2.39 (r(elem!1, z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[574, 11526, 11525])).
% 2.13/2.39 tff(11528,plain,
% 2.13/2.39 (~b(s(s(z)), s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[7870, 11527, 11515, 11512, 11522])).
% 2.13/2.39 tff(11529,plain,
% 2.13/2.39 (r(s(s(z)), s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[86, 11528])).
% 2.13/2.39 tff(11530,plain,
% 2.13/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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)), elem!1)))),
% 2.13/2.39 inference(rewrite,[status(thm)],[])).
% 2.13/2.39 tff(11531,plain,
% 2.13/2.39 (((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))) <=> ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 2.13/2.39 inference(rewrite,[status(thm)],[])).
% 2.13/2.39 tff(11532,plain,
% 2.13/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(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(X0, 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)), elem!1))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11531])).
% 2.13/2.39 tff(11533,plain,
% 2.13/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(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(X0, 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)), elem!1)))),
% 2.13/2.39 inference(transitivity,[status(thm)],[11532, 11530])).
% 2.13/2.39 tff(11534,plain,
% 2.13/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 2.13/2.39 inference(quant_inst,[status(thm)],[])).
% 2.13/2.39 tff(11535,plain,
% 2.13/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[11534, 11533])).
% 2.13/2.39 tff(11536,plain,
% 2.13/2.39 (~b(s(s(z)), elem!1)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11535, 128, 11522, 11515, 7825, 10906])).
% 2.13/2.39 tff(11537,plain,
% 2.13/2.39 (r(s(s(z)), elem!1)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[370, 11536, 11512])).
% 2.13/2.39 tff(11538,plain,
% 2.13/2.39 ($false),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[10257, 45, 11518, 11537, 11529])).
% 2.13/2.39 tff(11539,plain,((s(s(elem!1)) = s(s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.13/2.39 tff(11540,plain,
% 2.13/2.39 (s(s(elem!1)) = s(s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11539, 27])).
% 2.13/2.39 tff(11541,plain,
% 2.13/2.39 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11540])).
% 2.13/2.39 tff(11542,plain,
% 2.13/2.39 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.13/2.39 inference(symmetry,[status(thm)],[11541])).
% 2.13/2.39 tff(11543,plain,
% 2.13/2.39 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11542])).
% 2.13/2.39 tff(11544,plain,
% 2.13/2.39 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), elem!1)),
% 2.13/2.39 inference(symmetry,[status(thm)],[11543])).
% 2.13/2.39 tff(11545,plain,
% 2.13/2.39 (z = elem!1),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[4260, 11540])).
% 2.13/2.39 tff(11546,plain,
% 2.13/2.39 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11545])).
% 2.13/2.39 tff(11547,plain,
% 2.13/2.39 ((s(s(s(elem!1))) = z) <=> (elem!1 = s(s(s(elem!1))))),
% 2.13/2.39 inference(transitivity,[status(thm)],[11546, 705])).
% 2.13/2.39 tff(11548,plain,
% 2.13/2.39 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 2.13/2.39 inference(transitivity,[status(thm)],[11547, 982])).
% 2.13/2.39 tff(11549,plain,
% 2.13/2.39 ((~(s(s(s(elem!1))) = z)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11548])).
% 2.13/2.39 tff(11550,plain,
% 2.13/2.39 (~(s(s(s(elem!1))) = elem!1)),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[382, 11549])).
% 2.13/2.39 tff(11551,plain,
% 2.13/2.39 (r(s(s(s(z))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11542])).
% 2.13/2.39 tff(11552,plain,
% 2.13/2.39 ((~r(s(s(s(z))), elem!1)) <=> (~r(s(s(s(elem!1))), elem!1))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11551])).
% 2.13/2.39 tff(11553,plain,
% 2.13/2.39 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(z))), s(z))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11541])).
% 2.13/2.39 tff(11554,plain,
% 2.13/2.39 (b(s(z), s(s(s(z)))) <=> b(s(z), s(s(s(elem!1))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11542])).
% 2.13/2.39 tff(11555,plain,
% 2.13/2.39 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(s(s(z))))),
% 2.13/2.39 inference(symmetry,[status(thm)],[11554])).
% 2.13/2.39 tff(11556,plain,
% 2.13/2.39 (s(s(z)) = s(s(elem!1))),
% 2.13/2.39 inference(symmetry,[status(thm)],[11540])).
% 2.13/2.39 tff(11557,plain,
% 2.13/2.39 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11556])).
% 2.13/2.39 tff(11558,plain,
% 2.13/2.39 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11557])).
% 2.13/2.39 tff(11559,plain,
% 2.13/2.39 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[239, 11558])).
% 2.13/2.39 tff(11560,plain,
% 2.13/2.39 (~b(s(s(elem!1)), s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[7826, 453, 11559])).
% 2.13/2.39 tff(11561,plain,
% 2.13/2.39 (r(s(s(elem!1)), s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[292, 11560])).
% 2.13/2.39 tff(11562,plain,
% 2.13/2.39 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11556])).
% 2.13/2.39 tff(11563,plain,
% 2.13/2.39 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 2.13/2.39 inference(transitivity,[status(thm)],[11562, 799])).
% 2.13/2.39 tff(11564,plain,
% 2.13/2.39 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11563])).
% 2.13/2.39 tff(11565,plain,
% 2.13/2.39 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[283, 11564])).
% 2.13/2.39 tff(11566,plain,
% 2.13/2.39 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11541])).
% 2.13/2.39 tff(11567,plain,
% 2.13/2.39 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11566])).
% 2.13/2.39 tff(11568,plain,
% 2.13/2.39 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z))))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11567])).
% 2.13/2.39 tff(11569,plain,
% 2.13/2.39 (s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(elem!1))))))),
% 2.13/2.39 inference(symmetry,[status(thm)],[11568])).
% 2.13/2.39 tff(11570,plain,
% 2.13/2.39 ((s(s(s(z))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1)))))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11542, 11569])).
% 2.13/2.39 tff(11571,plain,
% 2.13/2.39 ((s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(z))) = s(s(s(s(s(s(z)))))))),
% 2.13/2.39 inference(symmetry,[status(thm)],[11570])).
% 2.13/2.39 tff(11572,plain,
% 2.13/2.39 ((~(s(s(s(elem!1))) = s(s(s(s(s(s(elem!1)))))))) <=> (~(s(s(s(z))) = s(s(s(s(s(s(z))))))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11571])).
% 2.13/2.39 tff(11573,plain,
% 2.13/2.39 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11540])).
% 2.13/2.39 tff(11574,plain,
% 2.13/2.39 (s(elem!1) = s(z)),
% 2.13/2.39 inference(transitivity,[status(thm)],[106, 11573, 69])).
% 2.13/2.39 tff(11575,plain,
% 2.13/2.39 ((s(elem!1) = s(s(s(s(elem!1))))) <=> (s(z) = s(s(s(s(elem!1)))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11574])).
% 2.13/2.39 tff(11576,plain,
% 2.13/2.39 ((s(elem!1) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(z))),
% 2.13/2.39 inference(transitivity,[status(thm)],[11575, 2245])).
% 2.13/2.39 tff(11577,plain,
% 2.13/2.39 ((s(s(s(s(elem!1)))) = s(z)) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 2.13/2.39 inference(symmetry,[status(thm)],[11576])).
% 2.13/2.39 tff(11578,plain,
% 2.13/2.39 ((~(s(s(s(s(elem!1)))) = s(z))) <=> (~(s(elem!1) = s(s(s(s(elem!1))))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11577])).
% 2.13/2.39 tff(11579,plain,
% 2.13/2.39 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[1723, 11578])).
% 2.13/2.39 tff(11580,plain,
% 2.13/2.39 (~(s(s(s(elem!1))) = s(s(s(s(s(s(elem!1)))))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[3236, 11579])).
% 2.13/2.39 tff(11581,plain,
% 2.13/2.39 (~(s(s(s(z))) = s(s(s(s(s(s(z)))))))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[11580, 11572])).
% 2.13/2.39 tff(11582,plain,
% 2.13/2.39 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(z))), elem!1)),
% 2.13/2.39 inference(symmetry,[status(thm)],[11551])).
% 2.13/2.39 tff(11583,plain,
% 2.13/2.39 (b(s(s(elem!1)), elem!1) <=> b(s(s(z)), elem!1)),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11540])).
% 2.13/2.39 tff(11584,plain,
% 2.13/2.39 (b(s(s(z)), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 2.13/2.39 inference(symmetry,[status(thm)],[11583])).
% 2.13/2.39 tff(11585,plain,
% 2.13/2.39 (b(s(s(z)), z) <=> b(s(s(z)), elem!1)),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11545])).
% 2.13/2.39 tff(11586,plain,
% 2.13/2.39 (b(s(s(z)), z) <=> b(s(s(elem!1)), elem!1)),
% 2.13/2.39 inference(transitivity,[status(thm)],[11585, 11584])).
% 2.13/2.39 tff(11587,plain,
% 2.13/2.39 (b(s(s(elem!1)), elem!1)),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[10906, 11586])).
% 2.13/2.39 tff(11588,plain,
% 2.13/2.39 (b(s(s(elem!1)), z) <=> b(s(s(z)), z)),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11540])).
% 2.13/2.39 tff(11589,plain,
% 2.13/2.39 (b(s(s(z)), z) <=> b(s(s(elem!1)), z)),
% 2.13/2.39 inference(symmetry,[status(thm)],[11588])).
% 2.13/2.39 tff(11590,plain,
% 2.13/2.39 (b(s(s(elem!1)), z)),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[10906, 11589])).
% 2.13/2.39 tff(11591,plain,
% 2.13/2.39 (~b(s(s(s(elem!1))), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[5297, 2106, 11590, 11587, 453])).
% 2.13/2.39 tff(11592,plain,
% 2.13/2.39 (r(s(s(s(elem!1))), z)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[5301, 11591])).
% 2.13/2.39 tff(11593,plain,
% 2.13/2.39 (r(s(s(s(elem!1))), elem!1)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[2558, 11592, 11545])).
% 2.13/2.39 tff(11594,plain,
% 2.13/2.39 (r(s(s(s(z))), elem!1)),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[11593, 11582])).
% 2.13/2.39 tff(11595,plain,
% 2.13/2.39 ((s(s(elem!1)) = elem!1) <=> (s(s(z)) = elem!1)),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11540])).
% 2.13/2.39 tff(11596,plain,
% 2.13/2.39 ((s(s(z)) = elem!1) <=> (s(s(elem!1)) = elem!1)),
% 2.13/2.39 inference(symmetry,[status(thm)],[11595])).
% 2.13/2.39 tff(11597,plain,
% 2.13/2.39 ((s(s(z)) = z) <=> (s(s(z)) = elem!1)),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11545])).
% 2.13/2.39 tff(11598,plain,
% 2.13/2.39 ((s(s(z)) = z) <=> (s(s(elem!1)) = elem!1)),
% 2.13/2.39 inference(transitivity,[status(thm)],[11597, 11596])).
% 2.13/2.39 tff(11599,plain,
% 2.13/2.39 ((~(s(s(z)) = z)) <=> (~(s(s(elem!1)) = elem!1))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11598])).
% 2.13/2.39 tff(11600,plain,
% 2.13/2.39 (~(s(s(elem!1)) = elem!1)),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[11, 11599])).
% 2.13/2.39 tff(11601,plain,
% 2.13/2.39 (r(s(s(elem!1)), s(z)) <=> r(s(s(z)), s(z))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11540])).
% 2.13/2.39 tff(11602,plain,
% 2.13/2.39 (r(s(s(z)), s(z))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[11561, 11601])).
% 2.13/2.39 tff(11603,plain,
% 2.13/2.39 (~b(s(s(elem!1)), s(s(z)))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[10926, 2006, 2993, 325])).
% 2.13/2.39 tff(11604,plain,
% 2.13/2.39 (s(s(elem!1)) = s(s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[9437, 11603])).
% 2.13/2.39 tff(11605,plain,
% 2.13/2.39 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(z)))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11604])).
% 2.13/2.39 tff(11606,plain,
% 2.13/2.39 ((s(s(s(s(s(s(z)))))) = z) <=> (s(s(s(s(s(s(z)))))) = elem!1)),
% 2.13/2.39 inference(monotonicity,[status(thm)],[8041])).
% 2.13/2.39 tff(11607,plain,
% 2.13/2.39 ((~(s(s(s(s(s(s(z)))))) = z)) <=> (~(s(s(s(s(s(s(z)))))) = elem!1))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11606])).
% 2.13/2.39 tff(11608,plain,
% 2.13/2.39 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[1019, 11607])).
% 2.13/2.39 tff(11609,plain,
% 2.13/2.39 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[1055, 11608, 29])).
% 2.13/2.39 tff(11610,plain,
% 2.13/2.39 ((s(s(elem!1)) = elem!1) <=> (s(s(z)) = elem!1)),
% 2.13/2.39 inference(monotonicity,[status(thm)],[4252])).
% 2.13/2.39 tff(11611,plain,
% 2.13/2.39 ((s(s(elem!1)) = elem!1) <=> (elem!1 = s(s(z)))),
% 2.13/2.39 inference(transitivity,[status(thm)],[11610, 650])).
% 2.13/2.39 tff(11612,plain,
% 2.13/2.39 ((~(s(s(elem!1)) = elem!1)) <=> (~(elem!1 = s(s(z))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11611])).
% 2.13/2.39 tff(11613,plain,
% 2.13/2.39 (~(elem!1 = s(s(z)))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[1086, 11612])).
% 2.13/2.39 tff(11614,plain,
% 2.13/2.39 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(z)))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[4252])).
% 2.13/2.39 tff(11615,plain,
% 2.13/2.39 (r(s(z), s(s(z)))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[89, 11614])).
% 2.13/2.39 tff(11616,plain,
% 2.13/2.39 ((s(z) = z) <=> (s(z) = elem!1)),
% 2.13/2.39 inference(monotonicity,[status(thm)],[8041])).
% 2.13/2.39 tff(11617,plain,
% 2.13/2.39 ((s(z) = z) <=> (elem!1 = s(z))),
% 2.13/2.39 inference(transitivity,[status(thm)],[11616, 252])).
% 2.13/2.39 tff(11618,plain,
% 2.13/2.39 ((~(s(z) = z)) <=> (~(elem!1 = s(z)))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11617])).
% 2.13/2.39 tff(11619,plain,
% 2.13/2.39 (~(elem!1 = s(z))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[166, 11618])).
% 2.13/2.39 tff(11620,plain,
% 2.13/2.39 (b(s(s(z)), z) <=> b(s(s(z)), elem!1)),
% 2.13/2.39 inference(monotonicity,[status(thm)],[8041])).
% 2.13/2.39 tff(11621,plain,
% 2.13/2.39 (b(s(s(z)), elem!1)),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[2993, 11620])).
% 2.13/2.39 tff(11622,plain,
% 2.13/2.39 (~b(elem!1, s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[2976, 11609, 35, 8123, 11621])).
% 2.13/2.39 tff(11623,plain,
% 2.13/2.39 (r(elem!1, s(z))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[305, 11622, 11619])).
% 2.13/2.39 tff(11624,plain,
% 2.13/2.39 (~r(elem!1, s(s(z)))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[10187, 11623, 11615])).
% 2.13/2.39 tff(11625,plain,
% 2.13/2.39 (b(elem!1, s(s(z)))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[493, 11624, 11613])).
% 2.13/2.39 tff(11626,plain,
% 2.13/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.13/2.39 inference(rewrite,[status(thm)],[])).
% 2.13/2.39 tff(11627,plain,
% 2.13/2.39 (((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.13/2.39 inference(rewrite,[status(thm)],[])).
% 2.13/2.39 tff(11628,plain,
% 2.13/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1))))),
% 2.13/2.39 inference(monotonicity,[status(thm)],[11627])).
% 2.13/2.39 tff(11629,plain,
% 2.13/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)))),
% 2.13/2.39 inference(transitivity,[status(thm)],[11628, 11626])).
% 2.13/2.39 tff(11630,plain,
% 2.13/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.13/2.39 inference(quant_inst,[status(thm)],[])).
% 2.13/2.39 tff(11631,plain,
% 2.13/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1))),
% 2.13/2.39 inference(modus_ponens,[status(thm)],[11630, 11629])).
% 2.13/2.39 tff(11632,plain,
% 2.13/2.39 (~b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[11631, 128, 11621, 11625, 11609])).
% 2.13/2.39 tff(11633,plain,
% 2.13/2.39 (r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.13/2.39 inference(unit_resolution,[status(thm)],[1176, 21, 1123, 11632])).
% 2.13/2.39 tff(11634,plain,
% 2.13/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 2.13/2.39 inference(rewrite,[status(thm)],[])).
% 2.13/2.39 tff(11635,plain,
% 2.13/2.39 (((~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(z))))))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 2.13/2.40 inference(rewrite,[status(thm)],[])).
% 2.13/2.40 tff(11636,plain,
% 2.13/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(z))))))))))),
% 2.13/2.40 inference(monotonicity,[status(thm)],[11635])).
% 2.13/2.40 tff(11637,plain,
% 2.13/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 2.13/2.40 inference(transitivity,[status(thm)],[11636, 11634])).
% 2.13/2.40 tff(11638,plain,
% 2.13/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 2.13/2.40 inference(quant_inst,[status(thm)],[])).
% 2.13/2.40 tff(11639,plain,
% 2.13/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(z))))))))),
% 2.13/2.40 inference(modus_ponens,[status(thm)],[11638, 11637])).
% 2.13/2.40 tff(11640,plain,
% 2.13/2.40 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[11639, 128, 8123, 11621, 11625, 11609])).
% 2.13/2.40 tff(11641,plain,
% 2.13/2.40 (r(s(z), s(s(s(s(s(s(z)))))))),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[1041, 21, 1038, 11640])).
% 2.13/2.40 tff(11642,plain,
% 2.13/2.40 ($false),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[2974, 45, 35, 11641, 11633])).
% 2.13/2.40 tff(11643,plain,((~(s(s(elem!1)) = s(s(z)))) | (~r(s(s(z)), s(z))) | r(s(s(s(s(s(s(z)))))), elem!1) | (~b(s(s(z)), z)) | (~r(s(z), s(s(elem!1)))) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.13/2.40 tff(11644,plain,
% 2.13/2.40 (~r(s(z), s(s(elem!1)))),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[11643, 11604, 29, 2993, 35, 1086])).
% 2.13/2.40 tff(11645,plain,
% 2.13/2.40 (b(s(z), s(s(elem!1)))),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[117, 11644])).
% 2.13/2.40 tff(11646,plain,
% 2.13/2.40 (b(s(z), s(s(z)))),
% 2.13/2.40 inference(modus_ponens,[status(thm)],[11645, 11605])).
% 2.13/2.40 tff(11647,plain,
% 2.13/2.40 (z = elem!1),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[4260, 11604])).
% 2.13/2.40 tff(11648,plain,
% 2.13/2.40 (b(z, s(s(z))) <=> b(elem!1, s(s(z)))),
% 2.13/2.40 inference(monotonicity,[status(thm)],[11647])).
% 2.13/2.40 tff(11649,plain,
% 2.13/2.40 (~b(z, s(z))),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[2014, 11645, 2006, 453])).
% 2.13/2.40 tff(11650,plain,
% 2.13/2.40 (r(z, s(z))),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[415, 11649])).
% 2.13/2.40 tff(11651,plain,
% 2.13/2.40 (~r(z, s(s(z)))),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[2946, 11650, 35])).
% 2.13/2.40 tff(11652,plain,
% 2.13/2.40 (b(z, s(s(z)))),
% 2.13/2.40 inference(unit_resolution,[status(thm)],[516, 11651])).
% 2.13/2.40 tff(11653,plain,
% 2.13/2.40 (b(elem!1, s(s(z)))),
% 2.13/2.40 inference(modus_ponens,[status(thm)],[11652, 11648])).
% 2.13/2.40 tff(11654,plain,
% 2.13/2.40 (b(s(s(z)), z) <=> b(s(s(z)), elem!1)),
% 2.13/2.40 inference(monotonicity,[status(thm)],[11647])).
% 2.13/2.40 tff(11655,plain,
% 2.13/2.40 (b(s(s(z)), elem!1)),
% 2.13/2.40 inference(modus_ponens,[status(thm)],[2993, 11654])).
% 2.13/2.40 tff(11656,plain,
% 2.13/2.40 (b(s(z), z) <=> b(s(z), elem!1)),
% 2.13/2.40 inference(monotonicity,[status(thm)],[11647])).
% 2.13/2.40 tff(11657,plain,
% 2.23/2.40 (b(s(z), elem!1)),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[7825, 11656])).
% 2.23/2.40 tff(11658,plain,
% 2.23/2.40 ($false),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[660, 128, 11657, 11655, 11653, 11646])).
% 2.23/2.40 tff(11659,plain,((~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~r(s(s(z)), s(z))) | (~b(z, s(s(elem!1)))) | r(s(s(s(s(s(s(z)))))), elem!1) | (s(s(elem!1)) = elem!1) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.40 tff(11660,plain,
% 2.23/2.40 ((~b(s(s(elem!1)), z)) | (~r(s(s(z)), s(z))) | (~b(z, s(s(elem!1)))) | r(s(s(s(s(s(s(z)))))), elem!1) | (s(s(elem!1)) = elem!1) | (~r(s(s(elem!1)), s(z)))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[11659, 10906])).
% 2.23/2.40 tff(11661,plain,
% 2.23/2.40 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[11660, 11602, 11590, 453, 11600, 11561])).
% 2.23/2.40 tff(11662,plain,
% 2.23/2.40 ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[10622, 45, 11661])).
% 2.23/2.40 tff(11663,plain,
% 2.23/2.40 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[11662, 11594])).
% 2.23/2.40 tff(11664,plain,
% 2.23/2.40 ((s(s(s(z))) = s(s(s(s(s(s(z))))))) | b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[8149, 21, 11663])).
% 2.23/2.40 tff(11665,plain,
% 2.23/2.40 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[11664, 11581])).
% 2.23/2.40 tff(11666,plain,
% 2.23/2.40 ((s(s(s(s(s(s(z)))))) = s(s(s(z)))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[11569, 11542])).
% 2.23/2.40 tff(11667,plain,
% 2.23/2.40 ((s(s(s(s(s(s(z)))))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1)))))))),
% 2.23/2.40 inference(transitivity,[status(thm)],[11666, 3226])).
% 2.23/2.40 tff(11668,plain,
% 2.23/2.40 ((s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(z)))))) = s(s(s(z))))),
% 2.23/2.40 inference(symmetry,[status(thm)],[11667])).
% 2.23/2.40 tff(11669,plain,
% 2.23/2.40 ((~(s(s(s(elem!1))) = s(s(s(s(s(s(elem!1)))))))) <=> (~(s(s(s(s(s(s(z)))))) = s(s(s(z)))))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[11668])).
% 2.23/2.40 tff(11670,plain,
% 2.23/2.40 (~(s(s(s(s(s(s(z)))))) = s(s(s(z))))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[11580, 11669])).
% 2.23/2.40 tff(11671,plain,
% 2.23/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~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(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.23/2.40 inference(rewrite,[status(thm)],[])).
% 2.23/2.40 tff(11672,plain,
% 2.23/2.40 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.23/2.40 inference(rewrite,[status(thm)],[])).
% 2.23/2.40 tff(11673,plain,
% 2.23/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~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(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[11672])).
% 2.23/2.40 tff(11674,plain,
% 2.23/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~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(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.23/2.40 inference(transitivity,[status(thm)],[11673, 11671])).
% 2.23/2.40 tff(11675,plain,
% 2.23/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.23/2.40 inference(quant_inst,[status(thm)],[])).
% 2.23/2.40 tff(11676,plain,
% 2.23/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[11675, 11674])).
% 2.23/2.40 tff(11677,plain,
% 2.23/2.40 ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[11676, 45, 11661])).
% 2.23/2.40 tff(11678,plain,
% 2.23/2.40 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[11677, 11594])).
% 2.23/2.40 tff(11679,plain,
% 2.23/2.40 ((s(s(s(s(s(s(z)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[8090, 21, 11678])).
% 2.23/2.40 tff(11680,plain,
% 2.23/2.40 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[11679, 11670])).
% 2.23/2.40 tff(11681,plain,
% 2.23/2.40 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[11542])).
% 2.23/2.40 tff(11682,plain,
% 2.23/2.40 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(z))))),
% 2.23/2.40 inference(symmetry,[status(thm)],[11681])).
% 2.23/2.40 tff(11683,plain,
% 2.23/2.40 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[11540])).
% 2.23/2.40 tff(11684,plain,
% 2.23/2.40 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(z))))),
% 2.23/2.40 inference(transitivity,[status(thm)],[11683, 11682])).
% 2.23/2.40 tff(11685,plain,
% 2.23/2.40 (b(s(s(z)), s(s(s(z))))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[2106, 11684])).
% 2.23/2.40 tff(11686,plain,
% 2.23/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.23/2.40 inference(rewrite,[status(thm)],[])).
% 2.23/2.40 tff(11687,plain,
% 2.23/2.40 (((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))) <=> ((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.23/2.40 inference(rewrite,[status(thm)],[])).
% 2.23/2.40 tff(11688,plain,
% 2.23/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[11687])).
% 2.23/2.40 tff(11689,plain,
% 2.23/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.23/2.40 inference(transitivity,[status(thm)],[11688, 11686])).
% 2.23/2.40 tff(11690,plain,
% 2.23/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 2.23/2.40 inference(quant_inst,[status(thm)],[])).
% 2.23/2.40 tff(11691,plain,
% 2.23/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[11690, 11689])).
% 2.23/2.40 tff(11692,plain,
% 2.23/2.40 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[11691, 128, 11685, 11680, 11665])).
% 2.23/2.40 tff(11693,plain,
% 2.23/2.40 ((s(s(s(s(s(s(z)))))) = s(s(z))) | r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[1134, 21, 11692])).
% 2.23/2.40 tff(11694,plain,
% 2.23/2.40 (r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[11693, 1124])).
% 2.23/2.40 tff(11695,plain,
% 2.23/2.40 (b(z, s(s(z))) <=> b(elem!1, s(s(z)))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[11545])).
% 2.23/2.40 tff(11696,plain,
% 2.23/2.40 (b(z, s(s(elem!1))) <=> b(z, s(s(z)))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[11540])).
% 2.23/2.40 tff(11697,plain,
% 2.23/2.40 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(z)))),
% 2.23/2.40 inference(transitivity,[status(thm)],[11696, 11695])).
% 2.23/2.40 tff(11698,plain,
% 2.23/2.40 (b(elem!1, s(s(z)))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[453, 11697])).
% 2.23/2.40 tff(11699,plain,
% 2.23/2.40 (b(s(s(z)), elem!1)),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[10906, 11585])).
% 2.23/2.40 tff(11700,plain,
% 2.23/2.40 (b(s(z), z) <=> b(s(z), elem!1)),
% 2.23/2.40 inference(monotonicity,[status(thm)],[11545])).
% 2.23/2.40 tff(11701,plain,
% 2.23/2.40 (b(s(z), elem!1)),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[7825, 11700])).
% 2.23/2.40 tff(11702,plain,
% 2.23/2.40 (~b(s(z), s(s(z)))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[9745, 128, 11701, 11699, 11698])).
% 2.23/2.40 tff(11703,plain,
% 2.23/2.40 (r(s(z), s(s(z)))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[648, 11702])).
% 2.23/2.40 tff(11704,plain,
% 2.23/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(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(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 2.23/2.40 inference(rewrite,[status(thm)],[])).
% 2.23/2.40 tff(11705,plain,
% 2.23/2.40 (((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z))))))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 2.23/2.40 inference(rewrite,[status(thm)],[])).
% 2.23/2.40 tff(11706,plain,
% 2.23/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(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(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z))))))))))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[11705])).
% 2.23/2.40 tff(11707,plain,
% 2.23/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(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(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 2.23/2.40 inference(transitivity,[status(thm)],[11706, 11704])).
% 2.23/2.40 tff(11708,plain,
% 2.23/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 2.23/2.40 inference(quant_inst,[status(thm)],[])).
% 2.23/2.40 tff(11709,plain,
% 2.23/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z))))))))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[11708, 11707])).
% 2.23/2.40 tff(11710,plain,
% 2.23/2.40 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[11709, 45, 11703, 11694])).
% 2.23/2.40 tff(11711,plain,
% 2.23/2.40 (b(s(z), s(s(s(s(s(s(z)))))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[1041, 21, 1038, 11710])).
% 2.23/2.40 tff(11712,plain,
% 2.23/2.40 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[11542])).
% 2.23/2.40 tff(11713,plain,
% 2.23/2.40 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(z))), s(z))),
% 2.23/2.40 inference(symmetry,[status(thm)],[11712])).
% 2.23/2.40 tff(11714,plain,
% 2.23/2.40 (~r(s(s(s(elem!1))), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[8202, 2106, 27, 453])).
% 2.23/2.40 tff(11715,plain,
% 2.23/2.40 (b(s(s(s(elem!1))), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[196, 11714])).
% 2.23/2.40 tff(11716,plain,
% 2.23/2.40 (b(s(s(s(z))), s(z))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[11715, 11713])).
% 2.23/2.40 tff(11717,plain,
% 2.23/2.40 (r(z, s(z)) <=> r(elem!1, s(z))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[11545])).
% 2.23/2.40 tff(11718,plain,
% 2.23/2.40 (r(elem!1, s(z))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[27, 11717])).
% 2.23/2.40 tff(11719,plain,
% 2.23/2.40 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[7620, 11661, 11718])).
% 2.23/2.40 tff(11720,plain,
% 2.23/2.40 (b(s(s(s(s(s(s(z)))))), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[1148, 21, 11719, 8155])).
% 2.23/2.40 tff(11721,plain,
% 2.23/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.23/2.40 inference(rewrite,[status(thm)],[])).
% 2.23/2.40 tff(11722,plain,
% 2.23/2.40 (((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.23/2.40 inference(rewrite,[status(thm)],[])).
% 2.23/2.40 tff(11723,plain,
% 2.23/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[11722])).
% 2.23/2.40 tff(11724,plain,
% 2.23/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.23/2.40 inference(transitivity,[status(thm)],[11723, 11721])).
% 2.23/2.40 tff(11725,plain,
% 2.23/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))))),
% 2.23/2.40 inference(quant_inst,[status(thm)],[])).
% 2.23/2.40 tff(11726,plain,
% 2.23/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[11725, 11724])).
% 2.23/2.40 tff(11727,plain,
% 2.23/2.40 ($false),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[11726, 128, 11720, 11716, 11665, 11711])).
% 2.23/2.40 tff(11728,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.40 tff(11729,plain,
% 2.23/2.40 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[11728, 453, 27])).
% 2.23/2.40 tff(11730,plain,
% 2.23/2.40 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[321, 11729, 11565])).
% 2.23/2.40 tff(11731,plain,
% 2.23/2.40 (~r(s(z), s(s(s(elem!1))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[333, 11730, 11561])).
% 2.23/2.40 tff(11732,plain,
% 2.23/2.40 (b(s(z), s(s(s(elem!1))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[339, 11731])).
% 2.23/2.40 tff(11733,plain,
% 2.23/2.40 (b(s(z), s(s(s(z))))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[11732, 11555])).
% 2.23/2.40 tff(11734,plain,
% 2.23/2.40 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(z))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[11574])).
% 2.23/2.40 tff(11735,plain,
% 2.23/2.40 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 2.23/2.40 inference(symmetry,[status(thm)],[11734])).
% 2.23/2.40 tff(11736,plain,
% 2.23/2.40 (~r(s(s(s(elem!1))), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[393, 11730, 11561])).
% 2.23/2.40 tff(11737,plain,
% 2.23/2.40 (b(s(s(s(elem!1))), s(z))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[196, 11736])).
% 2.23/2.40 tff(11738,plain,
% 2.23/2.40 (b(s(s(s(elem!1))), s(elem!1))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[11737, 11735])).
% 2.23/2.40 tff(11739,plain,
% 2.23/2.40 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(z), s(s(s(elem!1))))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[11574])).
% 2.23/2.40 tff(11740,plain,
% 2.23/2.40 (b(s(z), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 2.23/2.40 inference(symmetry,[status(thm)],[11739])).
% 2.23/2.40 tff(11741,plain,
% 2.23/2.40 (b(s(elem!1), s(s(s(elem!1))))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[11732, 11740])).
% 2.23/2.40 tff(11742,plain,
% 2.23/2.40 (~b(s(s(s(s(elem!1)))), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[3805, 11741, 27, 11561, 453, 11730, 11738, 11545])).
% 2.23/2.40 tff(11743,plain,
% 2.23/2.40 (r(s(s(s(s(elem!1)))), z)),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[2081, 11742])).
% 2.23/2.40 tff(11744,plain,
% 2.23/2.40 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[693, 11565])).
% 2.23/2.40 tff(11745,plain,
% 2.23/2.40 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.23/2.40 inference(unit_resolution,[status(thm)],[700, 11744])).
% 2.23/2.40 tff(11746,plain,
% 2.23/2.40 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[11566])).
% 2.23/2.40 tff(11747,plain,
% 2.23/2.40 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.23/2.40 inference(symmetry,[status(thm)],[11746])).
% 2.23/2.40 tff(11748,plain,
% 2.23/2.40 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[11542])).
% 2.23/2.40 tff(11749,plain,
% 2.23/2.40 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.23/2.40 inference(transitivity,[status(thm)],[11748, 11747])).
% 2.23/2.40 tff(11750,plain,
% 2.23/2.40 ((~b(s(s(s(s(z)))), s(s(s(z))))) <=> (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 2.23/2.40 inference(monotonicity,[status(thm)],[11749])).
% 2.23/2.40 tff(11751,plain,
% 2.23/2.40 (b(s(s(s(z))), s(z))),
% 2.23/2.40 inference(modus_ponens,[status(thm)],[11737, 11713])).
% 2.23/2.41 tff(11752,plain,
% 2.23/2.41 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 2.23/2.41 inference(symmetry,[status(thm)],[11566])).
% 2.23/2.41 tff(11753,plain,
% 2.23/2.41 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[11752])).
% 2.23/2.41 tff(11754,plain,
% 2.23/2.41 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 2.23/2.41 inference(symmetry,[status(thm)],[11753])).
% 2.23/2.41 tff(11755,plain,
% 2.23/2.41 ((~r(s(s(s(s(elem!1)))), s(z))) <=> (~r(s(s(s(s(z)))), s(z)))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[11754])).
% 2.23/2.41 tff(11756,plain,
% 2.23/2.41 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[2176, 11561, 27, 11559])).
% 2.23/2.41 tff(11757,plain,
% 2.23/2.41 (~r(s(s(s(s(z)))), s(z))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[11756, 11755])).
% 2.23/2.41 tff(11758,plain,
% 2.23/2.41 (b(s(s(s(s(z)))), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[782, 21, 779, 11757])).
% 2.23/2.41 tff(11759,plain,
% 2.23/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 2.23/2.41 inference(rewrite,[status(thm)],[])).
% 2.23/2.41 tff(11760,plain,
% 2.23/2.41 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 2.23/2.41 inference(rewrite,[status(thm)],[])).
% 2.23/2.41 tff(11761,plain,
% 2.23/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[11760])).
% 2.23/2.41 tff(11762,plain,
% 2.23/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 2.23/2.41 inference(transitivity,[status(thm)],[11761, 11759])).
% 2.23/2.41 tff(11763,plain,
% 2.23/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.23/2.41 inference(quant_inst,[status(thm)],[])).
% 2.23/2.41 tff(11764,plain,
% 2.23/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[11763, 11762])).
% 2.23/2.41 tff(11765,plain,
% 2.23/2.41 ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[11764, 128, 11758, 11751])).
% 2.23/2.41 tff(11766,plain,
% 2.23/2.41 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[11765, 11733])).
% 2.23/2.41 tff(11767,plain,
% 2.23/2.41 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[11766, 11750])).
% 2.23/2.41 tff(11768,plain,
% 2.23/2.41 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[1820, 11767, 11745])).
% 2.23/2.41 tff(11769,plain,
% 2.23/2.41 (~r(s(s(s(elem!1))), z)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[1780, 11768, 11743])).
% 2.23/2.41 tff(11770,plain,
% 2.23/2.41 (~r(s(s(s(elem!1))), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[2453, 11769, 11545])).
% 2.23/2.41 tff(11771,plain,
% 2.23/2.41 (b(s(s(s(elem!1))), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[742, 11770, 11550])).
% 2.23/2.41 tff(11772,plain,
% 2.23/2.41 (b(s(s(s(z))), elem!1)),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[11771, 11544])).
% 2.23/2.41 tff(11773,plain,
% 2.23/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.23/2.41 inference(rewrite,[status(thm)],[])).
% 2.23/2.41 tff(11774,plain,
% 2.23/2.41 (((~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.23/2.41 inference(rewrite,[status(thm)],[])).
% 2.23/2.41 tff(11775,plain,
% 2.23/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[11774])).
% 2.23/2.41 tff(11776,plain,
% 2.23/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.23/2.41 inference(transitivity,[status(thm)],[11775, 11773])).
% 2.23/2.41 tff(11777,plain,
% 2.23/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 2.23/2.41 inference(quant_inst,[status(thm)],[])).
% 2.23/2.41 tff(11778,plain,
% 2.23/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[11777, 11776])).
% 2.23/2.41 tff(11779,plain,
% 2.23/2.41 ($false),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[11778, 128, 11701, 11699, 11698, 11772, 11733])).
% 2.23/2.41 tff(11780,plain,((~b(z, s(s(elem!1)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.41 tff(11781,plain,
% 2.23/2.41 (~b(z, s(s(elem!1)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[11780, 27])).
% 2.23/2.41 tff(11782,plain,
% 2.23/2.41 (r(z, s(s(elem!1)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[160, 11781])).
% 2.23/2.41 tff(11783,plain,
% 2.23/2.41 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 2.23/2.41 inference(transitivity,[status(thm)],[11563, 7930])).
% 2.23/2.41 tff(11784,plain,
% 2.23/2.41 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[11783])).
% 2.23/2.41 tff(11785,plain,
% 2.23/2.41 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[283, 11784])).
% 2.23/2.41 tff(11786,plain,
% 2.23/2.41 (~r(s(s(elem!1)), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[405, 11782, 27])).
% 2.23/2.41 tff(11787,plain,
% 2.23/2.41 (b(s(s(elem!1)), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[292, 11786])).
% 2.23/2.41 tff(11788,plain,
% 2.23/2.41 (~b(s(s(s(elem!1))), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[10971, 11787, 27, 11785, 11782])).
% 2.23/2.41 tff(11789,plain,
% 2.23/2.41 (r(s(s(s(elem!1))), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[196, 11788])).
% 2.23/2.41 tff(11790,plain,
% 2.23/2.41 (r(s(s(s(z))), s(z))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[11789, 11553])).
% 2.23/2.41 tff(11791,plain,
% 2.23/2.41 (r(z, s(s(z))) <=> r(elem!1, s(s(z)))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[11545])).
% 2.23/2.41 tff(11792,plain,
% 2.23/2.41 (r(z, s(s(elem!1))) <=> r(z, s(s(z)))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[11540])).
% 2.23/2.41 tff(11793,plain,
% 2.23/2.41 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(z)))),
% 2.23/2.41 inference(transitivity,[status(thm)],[11792, 11791])).
% 2.23/2.41 tff(11794,plain,
% 2.23/2.41 (r(elem!1, s(s(z)))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[11782, 11793])).
% 2.23/2.41 tff(11795,plain,
% 2.23/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))),
% 2.23/2.41 inference(rewrite,[status(thm)],[])).
% 2.23/2.41 tff(11796,plain,
% 2.23/2.41 (((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), elem!1))) <=> ((~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))),
% 2.23/2.41 inference(rewrite,[status(thm)],[])).
% 2.23/2.41 tff(11797,plain,
% 2.23/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, 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(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1))))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[11796])).
% 2.23/2.41 tff(11798,plain,
% 2.23/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, 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(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))),
% 2.23/2.41 inference(transitivity,[status(thm)],[11797, 11795])).
% 2.23/2.41 tff(11799,plain,
% 2.23/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), elem!1)))),
% 2.23/2.41 inference(quant_inst,[status(thm)],[])).
% 2.23/2.41 tff(11800,plain,
% 2.23/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[11799, 11798])).
% 2.23/2.41 tff(11801,plain,
% 2.23/2.41 (~r(s(s(s(z))), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[11800, 45, 11718, 11794, 11790])).
% 2.23/2.41 tff(11802,plain,
% 2.23/2.41 (~r(s(s(s(elem!1))), elem!1)),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[11801, 11552])).
% 2.23/2.41 tff(11803,plain,
% 2.23/2.41 (b(s(s(s(elem!1))), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[742, 11802, 11550])).
% 2.23/2.41 tff(11804,plain,
% 2.23/2.41 (b(s(s(s(z))), elem!1)),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[11803, 11544])).
% 2.23/2.41 tff(11805,plain,
% 2.23/2.41 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[11542])).
% 2.23/2.41 tff(11806,plain,
% 2.23/2.41 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(z))))),
% 2.23/2.41 inference(symmetry,[status(thm)],[11805])).
% 2.23/2.41 tff(11807,plain,
% 2.23/2.41 ((~(s(s(s(elem!1))) = z)) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[11547])).
% 2.23/2.41 tff(11808,plain,
% 2.23/2.41 (~(elem!1 = s(s(s(elem!1))))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[382, 11807])).
% 2.23/2.41 tff(11809,plain,
% 2.23/2.41 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(s(elem!1))))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[11542])).
% 2.23/2.41 tff(11810,plain,
% 2.23/2.41 ((~r(elem!1, s(s(s(z))))) <=> (~r(elem!1, s(s(s(elem!1)))))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[11809])).
% 2.23/2.41 tff(11811,plain,
% 2.23/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(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(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))))),
% 2.23/2.41 inference(rewrite,[status(thm)],[])).
% 2.23/2.41 tff(11812,plain,
% 2.23/2.41 (((~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(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))))),
% 2.23/2.41 inference(rewrite,[status(thm)],[])).
% 2.23/2.41 tff(11813,plain,
% 2.23/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(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(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z)))))))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[11812])).
% 2.23/2.41 tff(11814,plain,
% 2.23/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(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(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))))),
% 2.23/2.41 inference(transitivity,[status(thm)],[11813, 11811])).
% 2.23/2.41 tff(11815,plain,
% 2.23/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))))),
% 2.23/2.41 inference(quant_inst,[status(thm)],[])).
% 2.23/2.41 tff(11816,plain,
% 2.23/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z)))))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[11815, 11814])).
% 2.23/2.41 tff(11817,plain,
% 2.23/2.41 (~r(elem!1, s(s(s(z))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[11816, 45, 11718, 11790])).
% 2.23/2.41 tff(11818,plain,
% 2.23/2.41 (~r(elem!1, s(s(s(elem!1))))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[11817, 11810])).
% 2.23/2.41 tff(11819,plain,
% 2.23/2.41 (b(elem!1, s(s(s(elem!1))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[2466, 11818, 11808])).
% 2.23/2.41 tff(11820,plain,
% 2.23/2.41 (b(elem!1, s(s(s(z))))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[11819, 11806])).
% 2.23/2.41 tff(11821,plain,
% 2.23/2.41 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(z)))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[11540])).
% 2.23/2.41 tff(11822,plain,
% 2.23/2.41 (~r(s(z), s(s(elem!1)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[97, 11782, 27])).
% 2.23/2.41 tff(11823,plain,
% 2.23/2.41 (b(s(z), s(s(elem!1)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[117, 11822])).
% 2.23/2.41 tff(11824,plain,
% 2.23/2.41 (b(s(z), s(s(z)))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[11823, 11821])).
% 2.23/2.41 tff(11825,plain,
% 2.23/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 2.23/2.41 inference(rewrite,[status(thm)],[])).
% 2.23/2.41 tff(11826,plain,
% 2.23/2.41 (((~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 2.23/2.41 inference(rewrite,[status(thm)],[])).
% 2.23/2.41 tff(11827,plain,
% 2.23/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[11826])).
% 2.23/2.41 tff(11828,plain,
% 2.23/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 2.23/2.41 inference(transitivity,[status(thm)],[11827, 11825])).
% 2.23/2.41 tff(11829,plain,
% 2.23/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))))),
% 2.23/2.41 inference(quant_inst,[status(thm)],[])).
% 2.23/2.41 tff(11830,plain,
% 2.23/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[11829, 11828])).
% 2.23/2.41 tff(11831,plain,
% 2.23/2.41 ($false),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[11830, 128, 11701, 11699, 11824, 11820, 11804])).
% 2.23/2.41 tff(11832,plain,(~r(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.41 tff(11833,plain,
% 2.23/2.41 (b(z, s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[415, 11832])).
% 2.23/2.41 tff(11834,plain,
% 2.23/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(X0, 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)))))),
% 2.23/2.41 inference(rewrite,[status(thm)],[])).
% 2.23/2.41 tff(11835,plain,
% 2.23/2.41 (((~b(s(z), z)) | (~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)))))),
% 2.23/2.41 inference(rewrite,[status(thm)],[])).
% 2.23/2.41 tff(11836,plain,
% 2.23/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~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(X0, 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))))))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[11835])).
% 2.23/2.41 tff(11837,plain,
% 2.23/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~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(X0, 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)))))),
% 2.23/2.41 inference(transitivity,[status(thm)],[11836, 11834])).
% 2.23/2.41 tff(11838,plain,
% 2.23/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))),
% 2.23/2.41 inference(quant_inst,[status(thm)],[])).
% 2.23/2.41 tff(11839,plain,
% 2.23/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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))))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[11838, 11837])).
% 2.23/2.41 tff(11840,plain,
% 2.23/2.41 (~b(s(z), s(s(z)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[11839, 128, 11833, 7825, 10906])).
% 2.23/2.41 tff(11841,plain,
% 2.23/2.41 (r(s(z), s(s(z)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[648, 11840])).
% 2.23/2.41 tff(11842,plain,
% 2.23/2.41 (((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 2.23/2.41 inference(rewrite,[status(thm)],[])).
% 2.23/2.41 tff(11843,plain,
% 2.23/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(z))) | (~b(s(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(X0, 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(s(z)), s(z)))))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[11842])).
% 2.23/2.41 tff(11844,plain,
% 2.23/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(z))) | (~b(s(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(X0, 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(s(z)), s(z))))),
% 2.23/2.41 inference(transitivity,[status(thm)],[11843, 9186])).
% 2.23/2.41 tff(11845,plain,
% 2.23/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 2.23/2.41 inference(quant_inst,[status(thm)],[])).
% 2.23/2.41 tff(11846,plain,
% 2.23/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)), s(z)))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[11845, 11844])).
% 2.23/2.41 tff(11847,plain,
% 2.23/2.41 (~b(s(s(z)), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[11846, 128, 11833, 7825, 10906])).
% 2.23/2.41 tff(11848,plain,
% 2.23/2.41 (r(s(s(z)), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[86, 11847])).
% 2.23/2.41 tff(11849,plain,
% 2.23/2.41 (~r(s(s(z)), s(s(elem!1)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[4431, 45, 325, 11848])).
% 2.23/2.41 tff(11850,plain,
% 2.23/2.41 ((s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[138, 21, 11849])).
% 2.23/2.41 tff(11851,plain,
% 2.23/2.41 (b(s(s(z)), s(s(elem!1)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[11850, 34])).
% 2.23/2.41 tff(11852,plain,
% 2.23/2.41 (~r(s(s(elem!1)), s(s(z)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[5461, 45, 325, 11848])).
% 2.23/2.41 tff(11853,plain,
% 2.23/2.41 (b(s(s(elem!1)), s(s(z)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[4339, 21, 1, 11852])).
% 2.23/2.41 tff(11854,plain,
% 2.23/2.41 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[6248, 385, 11848])).
% 2.23/2.41 tff(11855,plain,
% 2.23/2.41 (b(s(s(s(elem!1))), s(s(z)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[4350, 21, 11854, 283])).
% 2.23/2.41 tff(11856,plain,
% 2.23/2.41 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[9294, 325, 11833])).
% 2.23/2.41 tff(11857,plain,
% 2.23/2.41 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[803, 11856])).
% 2.23/2.41 tff(11858,plain,
% 2.23/2.41 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[889, 7276, 11857])).
% 2.23/2.41 tff(11859,plain,
% 2.23/2.41 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[393, 385, 325])).
% 2.23/2.41 tff(11860,plain,
% 2.23/2.41 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[321, 11859, 11856])).
% 2.23/2.41 tff(11861,plain,
% 2.23/2.41 ($false),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[9605, 128, 11860, 11858, 11855, 8523])).
% 2.23/2.41 tff(11862,plain,((~r(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.41 tff(11863,plain,
% 2.23/2.41 (~r(s(s(s(elem!1))), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[11862, 8523, 325])).
% 2.23/2.41 tff(11864,plain,
% 2.23/2.41 (b(s(s(s(elem!1))), s(z))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[196, 11863])).
% 2.23/2.41 tff(11865,plain,
% 2.23/2.41 (~b(z, s(s(s(elem!1))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[8605, 128, 11833, 7825, 11864])).
% 2.23/2.41 tff(11866,plain,
% 2.23/2.41 (r(z, s(s(s(elem!1))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[858, 11865])).
% 2.23/2.41 tff(11867,plain,
% 2.23/2.41 (~r(s(z), s(s(s(elem!1))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[10399, 1187, 11866])).
% 2.23/2.41 tff(11868,plain,
% 2.23/2.41 (b(s(z), s(s(s(elem!1))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[339, 11867])).
% 2.23/2.41 tff(11869,plain,
% 2.23/2.41 (r(s(s(s(s(elem!1)))), z) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 2.23/2.41 inference(monotonicity,[status(thm)],[8041])).
% 2.23/2.41 tff(11870,plain,
% 2.23/2.41 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(elem!1)))), z)),
% 2.23/2.41 inference(symmetry,[status(thm)],[11869])).
% 2.23/2.41 tff(11871,plain,
% 2.23/2.41 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 2.23/2.41 inference(monotonicity,[status(thm)],[7886])).
% 2.23/2.41 tff(11872,plain,
% 2.23/2.41 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 2.23/2.41 inference(symmetry,[status(thm)],[11871])).
% 2.23/2.41 tff(11873,plain,
% 2.23/2.41 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(elem!1)))), z)),
% 2.23/2.41 inference(transitivity,[status(thm)],[11872, 11870])).
% 2.23/2.41 tff(11874,plain,
% 2.23/2.41 (~b(s(s(s(s(z)))), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[2819, 10711, 8123, 11621])).
% 2.23/2.41 tff(11875,plain,
% 2.23/2.41 (r(s(s(s(s(z)))), elem!1)),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[632, 11874, 10732])).
% 2.23/2.41 tff(11876,plain,
% 2.23/2.41 (r(s(s(s(s(elem!1)))), z)),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[11875, 11873])).
% 2.23/2.41 tff(11877,plain,
% 2.23/2.41 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[1780, 11876, 520])).
% 2.23/2.41 tff(11878,plain,
% 2.23/2.41 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[1820, 11877, 1685])).
% 2.23/2.41 tff(11879,plain,
% 2.23/2.41 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[11878, 10709])).
% 2.23/2.41 tff(11880,plain,
% 2.23/2.41 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.23/2.41 inference(modus_ponens,[status(thm)],[11879, 10708])).
% 2.23/2.41 tff(11881,plain,
% 2.23/2.41 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[2986, 45, 11875, 1094])).
% 2.23/2.41 tff(11882,plain,
% 2.23/2.41 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[1215, 21, 1212, 11881])).
% 2.23/2.41 tff(11883,plain,
% 2.23/2.41 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(monotonicity,[status(thm)],[7885, 10733])).
% 2.23/2.41 tff(11884,plain,
% 2.23/2.41 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 2.23/2.41 inference(symmetry,[status(thm)],[11883])).
% 2.23/2.41 tff(11885,plain,
% 2.23/2.41 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[1874, 11876, 520])).
% 2.23/2.41 tff(11886,plain,
% 2.23/2.41 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.23/2.41 inference(unit_resolution,[status(thm)],[1856, 11885, 698])).
% 2.23/2.42 tff(11887,plain,
% 2.23/2.42 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[11886, 11884])).
% 2.23/2.42 tff(11888,plain,
% 2.23/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(11889,plain,
% 2.23/2.42 (((~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(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(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(s(z)))))), s(s(s(z))))))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(11890,plain,
% 2.23/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 2.23/2.42 inference(monotonicity,[status(thm)],[11889])).
% 2.23/2.42 tff(11891,plain,
% 2.23/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.23/2.42 inference(transitivity,[status(thm)],[11890, 11888])).
% 2.23/2.42 tff(11892,plain,
% 2.23/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(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(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 2.23/2.42 inference(quant_inst,[status(thm)],[])).
% 2.23/2.42 tff(11893,plain,
% 2.23/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[11892, 11891])).
% 2.23/2.42 tff(11894,plain,
% 2.23/2.42 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[11893, 128, 11887, 11882, 11880])).
% 2.23/2.42 tff(11895,plain,
% 2.23/2.42 (r(s(s(s(elem!1))), elem!1)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[2558, 8041, 520])).
% 2.23/2.42 tff(11896,plain,
% 2.23/2.42 (r(s(s(s(z))), elem!1)),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[11895, 10779])).
% 2.23/2.42 tff(11897,plain,
% 2.23/2.42 ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[11676, 45, 1094])).
% 2.23/2.42 tff(11898,plain,
% 2.23/2.42 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[11897, 11896])).
% 2.23/2.42 tff(11899,plain,
% 2.23/2.42 ((s(s(s(s(s(s(z)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[8090, 21, 11898])).
% 2.23/2.42 tff(11900,plain,
% 2.23/2.42 ($false),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[11899, 11894, 7900])).
% 2.23/2.42 tff(11901,plain,((~(s(s(elem!1)) = s(s(z)))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.42 tff(11902,plain,
% 2.23/2.42 (~(s(s(elem!1)) = s(s(z)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[11901, 9578, 1094, 1680, 2993, 550])).
% 2.23/2.42 tff(11903,plain,
% 2.23/2.42 (~(s(s(z)) = s(s(elem!1)))),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[11902, 33])).
% 2.23/2.42 tff(11904,plain,
% 2.23/2.42 ((s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[138, 21, 8650])).
% 2.23/2.42 tff(11905,plain,
% 2.23/2.42 (b(s(s(z)), s(s(elem!1)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[11904, 11903])).
% 2.23/2.42 tff(11906,plain,
% 2.23/2.42 ((s(s(elem!1)) = s(s(z))) | b(s(s(elem!1)), s(s(z)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[4339, 21, 8644])).
% 2.23/2.42 tff(11907,plain,
% 2.23/2.42 (b(s(s(elem!1)), s(s(z)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[11906, 11902])).
% 2.23/2.42 tff(11908,plain,
% 2.23/2.42 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[8789, 550, 2718, 2392])).
% 2.23/2.42 tff(11909,plain,
% 2.23/2.42 (r(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[1828, 11908])).
% 2.23/2.42 tff(11910,plain,
% 2.23/2.42 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[2141, 11909, 325])).
% 2.23/2.42 tff(11911,plain,
% 2.23/2.42 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[1897, 11910, 1063])).
% 2.23/2.42 tff(11912,plain,
% 2.23/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(elem!1)), 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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(11913,plain,
% 2.23/2.42 (((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(11914,plain,
% 2.23/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))))),
% 2.23/2.42 inference(monotonicity,[status(thm)],[11913])).
% 2.23/2.42 tff(11915,plain,
% 2.23/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.23/2.42 inference(transitivity,[status(thm)],[11914, 11912])).
% 2.23/2.42 tff(11916,plain,
% 2.23/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.23/2.42 inference(quant_inst,[status(thm)],[])).
% 2.23/2.42 tff(11917,plain,
% 2.23/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[11916, 11915])).
% 2.23/2.42 tff(11918,plain,
% 2.23/2.42 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[11917, 128, 11911, 11907, 11905])).
% 2.23/2.42 tff(11919,plain,
% 2.23/2.42 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[4309, 21, 239, 11918])).
% 2.23/2.42 tff(11920,plain,
% 2.23/2.42 (~b(s(z), s(s(z)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[11839, 128, 550, 7825, 2993])).
% 2.23/2.42 tff(11921,plain,
% 2.23/2.42 (r(s(z), s(s(z)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[648, 11920])).
% 2.23/2.42 tff(11922,plain,
% 2.23/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(11923,plain,
% 2.23/2.42 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(z)))) <=> ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(11924,plain,
% 2.23/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z))))))),
% 2.23/2.42 inference(monotonicity,[status(thm)],[11923])).
% 2.23/2.42 tff(11925,plain,
% 2.23/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.23/2.42 inference(transitivity,[status(thm)],[11924, 11922])).
% 2.23/2.42 tff(11926,plain,
% 2.23/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 2.23/2.42 inference(quant_inst,[status(thm)],[])).
% 2.23/2.42 tff(11927,plain,
% 2.23/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z))))),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[11926, 11925])).
% 2.23/2.42 tff(11928,plain,
% 2.23/2.42 ($false),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[11927, 45, 11909, 11921, 11919])).
% 2.23/2.42 tff(11929,plain,((~b(z, s(z))) | r(s(s(z)), s(s(elem!1))) | r(s(s(elem!1)), s(s(z))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(z))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.42 tff(11930,plain,
% 2.23/2.42 ((~b(z, s(z))) | r(s(s(z)), s(s(elem!1))) | r(s(s(elem!1)), s(s(z))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~r(s(s(elem!1)), s(z)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[11929, 10906])).
% 2.23/2.42 tff(11931,plain,
% 2.23/2.42 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[11930, 1063, 11833, 325, 11852, 2718, 11849])).
% 2.23/2.42 tff(11932,plain,
% 2.23/2.42 (~r(s(s(z)), z)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[9567, 35, 325, 1646, 2718])).
% 2.23/2.42 tff(11933,plain,
% 2.23/2.42 (b(s(s(z)), z)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[25, 11932])).
% 2.23/2.42 tff(11934,plain,
% 2.23/2.42 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[321, 7908, 2648])).
% 2.23/2.42 tff(11935,plain,
% 2.23/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(11936,plain,
% 2.23/2.42 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(11937,plain,
% 2.23/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))))),
% 2.23/2.42 inference(monotonicity,[status(thm)],[11936])).
% 2.23/2.42 tff(11938,plain,
% 2.23/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.23/2.42 inference(transitivity,[status(thm)],[11937, 11935])).
% 2.23/2.42 tff(11939,plain,
% 2.23/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))))),
% 2.23/2.42 inference(quant_inst,[status(thm)],[])).
% 2.23/2.42 tff(11940,plain,
% 2.23/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[11939, 11938])).
% 2.23/2.42 tff(11941,plain,
% 2.23/2.42 (~b(s(z), s(s(elem!1)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[11940, 128, 7825, 11934, 549, 2718])).
% 2.23/2.42 tff(11942,plain,
% 2.23/2.42 (r(s(z), s(s(elem!1)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[117, 11941])).
% 2.23/2.42 tff(11943,plain,
% 2.23/2.42 (~(s(s(elem!1)) = s(s(z)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[11643, 11942, 29, 11933, 35, 1086])).
% 2.23/2.42 tff(11944,plain,
% 2.23/2.42 (~(s(s(z)) = s(s(elem!1)))),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[11943, 33])).
% 2.23/2.42 tff(11945,plain,
% 2.23/2.42 (b(s(s(z)), s(s(elem!1)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[9416, 11944])).
% 2.23/2.42 tff(11946,plain,
% 2.23/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(11947,plain,
% 2.23/2.42 (((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1))))) <=> ((~b(s(z), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(11948,plain,
% 2.23/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1))))))),
% 2.23/2.42 inference(monotonicity,[status(thm)],[11947])).
% 2.23/2.42 tff(11949,plain,
% 2.23/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.23/2.42 inference(transitivity,[status(thm)],[11948, 11946])).
% 2.23/2.42 tff(11950,plain,
% 2.23/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.23/2.42 inference(quant_inst,[status(thm)],[])).
% 2.23/2.42 tff(11951,plain,
% 2.23/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1))))),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[11950, 11949])).
% 2.23/2.42 tff(11952,plain,
% 2.23/2.42 ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[11951, 128, 7825, 11934, 2718, 11933])).
% 2.23/2.42 tff(11953,plain,
% 2.23/2.42 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[11952, 11945])).
% 2.23/2.42 tff(11954,plain,
% 2.23/2.42 ((s(s(z)) = s(s(s(elem!1)))) | r(s(s(z)), s(s(s(elem!1))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[4283, 21, 11953])).
% 2.23/2.42 tff(11955,plain,
% 2.23/2.42 (r(s(s(z)), s(s(s(elem!1))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[11954, 4271])).
% 2.23/2.42 tff(11956,plain,
% 2.23/2.42 (b(s(s(elem!1)), s(s(z)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[9437, 11943])).
% 2.23/2.42 tff(11957,plain,
% 2.23/2.42 (~b(s(s(elem!1)), z)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[10926, 11956, 11933, 325])).
% 2.23/2.42 tff(11958,plain,
% 2.23/2.42 (r(s(s(elem!1)), z)),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[7835, 11957])).
% 2.23/2.42 tff(11959,plain,
% 2.23/2.42 (~r(z, s(z))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[8196, 11958, 325])).
% 2.23/2.42 tff(11960,plain,
% 2.23/2.42 (b(z, s(z))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[415, 11959])).
% 2.23/2.42 tff(11961,plain,
% 2.23/2.42 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[10774, 11960, 1646, 549, 7908])).
% 2.23/2.42 tff(11962,plain,
% 2.23/2.42 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[1820, 11961, 2650])).
% 2.23/2.42 tff(11963,plain,
% 2.23/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(11964,plain,
% 2.23/2.42 (((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.23/2.42 inference(rewrite,[status(thm)],[])).
% 2.23/2.42 tff(11965,plain,
% 2.23/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))))),
% 2.23/2.42 inference(monotonicity,[status(thm)],[11964])).
% 2.23/2.42 tff(11966,plain,
% 2.23/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.23/2.42 inference(transitivity,[status(thm)],[11965, 11963])).
% 2.23/2.42 tff(11967,plain,
% 2.23/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.23/2.42 inference(quant_inst,[status(thm)],[])).
% 2.23/2.42 tff(11968,plain,
% 2.23/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))),
% 2.23/2.42 inference(modus_ponens,[status(thm)],[11967, 11966])).
% 2.23/2.42 tff(11969,plain,
% 2.23/2.42 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[11968, 45, 11962, 35, 11955])).
% 2.23/2.42 tff(11970,plain,
% 2.23/2.42 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[4309, 21, 239, 11969])).
% 2.23/2.42 tff(11971,plain,
% 2.23/2.42 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[8789, 11960, 2718, 2650])).
% 2.23/2.42 tff(11972,plain,
% 2.23/2.42 (r(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[1828, 11971])).
% 2.23/2.42 tff(11973,plain,
% 2.23/2.42 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[2141, 11972, 325])).
% 2.23/2.42 tff(11974,plain,
% 2.23/2.42 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.23/2.42 inference(unit_resolution,[status(thm)],[1897, 11973, 1664])).
% 2.23/2.43 tff(11975,plain,
% 2.23/2.43 ($false),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[11917, 128, 11974, 11956, 11945, 11970])).
% 2.23/2.43 tff(11976,plain,(r(s(s(elem!1)), s(s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | r(s(s(s(s(s(s(z)))))), elem!1) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.23/2.43 tff(11977,plain,
% 2.23/2.43 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[11976, 29, 325, 549, 2718, 35, 1086])).
% 2.23/2.43 tff(11978,plain,
% 2.23/2.43 (~r(z, s(s(elem!1)))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[438, 11977, 325])).
% 2.23/2.43 tff(11979,plain,
% 2.23/2.43 (b(z, s(s(elem!1)))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[160, 11978])).
% 2.23/2.43 tff(11980,plain,
% 2.23/2.43 (~b(s(s(elem!1)), z)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[11659, 11979, 35, 11933, 29, 1086, 325])).
% 2.23/2.43 tff(11981,plain,
% 2.23/2.43 (r(s(s(elem!1)), z)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[7835, 11980])).
% 2.23/2.43 tff(11982,plain,
% 2.23/2.43 (~r(z, s(z))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[8196, 11981, 325])).
% 2.23/2.43 tff(11983,plain,
% 2.23/2.43 (b(z, s(z))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[415, 11982])).
% 2.23/2.43 tff(11984,plain,
% 2.23/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))))),
% 2.23/2.43 inference(rewrite,[status(thm)],[])).
% 2.23/2.43 tff(11985,plain,
% 2.23/2.43 (((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))))),
% 2.23/2.43 inference(rewrite,[status(thm)],[])).
% 2.23/2.43 tff(11986,plain,
% 2.23/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1)))))))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[11985])).
% 2.23/2.43 tff(11987,plain,
% 2.23/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))))),
% 2.23/2.43 inference(transitivity,[status(thm)],[11986, 11984])).
% 2.23/2.43 tff(11988,plain,
% 2.23/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))),
% 2.23/2.43 inference(quant_inst,[status(thm)],[])).
% 2.23/2.43 tff(11989,plain,
% 2.23/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1)))))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[11988, 11987])).
% 2.23/2.43 tff(11990,plain,
% 2.23/2.43 ((~b(z, s(z))) | (~b(z, s(s(s(elem!1)))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[11989, 128, 11979, 7825, 2718])).
% 2.23/2.43 tff(11991,plain,
% 2.23/2.43 (~b(z, s(s(s(elem!1))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[11990, 11983])).
% 2.23/2.43 tff(11992,plain,
% 2.23/2.43 (r(z, s(s(s(elem!1))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[858, 11991])).
% 2.23/2.43 tff(11993,plain,
% 2.23/2.43 ($false),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[4572, 45, 11977, 11992, 11981])).
% 2.23/2.43 tff(11994,plain,(r(s(s(s(s(s(s(z)))))), elem!1) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (s(s(elem!1)) = elem!1) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.43 tff(11995,plain,
% 2.23/2.43 ($false),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[11994, 11931, 2510, 11848, 325, 2718, 549])).
% 2.23/2.43 tff(11996,plain,((s(s(s(s(elem!1)))) = s(s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.43 tff(11997,plain,
% 2.23/2.43 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[11996, 11868, 11864, 325])).
% 2.23/2.43 tff(11998,plain,
% 2.23/2.43 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[1073, 11997])).
% 2.23/2.43 tff(11999,plain,
% 2.23/2.43 (s(s(elem!1)) = elem!1),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[1089, 11998])).
% 2.23/2.43 tff(12000,plain,
% 2.23/2.43 (elem!1 = s(s(elem!1))),
% 2.23/2.43 inference(symmetry,[status(thm)],[11999])).
% 2.23/2.43 tff(12001,plain,
% 2.23/2.43 (r(elem!1, s(z)) <=> r(s(s(elem!1)), s(z))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[12000])).
% 2.23/2.43 tff(12002,plain,
% 2.23/2.43 (r(s(s(elem!1)), s(z)) <=> r(elem!1, s(z))),
% 2.23/2.43 inference(symmetry,[status(thm)],[12001])).
% 2.23/2.43 tff(12003,plain,
% 2.23/2.43 (r(elem!1, s(z))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[325, 12002])).
% 2.23/2.43 tff(12004,plain,
% 2.23/2.43 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[245, 11999])).
% 2.23/2.43 tff(12005,plain,
% 2.23/2.43 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(elem!1)))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[11997])).
% 2.23/2.43 tff(12006,plain,
% 2.23/2.43 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 2.23/2.43 inference(symmetry,[status(thm)],[12005])).
% 2.23/2.43 tff(12007,plain,
% 2.23/2.43 (s(elem!1) = s(s(s(elem!1)))),
% 2.23/2.43 inference(transitivity,[status(thm)],[106, 12006, 233])).
% 2.23/2.43 tff(12008,plain,
% 2.23/2.43 ((s(elem!1) = s(s(z))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[12007])).
% 2.23/2.43 tff(12009,plain,
% 2.23/2.43 ((s(s(s(elem!1))) = s(s(z))) <=> (s(elem!1) = s(s(z)))),
% 2.23/2.43 inference(symmetry,[status(thm)],[12008])).
% 2.23/2.43 tff(12010,plain,
% 2.23/2.43 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(elem!1) = s(s(z))))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[12009])).
% 2.23/2.43 tff(12011,plain,
% 2.23/2.43 (~(s(elem!1) = s(s(z)))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[283, 12010])).
% 2.23/2.43 tff(12012,plain,
% 2.23/2.43 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(elem!1)))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[12000])).
% 2.23/2.43 tff(12013,plain,
% 2.23/2.43 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), elem!1)),
% 2.23/2.43 inference(symmetry,[status(thm)],[12012])).
% 2.23/2.43 tff(12014,plain,
% 2.23/2.43 (s(s(s(elem!1))) = s(elem!1)),
% 2.23/2.43 inference(transitivity,[status(thm)],[1720, 12005, 105])).
% 2.23/2.43 tff(12015,plain,
% 2.23/2.43 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[12014])).
% 2.23/2.43 tff(12016,plain,
% 2.23/2.43 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(elem!1), elem!1)),
% 2.23/2.43 inference(transitivity,[status(thm)],[12015, 12013])).
% 2.23/2.43 tff(12017,plain,
% 2.23/2.43 ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[10914, 10906])).
% 2.23/2.43 tff(12018,plain,
% 2.23/2.43 (~b(s(s(elem!1)), z)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[12017, 8522, 11833])).
% 2.23/2.43 tff(12019,plain,
% 2.23/2.43 (r(s(s(elem!1)), z)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[7835, 12018])).
% 2.23/2.43 tff(12020,plain,
% 2.23/2.43 (~b(s(s(s(elem!1))), z)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[8768, 128, 11833, 7825, 11864])).
% 2.23/2.43 tff(12021,plain,
% 2.23/2.43 (r(s(s(s(elem!1))), z)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[5301, 12020])).
% 2.23/2.43 tff(12022,plain,
% 2.23/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.23/2.43 inference(rewrite,[status(thm)],[])).
% 2.23/2.43 tff(12023,plain,
% 2.23/2.43 (((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.23/2.43 inference(rewrite,[status(thm)],[])).
% 2.23/2.43 tff(12024,plain,
% 2.23/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1))))))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[12023])).
% 2.23/2.43 tff(12025,plain,
% 2.23/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.23/2.43 inference(transitivity,[status(thm)],[12024, 12022])).
% 2.23/2.43 tff(12026,plain,
% 2.23/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.23/2.43 inference(quant_inst,[status(thm)],[])).
% 2.23/2.43 tff(12027,plain,
% 2.23/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[12026, 12025])).
% 2.23/2.43 tff(12028,plain,
% 2.23/2.43 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[12027, 45, 12021, 12019])).
% 2.23/2.43 tff(12029,plain,
% 2.23/2.43 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[889, 12028, 11857])).
% 2.23/2.43 tff(12030,plain,
% 2.23/2.43 (b(s(elem!1), elem!1)),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[12029, 12016])).
% 2.23/2.43 tff(12031,plain,
% 2.23/2.43 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(elem!1)))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[12000])).
% 2.23/2.43 tff(12032,plain,
% 2.23/2.43 (b(s(s(z)), s(s(elem!1))) <=> b(s(s(z)), elem!1)),
% 2.23/2.43 inference(symmetry,[status(thm)],[12031])).
% 2.23/2.43 tff(12033,plain,
% 2.23/2.43 (b(s(s(z)), elem!1)),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[8523, 12032])).
% 2.23/2.43 tff(12034,plain,
% 2.23/2.43 (~(s(s(s(s(s(s(z)))))) = s(elem!1))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[9657, 11999])).
% 2.23/2.43 tff(12035,plain,
% 2.23/2.43 (b(elem!1, s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[12000])).
% 2.23/2.43 tff(12036,plain,
% 2.23/2.43 (b(s(s(elem!1)), s(s(z))) <=> b(elem!1, s(s(z)))),
% 2.23/2.43 inference(symmetry,[status(thm)],[12035])).
% 2.23/2.43 tff(12037,plain,
% 2.23/2.43 (b(elem!1, s(s(z)))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[8522, 12036])).
% 2.23/2.43 tff(12038,plain,
% 2.23/2.43 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[9688, 12037, 12034, 12033, 12030, 12011])).
% 2.23/2.43 tff(12039,plain,
% 2.23/2.43 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[1055, 12038, 12004])).
% 2.23/2.43 tff(12040,plain,
% 2.23/2.43 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[7620, 12039, 12003])).
% 2.23/2.43 tff(12041,plain,
% 2.23/2.43 (b(s(s(s(s(s(s(z)))))), s(z))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[1148, 21, 12040, 8155])).
% 2.23/2.43 tff(12042,plain,
% 2.23/2.43 (~b(s(s(s(s(s(s(z)))))), z)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[9175, 128, 11833, 7825, 12041])).
% 2.23/2.43 tff(12043,plain,
% 2.23/2.43 (r(s(s(s(s(s(s(z)))))), s(s(elem!1))) <=> r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.23/2.43 inference(monotonicity,[status(thm)],[11999])).
% 2.23/2.43 tff(12044,plain,
% 2.23/2.43 (r(s(s(s(s(s(s(z)))))), elem!1) <=> r(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 2.23/2.43 inference(symmetry,[status(thm)],[12043])).
% 2.23/2.43 tff(12045,plain,
% 2.23/2.43 (r(s(s(s(s(s(s(z)))))), s(s(elem!1)))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[12039, 12044])).
% 2.23/2.43 tff(12046,plain,
% 2.23/2.43 (~r(z, s(s(z)))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[8881, 45, 11866, 1187])).
% 2.23/2.43 tff(12047,plain,
% 2.23/2.43 (b(z, s(s(z)))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[516, 12046])).
% 2.23/2.43 tff(12048,plain,
% 2.23/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.23/2.43 inference(rewrite,[status(thm)],[])).
% 2.23/2.43 tff(12049,plain,
% 2.23/2.43 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.23/2.43 inference(rewrite,[status(thm)],[])).
% 2.23/2.43 tff(12050,plain,
% 2.23/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z))))))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[12049])).
% 2.23/2.43 tff(12051,plain,
% 2.23/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.23/2.43 inference(transitivity,[status(thm)],[12050, 12048])).
% 2.23/2.43 tff(12052,plain,
% 2.23/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))))),
% 2.23/2.43 inference(quant_inst,[status(thm)],[])).
% 2.23/2.43 tff(12053,plain,
% 2.23/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z))))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[12052, 12051])).
% 2.23/2.43 tff(12054,plain,
% 2.23/2.43 ((~b(z, s(s(elem!1)))) | (~b(z, s(s(z))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[12053, 128, 11833, 10906, 8522])).
% 2.23/2.43 tff(12055,plain,
% 2.23/2.43 (~b(z, s(s(elem!1)))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[12054, 12047])).
% 2.23/2.43 tff(12056,plain,
% 2.23/2.43 (r(z, s(s(elem!1)))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[160, 12055])).
% 2.23/2.43 tff(12057,plain,
% 2.23/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 2.23/2.43 inference(rewrite,[status(thm)],[])).
% 2.23/2.43 tff(12058,plain,
% 2.23/2.43 (((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), z))) <=> ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 2.23/2.43 inference(rewrite,[status(thm)],[])).
% 2.23/2.43 tff(12059,plain,
% 2.23/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~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(s(s(s(s(s(s(z)))))), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1))))))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[12058])).
% 2.23/2.43 tff(12060,plain,
% 2.23/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~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(s(s(s(s(s(s(z)))))), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))))),
% 2.23/2.43 inference(transitivity,[status(thm)],[12059, 12057])).
% 2.23/2.43 tff(12061,plain,
% 2.23/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 2.23/2.43 inference(quant_inst,[status(thm)],[])).
% 2.23/2.43 tff(12062,plain,
% 2.23/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1))))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[12061, 12060])).
% 2.23/2.43 tff(12063,plain,
% 2.23/2.43 ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(elem!1))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[12062, 45, 12056])).
% 2.23/2.43 tff(12064,plain,
% 2.23/2.43 (~r(s(s(s(s(s(s(z)))))), z)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[12063, 12045])).
% 2.23/2.43 tff(12065,plain,
% 2.23/2.43 ($false),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[1022, 21, 1019, 12064, 12042])).
% 2.23/2.43 tff(12066,plain,((~r(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.43 tff(12067,plain,
% 2.23/2.43 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[12066, 11853, 11851, 325])).
% 2.23/2.43 tff(12068,plain,
% 2.23/2.43 ((s(s(z)) = s(s(s(elem!1)))) | b(s(s(z)), s(s(s(elem!1))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[4283, 21, 12067])).
% 2.23/2.43 tff(12069,plain,
% 2.23/2.43 (b(s(s(z)), s(s(s(elem!1))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[12068, 4271])).
% 2.23/2.43 tff(12070,plain,
% 2.23/2.43 (~r(s(s(s(elem!1))), s(z))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[11862, 11851, 325])).
% 2.23/2.43 tff(12071,plain,
% 2.23/2.43 (b(s(s(s(elem!1))), s(z))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[196, 12070])).
% 2.23/2.43 tff(12072,plain,
% 2.23/2.43 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[693, 11856])).
% 2.23/2.43 tff(12073,plain,
% 2.23/2.43 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[700, 12072])).
% 2.23/2.43 tff(12074,plain,
% 2.23/2.43 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[8789, 2718, 11833, 12073])).
% 2.23/2.43 tff(12075,plain,
% 2.23/2.43 (r(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[1828, 12074])).
% 2.23/2.43 tff(12076,plain,
% 2.23/2.43 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[2141, 12075, 325])).
% 2.23/2.43 tff(12077,plain,
% 2.23/2.43 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[1897, 1063, 12076])).
% 2.23/2.43 tff(12078,plain,
% 2.23/2.43 (~b(s(z), s(s(s(elem!1))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[11996, 1063, 2718, 325])).
% 2.23/2.43 tff(12079,plain,
% 2.23/2.43 (r(s(z), s(s(s(elem!1))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[339, 12078])).
% 2.23/2.43 tff(12080,plain,
% 2.23/2.43 (~b(z, s(s(s(elem!1))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[8605, 128, 11833, 7825, 2718])).
% 2.23/2.43 tff(12081,plain,
% 2.23/2.43 (r(z, s(s(s(elem!1))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[858, 12080])).
% 2.23/2.43 tff(12082,plain,
% 2.23/2.43 (~b(s(s(s(elem!1))), z)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[8768, 128, 11833, 7825, 2718])).
% 2.23/2.43 tff(12083,plain,
% 2.23/2.43 (r(s(s(s(elem!1))), z)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[5301, 12082])).
% 2.23/2.43 tff(12084,plain,
% 2.23/2.43 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[9354, 12077, 2718, 11848, 8557, 12073, 12075, 12083, 12081, 325])).
% 2.23/2.43 tff(12085,plain,
% 2.23/2.43 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[321, 12084, 11856])).
% 2.23/2.43 tff(12086,plain,
% 2.23/2.43 ($false),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[9405, 12085, 12079, 325, 12075, 12073, 11857, 12077, 2511])).
% 2.23/2.43 tff(12087,plain,((s(s(s(s(elem!1)))) = s(s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.43 tff(12088,plain,
% 2.23/2.43 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[12087, 325, 12071, 12069])).
% 2.23/2.43 tff(12089,plain,
% 2.23/2.43 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(elem!1)))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[12088])).
% 2.23/2.43 tff(12090,plain,
% 2.23/2.43 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 2.23/2.43 inference(symmetry,[status(thm)],[12089])).
% 2.23/2.43 tff(12091,plain,
% 2.23/2.43 (s(elem!1) = s(s(s(elem!1)))),
% 2.23/2.43 inference(transitivity,[status(thm)],[106, 12090, 233])).
% 2.23/2.43 tff(12092,plain,
% 2.23/2.43 (b(s(s(z)), s(elem!1)) <=> b(s(s(z)), s(s(s(elem!1))))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[12091])).
% 2.23/2.43 tff(12093,plain,
% 2.23/2.43 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(elem!1))),
% 2.23/2.43 inference(symmetry,[status(thm)],[12092])).
% 2.23/2.43 tff(12094,plain,
% 2.23/2.43 (b(s(s(z)), s(elem!1))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[12069, 12093])).
% 2.23/2.43 tff(12095,plain,
% 2.23/2.43 (s(s(s(elem!1))) = s(elem!1)),
% 2.23/2.43 inference(transitivity,[status(thm)],[1720, 12089, 105])).
% 2.23/2.43 tff(12096,plain,
% 2.23/2.43 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(elem!1))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[12095])).
% 2.23/2.43 tff(12097,plain,
% 2.23/2.43 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[12088])).
% 2.23/2.43 tff(12098,plain,
% 2.23/2.43 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(elem!1))),
% 2.23/2.43 inference(transitivity,[status(thm)],[12097, 12096])).
% 2.23/2.43 tff(12099,plain,
% 2.23/2.43 (~b(s(s(s(elem!1))), z)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[8768, 128, 11833, 7825, 12071])).
% 2.23/2.43 tff(12100,plain,
% 2.23/2.43 (r(s(s(s(elem!1))), z)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[5301, 12099])).
% 2.23/2.43 tff(12101,plain,
% 2.23/2.43 (r(s(s(s(s(elem!1)))), z) <=> r(s(s(elem!1)), z)),
% 2.23/2.43 inference(monotonicity,[status(thm)],[12088])).
% 2.23/2.43 tff(12102,plain,
% 2.23/2.43 (r(s(s(elem!1)), z) <=> r(s(s(s(s(elem!1)))), z)),
% 2.23/2.43 inference(symmetry,[status(thm)],[12101])).
% 2.23/2.43 tff(12103,plain,
% 2.23/2.43 (~b(s(s(elem!1)), z)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[12017, 11853, 11833])).
% 2.23/2.43 tff(12104,plain,
% 2.23/2.43 (r(s(s(elem!1)), z)),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[7835, 12103])).
% 2.23/2.43 tff(12105,plain,
% 2.23/2.43 (r(s(s(s(s(elem!1)))), z)),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[12104, 12102])).
% 2.23/2.43 tff(12106,plain,
% 2.23/2.43 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[1780, 12105, 12100])).
% 2.23/2.43 tff(12107,plain,
% 2.23/2.43 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[1820, 12106, 12073])).
% 2.23/2.43 tff(12108,plain,
% 2.23/2.43 (b(s(s(elem!1)), s(elem!1))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[12107, 12098])).
% 2.23/2.43 tff(12109,plain,
% 2.23/2.43 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[12095])).
% 2.23/2.43 tff(12110,plain,
% 2.23/2.43 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[12088])).
% 2.23/2.43 tff(12111,plain,
% 2.23/2.43 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.23/2.43 inference(transitivity,[status(thm)],[12110, 12109])).
% 2.23/2.43 tff(12112,plain,
% 2.23/2.43 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[1874, 12105, 12100])).
% 2.23/2.43 tff(12113,plain,
% 2.23/2.43 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[1856, 12112, 12072])).
% 2.23/2.43 tff(12114,plain,
% 2.23/2.43 (b(s(elem!1), s(s(elem!1)))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[12113, 12111])).
% 2.23/2.43 tff(12115,plain,
% 2.23/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.23/2.43 inference(rewrite,[status(thm)],[])).
% 2.23/2.43 tff(12116,plain,
% 2.23/2.43 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.23/2.43 inference(rewrite,[status(thm)],[])).
% 2.23/2.43 tff(12117,plain,
% 2.23/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1))))))),
% 2.23/2.43 inference(monotonicity,[status(thm)],[12116])).
% 2.23/2.43 tff(12118,plain,
% 2.23/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.23/2.43 inference(transitivity,[status(thm)],[12117, 12115])).
% 2.23/2.43 tff(12119,plain,
% 2.23/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.23/2.43 inference(quant_inst,[status(thm)],[])).
% 2.23/2.43 tff(12120,plain,
% 2.23/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1))))),
% 2.23/2.43 inference(modus_ponens,[status(thm)],[12119, 12118])).
% 2.23/2.43 tff(12121,plain,
% 2.23/2.43 ($false),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[12120, 128, 12114, 12108, 11851, 12094])).
% 2.23/2.43 tff(12122,plain,((~r(s(s(elem!1)), s(z))) | (s(s(elem!1)) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.43 tff(12123,plain,
% 2.23/2.43 (~r(s(s(elem!1)), s(z))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[12122, 1])).
% 2.23/2.43 tff(12124,plain,
% 2.23/2.43 (b(s(s(elem!1)), s(z))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[292, 12123])).
% 2.23/2.43 tff(12125,plain,
% 2.23/2.43 (~b(z, s(s(elem!1)))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[9870, 12124, 11833])).
% 2.23/2.43 tff(12126,plain,
% 2.23/2.43 (r(z, s(s(elem!1)))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[160, 12125])).
% 2.23/2.43 tff(12127,plain,
% 2.23/2.43 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[8961, 385, 11833, 12126])).
% 2.23/2.43 tff(12128,plain,
% 2.23/2.43 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.23/2.43 inference(unit_resolution,[status(thm)],[693, 12127])).
% 2.23/2.43 tff(12129,plain,
% 2.23/2.43 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[700, 12128])).
% 2.23/2.44 tff(12130,plain,
% 2.23/2.44 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[8542, 45, 385, 11848])).
% 2.23/2.44 tff(12131,plain,
% 2.23/2.44 ((s(s(z)) = s(s(s(elem!1)))) | b(s(s(z)), s(s(s(elem!1))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[4283, 21, 12130])).
% 2.23/2.44 tff(12132,plain,
% 2.23/2.44 (b(s(s(z)), s(s(s(elem!1))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[12131, 4271])).
% 2.23/2.44 tff(12133,plain,
% 2.23/2.44 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[803, 12127])).
% 2.23/2.44 tff(12134,plain,
% 2.23/2.44 (((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~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)), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(12135,plain,
% 2.23/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))))),
% 2.23/2.44 inference(monotonicity,[status(thm)],[12134])).
% 2.23/2.44 tff(12136,plain,
% 2.23/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~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(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 2.23/2.44 inference(transitivity,[status(thm)],[12135, 9952])).
% 2.23/2.44 tff(12137,plain,
% 2.23/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))),
% 2.23/2.44 inference(quant_inst,[status(thm)],[])).
% 2.23/2.44 tff(12138,plain,
% 2.23/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[12137, 12136])).
% 2.23/2.44 tff(12139,plain,
% 2.23/2.44 (~b(s(s(elem!1)), z)),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[12138, 128, 12124, 11833, 7825])).
% 2.23/2.44 tff(12140,plain,
% 2.23/2.44 (r(s(s(elem!1)), z)),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[7835, 12139])).
% 2.23/2.44 tff(12141,plain,
% 2.23/2.44 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[8524, 2511, 11833, 12124])).
% 2.23/2.44 tff(12142,plain,
% 2.23/2.44 (r(s(s(s(s(elem!1)))), s(z))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[1828, 12141])).
% 2.23/2.44 tff(12143,plain,
% 2.23/2.44 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[10059, 12142, 385])).
% 2.23/2.44 tff(12144,plain,
% 2.23/2.44 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[1856, 12143, 12128])).
% 2.23/2.44 tff(12145,plain,
% 2.23/2.44 (b(s(s(s(elem!1))), z)),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[5301, 544])).
% 2.23/2.44 tff(12146,plain,
% 2.23/2.44 (((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(12147,plain,
% 2.23/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z))))))),
% 2.23/2.44 inference(monotonicity,[status(thm)],[12146])).
% 2.23/2.44 tff(12148,plain,
% 2.23/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))))),
% 2.23/2.44 inference(transitivity,[status(thm)],[12147, 6828])).
% 2.23/2.44 tff(12149,plain,
% 2.23/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)))),
% 2.23/2.44 inference(quant_inst,[status(thm)],[])).
% 2.23/2.44 tff(12150,plain,
% 2.23/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z))))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[12149, 12148])).
% 2.23/2.44 tff(12151,plain,
% 2.23/2.44 ($false),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[12150, 128, 3452, 495, 10906, 9056])).
% 2.23/2.44 tff(12152,plain,((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.44 tff(12153,plain,
% 2.23/2.44 (~b(z, s(s(z)))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[12152, 12145, 9056])).
% 2.23/2.44 tff(12154,plain,
% 2.23/2.44 (r(z, s(s(z)))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[516, 12153])).
% 2.23/2.44 tff(12155,assumption,(r(s(s(elem!1)), s(s(z)))), introduced(assumption)).
% 2.23/2.44 tff(12156,plain,
% 2.23/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(12157,plain,
% 2.23/2.44 (((~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(12158,plain,
% 2.23/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z))))))),
% 2.23/2.44 inference(monotonicity,[status(thm)],[12157])).
% 2.23/2.44 tff(12159,plain,
% 2.23/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.23/2.44 inference(transitivity,[status(thm)],[12158, 12156])).
% 2.23/2.44 tff(12160,plain,
% 2.23/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(elem!1)))))),
% 2.23/2.44 inference(quant_inst,[status(thm)],[])).
% 2.23/2.44 tff(12161,plain,
% 2.23/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z))))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[12160, 12159])).
% 2.23/2.44 tff(12162,plain,
% 2.23/2.44 ($false),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[12161, 45, 88, 519, 12155])).
% 2.23/2.44 tff(12163,plain,((~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.44 tff(12164,plain,
% 2.23/2.44 (~r(s(s(elem!1)), s(s(z)))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[12163, 12154, 12126])).
% 2.23/2.44 tff(12165,plain,
% 2.23/2.44 (b(s(s(elem!1)), s(s(z)))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[4339, 21, 1, 12164])).
% 2.23/2.44 tff(12166,plain,
% 2.23/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(12167,plain,
% 2.23/2.44 (((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(12168,plain,
% 2.23/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z))))))),
% 2.23/2.44 inference(monotonicity,[status(thm)],[12167])).
% 2.23/2.44 tff(12169,plain,
% 2.23/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.23/2.44 inference(transitivity,[status(thm)],[12168, 12166])).
% 2.23/2.44 tff(12170,plain,
% 2.23/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.23/2.44 inference(quant_inst,[status(thm)],[])).
% 2.23/2.44 tff(12171,plain,
% 2.23/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z))))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[12170, 12169])).
% 2.23/2.44 tff(12172,plain,
% 2.23/2.44 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[12171, 128, 1843, 8557, 9056, 12165])).
% 2.23/2.44 tff(12173,plain,
% 2.23/2.44 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[889, 12172, 1691])).
% 2.23/2.44 tff(12174,plain,
% 2.23/2.44 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[8584, 12173, 11833, 12126, 8557, 12154])).
% 2.23/2.44 tff(12175,plain,
% 2.23/2.44 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[1820, 12174, 712])).
% 2.23/2.44 tff(12176,plain,
% 2.23/2.44 (~r(z, s(s(s(elem!1))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[4402, 45, 12126, 12173])).
% 2.23/2.44 tff(12177,plain,
% 2.23/2.44 (~b(s(z), s(s(s(elem!1))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[561, 12176, 11833, 544])).
% 2.23/2.44 tff(12178,plain,
% 2.23/2.44 (r(s(z), s(s(s(elem!1))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[339, 12177])).
% 2.23/2.44 tff(12179,plain,
% 2.23/2.44 ($false),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[8595, 45, 1737, 12178, 12175])).
% 2.23/2.44 tff(12180,plain,(r(s(s(s(elem!1))), z) | (~r(s(s(s(s(elem!1)))), s(z))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (s(s(elem!1)) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.44 tff(12181,plain,
% 2.23/2.44 (r(s(s(s(elem!1))), z)),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[12180, 12142, 12129, 12132, 12133, 12144, 11855, 1])).
% 2.23/2.44 tff(12182,plain,
% 2.23/2.44 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[12027, 45, 12181, 12140])).
% 2.23/2.44 tff(12183,plain,
% 2.23/2.44 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[889, 12182, 12133])).
% 2.23/2.44 tff(12184,plain,
% 2.23/2.44 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[9909, 45, 12181, 12140])).
% 2.23/2.44 tff(12185,plain,
% 2.23/2.44 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[321, 12184, 12127])).
% 2.23/2.44 tff(12186,plain,
% 2.23/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(12187,plain,
% 2.23/2.44 (((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(12188,plain,
% 2.23/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z))))))),
% 2.23/2.44 inference(monotonicity,[status(thm)],[12187])).
% 2.23/2.44 tff(12189,plain,
% 2.23/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.23/2.44 inference(transitivity,[status(thm)],[12188, 12186])).
% 2.23/2.44 tff(12190,plain,
% 2.23/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.23/2.44 inference(quant_inst,[status(thm)],[])).
% 2.23/2.44 tff(12191,plain,
% 2.23/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z))))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[12190, 12189])).
% 2.23/2.44 tff(12192,plain,
% 2.23/2.44 ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[12191, 128, 12124, 11833, 10906, 11855])).
% 2.23/2.44 tff(12193,plain,
% 2.23/2.44 (~b(s(s(elem!1)), s(s(z)))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[12192, 12185])).
% 2.23/2.44 tff(12194,plain,
% 2.23/2.44 (r(s(s(elem!1)), s(s(z)))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[4339, 21, 1, 12193])).
% 2.23/2.44 tff(12195,plain,
% 2.23/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(12196,plain,
% 2.23/2.44 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(12197,plain,
% 2.23/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z))))))),
% 2.23/2.44 inference(monotonicity,[status(thm)],[12196])).
% 2.23/2.44 tff(12198,plain,
% 2.23/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.23/2.44 inference(transitivity,[status(thm)],[12197, 12195])).
% 2.23/2.44 tff(12199,plain,
% 2.23/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.23/2.44 inference(quant_inst,[status(thm)],[])).
% 2.23/2.44 tff(12200,plain,
% 2.23/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[12199, 12198])).
% 2.23/2.44 tff(12201,plain,
% 2.23/2.44 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[12200, 128, 2106, 875, 1842, 8557])).
% 2.23/2.44 tff(12202,plain,
% 2.23/2.44 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[4309, 21, 239, 12201])).
% 2.23/2.44 tff(12203,plain,
% 2.23/2.44 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[10761, 128, 2106, 875, 1842])).
% 2.23/2.44 tff(12204,plain,
% 2.23/2.44 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[1897, 12203, 1063])).
% 2.23/2.44 tff(12205,plain,
% 2.23/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(12206,plain,
% 2.23/2.44 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(12207,plain,
% 2.23/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 2.23/2.44 inference(monotonicity,[status(thm)],[12206])).
% 2.23/2.44 tff(12208,plain,
% 2.23/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.23/2.44 inference(transitivity,[status(thm)],[12207, 12205])).
% 2.23/2.44 tff(12209,plain,
% 2.23/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.23/2.44 inference(quant_inst,[status(thm)],[])).
% 2.23/2.44 tff(12210,plain,
% 2.23/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 2.23/2.44 inference(modus_ponens,[status(thm)],[12209, 12208])).
% 2.23/2.44 tff(12211,plain,
% 2.23/2.44 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[12210, 128, 30, 2106, 875, 1842])).
% 2.23/2.44 tff(12212,plain,
% 2.23/2.44 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.23/2.44 inference(unit_resolution,[status(thm)],[2212, 21, 2511, 12211])).
% 2.23/2.44 tff(12213,plain,
% 2.23/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(12214,plain,
% 2.23/2.44 (((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.23/2.44 inference(rewrite,[status(thm)],[])).
% 2.23/2.44 tff(12215,plain,
% 2.23/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z))))))),
% 2.23/2.44 inference(monotonicity,[status(thm)],[12214])).
% 2.23/2.44 tff(12216,plain,
% 2.23/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.23/2.44 inference(transitivity,[status(thm)],[12215, 12213])).
% 2.23/2.44 tff(12217,plain,
% 2.23/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.23/2.44 inference(quant_inst,[status(thm)],[])).
% 2.23/2.44 tff(12218,plain,
% 2.23/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z))))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[12217, 12216])).
% 2.23/2.45 tff(12219,plain,
% 2.23/2.45 ($false),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[12218, 45, 12212, 12204, 12155, 12202])).
% 2.23/2.45 tff(12220,plain,((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.45 tff(12221,plain,
% 2.23/2.45 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[12220, 12194, 1063, 12185, 12183, 12132, 12124])).
% 2.23/2.45 tff(12222,plain,
% 2.23/2.45 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[1820, 12221, 12129])).
% 2.23/2.45 tff(12223,plain,
% 2.23/2.45 (~b(s(z), s(s(s(elem!1))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[7941, 12184, 12124, 1063])).
% 2.23/2.45 tff(12224,plain,
% 2.23/2.45 (r(s(z), s(s(s(elem!1))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[339, 12223])).
% 2.23/2.45 tff(12225,plain,
% 2.23/2.45 ($false),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[8595, 45, 12142, 12224, 12222])).
% 2.23/2.45 tff(12226,plain,((s(s(s(s(elem!1)))) = s(s(elem!1))) | (s(s(elem!1)) = s(s(z))) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.45 tff(12227,plain,
% 2.23/2.45 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[12226, 385, 1])).
% 2.23/2.45 tff(12228,plain,
% 2.23/2.45 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[1073, 12227])).
% 2.23/2.45 tff(12229,plain,
% 2.23/2.45 (s(s(elem!1)) = elem!1),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[1089, 12228])).
% 2.23/2.45 tff(12230,plain,
% 2.23/2.45 ((s(s(elem!1)) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[12229])).
% 2.23/2.45 tff(12231,plain,
% 2.23/2.45 ((s(s(elem!1)) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 2.23/2.45 inference(transitivity,[status(thm)],[12230, 225])).
% 2.23/2.45 tff(12232,plain,
% 2.23/2.45 ((s(s(elem!1)) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 2.23/2.45 inference(transitivity,[status(thm)],[12231, 650])).
% 2.23/2.45 tff(12233,plain,
% 2.23/2.45 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(elem!1 = s(s(z))))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[12232])).
% 2.23/2.45 tff(12234,plain,
% 2.23/2.45 (~(elem!1 = s(s(z)))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[1, 12233])).
% 2.23/2.45 tff(12235,plain,
% 2.23/2.45 (s(s(s(elem!1))) = s(elem!1)),
% 2.23/2.45 inference(monotonicity,[status(thm)],[12229])).
% 2.23/2.45 tff(12236,plain,
% 2.23/2.45 (s(elem!1) = s(s(s(elem!1)))),
% 2.23/2.45 inference(symmetry,[status(thm)],[12235])).
% 2.23/2.45 tff(12237,plain,
% 2.23/2.45 (b(s(elem!1), s(s(z))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[12236])).
% 2.23/2.45 tff(12238,plain,
% 2.23/2.45 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(elem!1), s(s(z)))),
% 2.23/2.45 inference(symmetry,[status(thm)],[12237])).
% 2.23/2.45 tff(12239,plain,
% 2.23/2.45 (b(s(elem!1), s(s(z)))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[11855, 12238])).
% 2.23/2.45 tff(12240,plain,
% 2.23/2.45 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[12235])).
% 2.23/2.45 tff(12241,plain,
% 2.23/2.45 (s(s(s(s(elem!1)))) = elem!1),
% 2.23/2.45 inference(transitivity,[status(thm)],[12240, 12229])).
% 2.23/2.45 tff(12242,plain,
% 2.23/2.45 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[12241])).
% 2.23/2.45 tff(12243,plain,
% 2.23/2.45 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[12235])).
% 2.23/2.45 tff(12244,plain,
% 2.23/2.45 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(elem!1, s(elem!1))),
% 2.23/2.45 inference(transitivity,[status(thm)],[12243, 12242])).
% 2.23/2.45 tff(12245,plain,
% 2.23/2.45 (r(s(s(s(s(elem!1)))), z) <=> r(elem!1, z)),
% 2.23/2.45 inference(monotonicity,[status(thm)],[12241])).
% 2.23/2.45 tff(12246,plain,
% 2.23/2.45 (r(elem!1, z) <=> r(s(s(s(s(elem!1)))), z)),
% 2.23/2.45 inference(symmetry,[status(thm)],[12245])).
% 2.23/2.45 tff(12247,plain,
% 2.23/2.45 (r(s(s(elem!1)), z) <=> r(elem!1, z)),
% 2.23/2.45 inference(monotonicity,[status(thm)],[12229])).
% 2.23/2.45 tff(12248,plain,
% 2.23/2.45 (r(elem!1, z)),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[12140, 12247])).
% 2.23/2.45 tff(12249,plain,
% 2.23/2.45 (r(s(s(s(s(elem!1)))), z)),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[12248, 12246])).
% 2.23/2.45 tff(12250,plain,
% 2.23/2.45 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[12231])).
% 2.23/2.45 tff(12251,plain,
% 2.23/2.45 (~(s(s(z)) = elem!1)),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[1, 12250])).
% 2.23/2.45 tff(12252,plain,
% 2.23/2.45 (b(s(s(elem!1)), s(z)) <=> b(elem!1, s(z))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[12229])).
% 2.23/2.45 tff(12253,plain,
% 2.23/2.45 (b(elem!1, s(z))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[12124, 12252])).
% 2.23/2.45 tff(12254,plain,
% 2.23/2.45 (b(s(elem!1), s(s(z))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[354])).
% 2.23/2.45 tff(12255,plain,
% 2.23/2.45 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(elem!1), s(s(z)))),
% 2.23/2.45 inference(symmetry,[status(thm)],[12254])).
% 2.23/2.45 tff(12256,plain,
% 2.23/2.45 (b(s(elem!1), s(s(z)))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[9056, 12255])).
% 2.23/2.45 tff(12257,plain,
% 2.23/2.45 (r(z, s(s(s(s(elem!1))))) <=> r(z, elem!1)),
% 2.23/2.45 inference(monotonicity,[status(thm)],[228])).
% 2.23/2.45 tff(12258,plain,
% 2.23/2.45 (r(z, elem!1) <=> r(z, s(s(s(s(elem!1)))))),
% 2.23/2.45 inference(symmetry,[status(thm)],[12257])).
% 2.23/2.45 tff(12259,plain,
% 2.23/2.45 (r(z, elem!1)),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[88, 796])).
% 2.23/2.45 tff(12260,plain,
% 2.23/2.45 (r(z, s(s(s(s(elem!1)))))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[12259, 12258])).
% 2.23/2.45 tff(12261,plain,
% 2.23/2.45 (~r(s(s(z)), elem!1)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[10267, 12154, 12259])).
% 2.23/2.45 tff(12262,plain,
% 2.23/2.45 (b(s(s(z)), elem!1)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[370, 12261, 484])).
% 2.23/2.45 tff(12263,plain,
% 2.23/2.45 (~b(s(s(s(s(z)))), elem!1)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[2819, 922, 297, 591])).
% 2.23/2.45 tff(12264,plain,
% 2.23/2.45 (r(s(s(s(s(z)))), elem!1)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[632, 12263, 2953])).
% 2.23/2.45 tff(12265,plain,
% 2.23/2.45 (~r(s(s(s(s(z)))), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[1459, 45, 1416, 12264])).
% 2.23/2.45 tff(12266,plain,
% 2.23/2.45 (b(s(s(s(s(z)))), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[589, 21, 586, 12265])).
% 2.23/2.45 tff(12267,plain,
% 2.23/2.45 (~b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[2976, 922, 297, 591, 11848])).
% 2.23/2.45 tff(12268,plain,
% 2.23/2.45 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[1055, 12267, 2956])).
% 2.23/2.45 tff(12269,plain,
% 2.23/2.45 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[2986, 45, 12264, 12268])).
% 2.23/2.45 tff(12270,plain,
% 2.23/2.45 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[1215, 21, 1212, 12269])).
% 2.23/2.45 tff(12271,plain,
% 2.23/2.45 (~r(s(s(s(s(s(s(z)))))), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[1423, 45, 1416, 12268])).
% 2.23/2.45 tff(12272,plain,
% 2.23/2.45 (b(s(s(s(s(s(s(z)))))), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[1022, 21, 1019, 12271])).
% 2.23/2.45 tff(12273,plain,
% 2.23/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.23/2.45 inference(rewrite,[status(thm)],[])).
% 2.23/2.45 tff(12274,plain,
% 2.23/2.45 (((~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.23/2.45 inference(rewrite,[status(thm)],[])).
% 2.23/2.45 tff(12275,plain,
% 2.23/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[12274])).
% 2.23/2.45 tff(12276,plain,
% 2.23/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.23/2.45 inference(transitivity,[status(thm)],[12275, 12273])).
% 2.23/2.45 tff(12277,plain,
% 2.23/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.23/2.45 inference(quant_inst,[status(thm)],[])).
% 2.23/2.45 tff(12278,plain,
% 2.23/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[12277, 12276])).
% 2.23/2.45 tff(12279,plain,
% 2.23/2.45 ($false),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[12278, 128, 11833, 7825, 12272, 12270, 12266])).
% 2.23/2.45 tff(12280,plain,((~b(s(z), elem!1)) | (~r(z, elem!1)) | (s(s(s(s(z)))) = elem!1) | (s(s(s(s(s(s(z)))))) = elem!1) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.45 tff(12281,plain,
% 2.23/2.45 (~b(s(z), elem!1)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[12280, 12262, 243, 246, 297, 12259])).
% 2.23/2.45 tff(12282,plain,
% 2.23/2.45 (r(s(z), elem!1)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[665, 12281, 257])).
% 2.23/2.45 tff(12283,plain,
% 2.23/2.45 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[226])).
% 2.23/2.45 tff(12284,plain,
% 2.23/2.45 (r(s(s(s(s(elem!1)))), s(elem!1)) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.23/2.45 inference(symmetry,[status(thm)],[12283])).
% 2.23/2.45 tff(12285,plain,
% 2.23/2.45 (r(s(s(s(s(elem!1)))), s(elem!1)) <=> r(elem!1, s(elem!1))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[228])).
% 2.23/2.45 tff(12286,plain,
% 2.23/2.45 (r(elem!1, s(elem!1)) <=> r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.23/2.45 inference(symmetry,[status(thm)],[12285])).
% 2.23/2.45 tff(12287,plain,
% 2.23/2.45 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.23/2.45 inference(transitivity,[status(thm)],[357, 356, 12286, 12284])).
% 2.23/2.45 tff(12288,plain,
% 2.23/2.45 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[324, 12287])).
% 2.23/2.45 tff(12289,plain,
% 2.23/2.45 (~r(z, s(s(s(elem!1))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[1790, 12288, 1782])).
% 2.23/2.45 tff(12290,plain,
% 2.23/2.45 (~b(s(z), s(s(s(elem!1))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[561, 12289, 11833, 544])).
% 2.23/2.45 tff(12291,plain,
% 2.23/2.45 (r(s(z), s(s(s(elem!1))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[339, 12290])).
% 2.23/2.45 tff(12292,plain,
% 2.23/2.45 (r(s(z), s(elem!1))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[12291, 863])).
% 2.23/2.45 tff(12293,plain,
% 2.23/2.45 (r(elem!1, s(elem!1))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[324, 358])).
% 2.23/2.45 tff(12294,plain,
% 2.23/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, z)) | (~r(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(z), elem!1)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))))),
% 2.23/2.45 inference(rewrite,[status(thm)],[])).
% 2.23/2.45 tff(12295,plain,
% 2.23/2.45 (((~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(elem!1, z)) | (~r(s(z), elem!1))) <=> ((~r(s(z), elem!1)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))))),
% 2.23/2.45 inference(rewrite,[status(thm)],[])).
% 2.23/2.45 tff(12296,plain,
% 2.23/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), 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(s(z), elem!1)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1)))))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[12295])).
% 2.23/2.45 tff(12297,plain,
% 2.23/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), 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(s(z), elem!1)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))))),
% 2.23/2.45 inference(transitivity,[status(thm)],[12296, 12294])).
% 2.23/2.45 tff(12298,plain,
% 2.23/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(elem!1, z)) | (~r(s(z), elem!1)))),
% 2.23/2.45 inference(quant_inst,[status(thm)],[])).
% 2.23/2.45 tff(12299,plain,
% 2.23/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1)))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[12298, 12297])).
% 2.23/2.45 tff(12300,plain,
% 2.23/2.45 (~r(s(z), s(elem!1))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[12299, 45, 1004, 1340, 12293])).
% 2.23/2.45 tff(12301,plain,
% 2.23/2.45 ($false),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[12300, 12292])).
% 2.23/2.45 tff(12302,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~(s(s(elem!1)) = elem!1)) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | r(s(s(s(elem!1))), z) | (~r(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.45 tff(12303,plain,
% 2.23/2.45 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[12302, 12282, 1004, 199, 544, 12260])).
% 2.23/2.45 tff(12304,plain,
% 2.23/2.45 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[321, 12303, 691])).
% 2.23/2.45 tff(12305,plain,
% 2.23/2.45 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[5237, 12304, 199])).
% 2.23/2.45 tff(12306,plain,
% 2.23/2.45 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[8584, 12305, 11833, 88, 8557, 12154])).
% 2.23/2.45 tff(12307,plain,
% 2.23/2.45 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[889, 12306, 804])).
% 2.23/2.45 tff(12308,plain,
% 2.23/2.45 (b(s(elem!1), elem!1)),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[12307, 11056])).
% 2.23/2.45 tff(12309,plain,
% 2.23/2.45 (b(elem!1, s(elem!1))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[12304, 11013])).
% 2.23/2.45 tff(12310,plain,
% 2.23/2.45 ($false),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[10275, 128, 12262, 12309, 12308, 12256])).
% 2.23/2.45 tff(12311,plain,(r(s(s(s(elem!1))), z) | (~(s(s(elem!1)) = elem!1)) | (~r(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(elem!1, z)) | (~b(elem!1, s(z))) | (s(s(z)) = elem!1) | (~b(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.45 tff(12312,plain,
% 2.23/2.45 (r(s(s(s(elem!1))), z)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[12311, 12229, 12126, 12132, 12127, 12248, 12253, 12251, 11855])).
% 2.23/2.45 tff(12313,plain,
% 2.23/2.45 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[1780, 12312, 12249])).
% 2.23/2.45 tff(12314,plain,
% 2.23/2.45 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[1820, 12313, 12129])).
% 2.23/2.45 tff(12315,plain,
% 2.23/2.45 (b(elem!1, s(elem!1))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[12314, 12244])).
% 2.23/2.45 tff(12316,plain,
% 2.23/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(z)))))),
% 2.23/2.45 inference(rewrite,[status(thm)],[])).
% 2.23/2.45 tff(12317,plain,
% 2.23/2.45 (((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(z)))))),
% 2.23/2.45 inference(rewrite,[status(thm)],[])).
% 2.23/2.45 tff(12318,plain,
% 2.23/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(z))))))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[12317])).
% 2.23/2.45 tff(12319,plain,
% 2.23/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(z)))))),
% 2.23/2.45 inference(transitivity,[status(thm)],[12318, 12316])).
% 2.23/2.45 tff(12320,plain,
% 2.23/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1))))),
% 2.23/2.45 inference(quant_inst,[status(thm)],[])).
% 2.23/2.45 tff(12321,plain,
% 2.23/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(z))))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[12320, 12319])).
% 2.23/2.45 tff(12322,plain,
% 2.23/2.45 ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(z))))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[12321, 128, 12253, 11833, 10906])).
% 2.23/2.45 tff(12323,plain,
% 2.23/2.45 (~b(elem!1, s(s(z)))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[12322, 12315, 12239])).
% 2.23/2.45 tff(12324,plain,
% 2.23/2.45 (r(elem!1, s(s(z)))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[493, 12323, 12234])).
% 2.23/2.45 tff(12325,plain,
% 2.23/2.45 ((s(s(elem!1)) = s(z)) <=> (elem!1 = s(z))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[12229])).
% 2.23/2.45 tff(12326,plain,
% 2.23/2.45 ((s(s(elem!1)) = s(z)) <=> (s(z) = elem!1)),
% 2.23/2.45 inference(transitivity,[status(thm)],[12325, 253])).
% 2.23/2.45 tff(12327,plain,
% 2.23/2.45 ((~(s(s(elem!1)) = s(z))) <=> (~(s(z) = elem!1))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[12326])).
% 2.23/2.45 tff(12328,plain,
% 2.23/2.45 (~(s(z) = elem!1)),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[111, 12327])).
% 2.23/2.45 tff(12329,plain,
% 2.23/2.45 (r(z, s(s(elem!1))) <=> r(z, elem!1)),
% 2.23/2.45 inference(monotonicity,[status(thm)],[12229])).
% 2.23/2.45 tff(12330,plain,
% 2.23/2.45 (r(z, elem!1)),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[12126, 12329])).
% 2.23/2.45 tff(12331,plain,
% 2.23/2.45 ((s(elem!1) = s(s(z))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[12236])).
% 2.23/2.45 tff(12332,plain,
% 2.23/2.45 ((s(s(s(elem!1))) = s(s(z))) <=> (s(elem!1) = s(s(z)))),
% 2.23/2.45 inference(symmetry,[status(thm)],[12331])).
% 2.23/2.45 tff(12333,plain,
% 2.23/2.45 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(elem!1) = s(s(z))))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[12332])).
% 2.23/2.45 tff(12334,plain,
% 2.23/2.45 (~(s(elem!1) = s(s(z)))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[283, 12333])).
% 2.23/2.45 tff(12335,plain,
% 2.23/2.45 (b(s(s(s(elem!1))), elem!1) <=> b(s(elem!1), elem!1)),
% 2.23/2.45 inference(monotonicity,[status(thm)],[12235])).
% 2.23/2.45 tff(12336,plain,
% 2.23/2.45 (~(s(s(s(elem!1))) = elem!1)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[714, 12229, 12129])).
% 2.23/2.45 tff(12337,plain,
% 2.23/2.45 (~r(s(s(s(elem!1))), elem!1)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[5310, 12312, 12330])).
% 2.23/2.45 tff(12338,plain,
% 2.23/2.45 (b(s(s(s(elem!1))), elem!1)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[742, 12337, 12336])).
% 2.23/2.45 tff(12339,plain,
% 2.23/2.45 (b(s(elem!1), elem!1)),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[12338, 12335])).
% 2.23/2.45 tff(12340,plain,
% 2.23/2.45 ((~b(s(elem!1), s(z))) <=> (~b(s(s(s(elem!1))), s(z)))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[11020])).
% 2.23/2.45 tff(12341,plain,
% 2.23/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(X0, 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))))),
% 2.23/2.45 inference(rewrite,[status(thm)],[])).
% 2.23/2.45 tff(12342,plain,
% 2.23/2.45 (((~b(s(z), elem!1)) | (~b(s(elem!1), 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))))),
% 2.23/2.45 inference(rewrite,[status(thm)],[])).
% 2.23/2.45 tff(12343,plain,
% 2.23/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(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(X0, 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)))))),
% 2.23/2.45 inference(monotonicity,[status(thm)],[12342])).
% 2.23/2.45 tff(12344,plain,
% 2.23/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(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(X0, 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))))),
% 2.23/2.45 inference(transitivity,[status(thm)],[12343, 12341])).
% 2.23/2.45 tff(12345,plain,
% 2.23/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))),
% 2.23/2.45 inference(quant_inst,[status(thm)],[])).
% 2.23/2.45 tff(12346,plain,
% 2.23/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z)))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[12345, 12344])).
% 2.23/2.45 tff(12347,plain,
% 2.23/2.45 (~b(s(elem!1), s(z))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[12346, 128, 297, 922, 4791])).
% 2.23/2.45 tff(12348,plain,
% 2.23/2.45 (~b(s(s(s(elem!1))), s(z))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[12347, 12340])).
% 2.23/2.45 tff(12349,plain,
% 2.23/2.45 (r(s(s(s(elem!1))), s(z))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[196, 12348])).
% 2.23/2.45 tff(12350,plain,
% 2.23/2.45 (r(s(elem!1), s(z))),
% 2.23/2.45 inference(modus_ponens,[status(thm)],[12349, 11152])).
% 2.23/2.45 tff(12351,plain,
% 2.23/2.45 (~r(s(elem!1), s(z))),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[11182, 4791, 11150, 297, 922, 243, 1416, 240, 759])).
% 2.23/2.45 tff(12352,plain,
% 2.23/2.45 ($false),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[12351, 12350])).
% 2.23/2.45 tff(12353,plain,((~b(s(elem!1), elem!1)) | (~(s(s(elem!1)) = elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~r(z, elem!1)) | (s(elem!1) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.45 tff(12354,plain,
% 2.23/2.45 (~b(s(z), elem!1)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[12353, 12339, 12229, 12334, 12253, 12330])).
% 2.23/2.45 tff(12355,plain,
% 2.23/2.45 (r(s(z), elem!1)),
% 2.23/2.45 inference(unit_resolution,[status(thm)],[665, 12354, 12328])).
% 2.23/2.45 tff(12356,plain,
% 2.23/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(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)))))),
% 2.23/2.45 inference(rewrite,[status(thm)],[])).
% 2.23/2.45 tff(12357,plain,
% 2.23/2.45 (((~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)))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(12358,plain,
% 2.23/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(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))))))),
% 2.23/2.46 inference(monotonicity,[status(thm)],[12357])).
% 2.23/2.46 tff(12359,plain,
% 2.23/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(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)))))),
% 2.23/2.46 inference(transitivity,[status(thm)],[12358, 12356])).
% 2.23/2.46 tff(12360,plain,
% 2.23/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(z), elem!1)))),
% 2.23/2.46 inference(quant_inst,[status(thm)],[])).
% 2.23/2.46 tff(12361,plain,
% 2.23/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z))))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[12360, 12359])).
% 2.23/2.46 tff(12362,plain,
% 2.23/2.46 ($false),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12361, 45, 12355, 12324, 11841])).
% 2.23/2.46 tff(12363,plain,((~r(s(s(s(elem!1))), s(z))) | (s(s(elem!1)) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.46 tff(12364,plain,
% 2.23/2.46 (~r(s(s(s(elem!1))), s(z))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12363, 1])).
% 2.23/2.46 tff(12365,plain,
% 2.23/2.46 (b(s(s(s(elem!1))), s(z))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[196, 12364])).
% 2.23/2.46 tff(12366,plain,
% 2.23/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(12367,plain,
% 2.23/2.46 (((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(12368,plain,
% 2.23/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))))),
% 2.23/2.46 inference(monotonicity,[status(thm)],[12367])).
% 2.23/2.46 tff(12369,plain,
% 2.23/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.23/2.46 inference(transitivity,[status(thm)],[12368, 12366])).
% 2.23/2.46 tff(12370,plain,
% 2.23/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.23/2.46 inference(quant_inst,[status(thm)],[])).
% 2.23/2.46 tff(12371,plain,
% 2.23/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[12370, 12369])).
% 2.23/2.46 tff(12372,plain,
% 2.23/2.46 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12371, 128, 12124, 11833, 7825, 12365])).
% 2.23/2.46 tff(12373,plain,
% 2.23/2.46 (~b(s(s(s(elem!1))), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[8768, 128, 11833, 7825, 12365])).
% 2.23/2.46 tff(12374,plain,
% 2.23/2.46 (r(s(s(s(elem!1))), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[5301, 12373])).
% 2.23/2.46 tff(12375,plain,
% 2.23/2.46 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[9909, 45, 12374, 12140])).
% 2.23/2.46 tff(12376,plain,
% 2.23/2.46 (s(s(elem!1)) = s(s(s(elem!1)))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[321, 12375, 12372])).
% 2.23/2.46 tff(12377,plain,
% 2.23/2.46 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[1065, 12376])).
% 2.23/2.46 tff(12378,plain,
% 2.23/2.46 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[1073, 12377])).
% 2.23/2.46 tff(12379,plain,
% 2.23/2.46 (s(s(elem!1)) = elem!1),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[1089, 12378])).
% 2.23/2.46 tff(12380,plain,
% 2.23/2.46 (s(s(s(elem!1))) = s(s(elem!1))),
% 2.23/2.46 inference(symmetry,[status(thm)],[12376])).
% 2.23/2.46 tff(12381,plain,
% 2.23/2.46 (s(s(s(elem!1))) = elem!1),
% 2.23/2.46 inference(transitivity,[status(thm)],[12380, 12379])).
% 2.23/2.46 tff(12382,plain,
% 2.23/2.46 (b(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.23/2.46 inference(monotonicity,[status(thm)],[12381])).
% 2.23/2.46 tff(12383,plain,
% 2.23/2.46 (b(s(s(s(s(s(s(z)))))), elem!1) <=> b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 2.23/2.46 inference(symmetry,[status(thm)],[12382])).
% 2.23/2.46 tff(12384,plain,
% 2.23/2.46 (~(s(s(s(s(s(s(z)))))) = elem!1)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[1414, 12376])).
% 2.23/2.46 tff(12385,plain,
% 2.23/2.46 (elem!1 = s(s(elem!1))),
% 2.23/2.46 inference(symmetry,[status(thm)],[12379])).
% 2.23/2.46 tff(12386,plain,
% 2.23/2.46 (elem!1 = s(s(s(elem!1)))),
% 2.23/2.46 inference(transitivity,[status(thm)],[12385, 12376])).
% 2.23/2.46 tff(12387,plain,
% 2.23/2.46 (r(z, elem!1) <=> r(z, s(s(s(elem!1))))),
% 2.23/2.46 inference(monotonicity,[status(thm)],[12386])).
% 2.23/2.46 tff(12388,plain,
% 2.23/2.46 (r(z, s(s(s(elem!1)))) <=> r(z, elem!1)),
% 2.23/2.46 inference(symmetry,[status(thm)],[12387])).
% 2.23/2.46 tff(12389,plain,
% 2.23/2.46 (~b(z, s(s(s(elem!1))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[8605, 128, 11833, 7825, 12365])).
% 2.23/2.46 tff(12390,plain,
% 2.23/2.46 (r(z, s(s(s(elem!1))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[858, 12389])).
% 2.23/2.46 tff(12391,plain,
% 2.23/2.46 (r(z, elem!1)),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[12390, 12388])).
% 2.23/2.46 tff(12392,plain,
% 2.23/2.46 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(s(elem!1))))),
% 2.23/2.46 inference(monotonicity,[status(thm)],[12386])).
% 2.23/2.46 tff(12393,plain,
% 2.23/2.46 ((s(s(z)) = elem!1) <=> (s(s(s(elem!1))) = s(s(z)))),
% 2.23/2.46 inference(transitivity,[status(thm)],[12392, 4268])).
% 2.23/2.46 tff(12394,plain,
% 2.23/2.46 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 2.23/2.46 inference(symmetry,[status(thm)],[12393])).
% 2.23/2.46 tff(12395,plain,
% 2.23/2.46 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 2.23/2.46 inference(monotonicity,[status(thm)],[12394])).
% 2.23/2.46 tff(12396,plain,
% 2.23/2.46 (~(s(s(z)) = elem!1)),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[283, 12395])).
% 2.23/2.46 tff(12397,plain,
% 2.23/2.46 (b(elem!1, s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 2.23/2.46 inference(monotonicity,[status(thm)],[12386])).
% 2.23/2.46 tff(12398,plain,
% 2.23/2.46 (b(s(s(s(elem!1))), s(z)) <=> b(elem!1, s(z))),
% 2.23/2.46 inference(symmetry,[status(thm)],[12397])).
% 2.23/2.46 tff(12399,plain,
% 2.23/2.46 (b(elem!1, s(z))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[12365, 12398])).
% 2.23/2.46 tff(12400,plain,
% 2.23/2.46 (~(s(s(s(s(z)))) = elem!1)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[242, 12379])).
% 2.23/2.46 tff(12401,plain,
% 2.23/2.46 (b(s(z), elem!1) <=> b(s(z), s(s(s(elem!1))))),
% 2.23/2.46 inference(monotonicity,[status(thm)],[12386])).
% 2.23/2.46 tff(12402,plain,
% 2.23/2.46 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), elem!1)),
% 2.23/2.46 inference(symmetry,[status(thm)],[12401])).
% 2.23/2.46 tff(12403,plain,
% 2.23/2.46 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 2.23/2.46 inference(monotonicity,[status(thm)],[12380])).
% 2.23/2.46 tff(12404,plain,
% 2.23/2.46 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(elem!1))), s(s(s(elem!1))))),
% 2.23/2.46 inference(monotonicity,[status(thm)],[12403])).
% 2.23/2.46 tff(12405,plain,
% 2.23/2.46 (b(s(s(s(elem!1))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.23/2.46 inference(symmetry,[status(thm)],[12404])).
% 2.23/2.46 tff(12406,plain,
% 2.23/2.46 ((~b(s(s(s(elem!1))), s(s(s(elem!1))))) <=> (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 2.23/2.46 inference(monotonicity,[status(thm)],[12405])).
% 2.23/2.46 tff(12407,plain,
% 2.23/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(12408,plain,
% 2.23/2.46 (((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(elem!1)))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(12409,plain,
% 2.23/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))))),
% 2.23/2.46 inference(monotonicity,[status(thm)],[12408])).
% 2.23/2.46 tff(12410,plain,
% 2.23/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.23/2.46 inference(transitivity,[status(thm)],[12409, 12407])).
% 2.23/2.46 tff(12411,plain,
% 2.23/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(elem!1))))))),
% 2.23/2.46 inference(quant_inst,[status(thm)],[])).
% 2.23/2.46 tff(12412,plain,
% 2.23/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(elem!1))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[12411, 12410])).
% 2.23/2.46 tff(12413,plain,
% 2.23/2.46 (~b(s(s(s(elem!1))), s(s(s(elem!1))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12412, 128, 11833, 7825, 12365])).
% 2.23/2.46 tff(12414,plain,
% 2.23/2.46 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[12413, 12406])).
% 2.23/2.46 tff(12415,plain,
% 2.23/2.46 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(elem!1))), s(s(s(elem!1))))),
% 2.23/2.46 inference(monotonicity,[status(thm)],[12403])).
% 2.23/2.46 tff(12416,plain,
% 2.23/2.46 (r(s(s(s(elem!1))), s(s(s(elem!1)))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.23/2.46 inference(symmetry,[status(thm)],[12415])).
% 2.23/2.46 tff(12417,plain,
% 2.23/2.46 ((~r(s(s(s(elem!1))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 2.23/2.46 inference(monotonicity,[status(thm)],[12416])).
% 2.23/2.46 tff(12418,plain,
% 2.23/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(elem!1))))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(12419,plain,
% 2.23/2.46 (((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(elem!1))))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(12420,plain,
% 2.23/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(elem!1)))))))),
% 2.23/2.46 inference(monotonicity,[status(thm)],[12419])).
% 2.23/2.46 tff(12421,plain,
% 2.23/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(elem!1))))))),
% 2.23/2.46 inference(transitivity,[status(thm)],[12420, 12418])).
% 2.23/2.46 tff(12422,plain,
% 2.23/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(elem!1))))))),
% 2.23/2.46 inference(quant_inst,[status(thm)],[])).
% 2.23/2.46 tff(12423,plain,
% 2.23/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(elem!1)))))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[12422, 12421])).
% 2.23/2.46 tff(12424,plain,
% 2.23/2.46 (~r(s(s(s(elem!1))), s(s(s(elem!1))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12423, 45, 12374])).
% 2.23/2.46 tff(12425,plain,
% 2.23/2.46 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[12424, 12417])).
% 2.23/2.46 tff(12426,plain,
% 2.23/2.46 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[1820, 12425, 12414])).
% 2.23/2.46 tff(12427,plain,
% 2.23/2.46 ((elem!1 = s(z)) <=> (s(s(s(elem!1))) = s(z))),
% 2.23/2.46 inference(monotonicity,[status(thm)],[1101])).
% 2.23/2.46 tff(12428,plain,
% 2.23/2.46 ((elem!1 = s(z)) <=> (s(z) = s(s(s(elem!1))))),
% 2.23/2.46 inference(transitivity,[status(thm)],[12427, 179])).
% 2.23/2.46 tff(12429,plain,
% 2.23/2.46 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(z))),
% 2.23/2.46 inference(symmetry,[status(thm)],[12428])).
% 2.23/2.46 tff(12430,plain,
% 2.23/2.46 ((s(z) = s(s(s(elem!1)))) <=> (s(z) = elem!1)),
% 2.23/2.46 inference(transitivity,[status(thm)],[12429, 253])).
% 2.23/2.46 tff(12431,plain,
% 2.23/2.46 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(z) = elem!1))),
% 2.23/2.46 inference(monotonicity,[status(thm)],[12430])).
% 2.23/2.46 tff(12432,plain,
% 2.23/2.46 (~(s(z) = elem!1)),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[190, 12431])).
% 2.23/2.46 tff(12433,plain,
% 2.23/2.46 (r(z, elem!1)),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[424, 8848])).
% 2.23/2.46 tff(12434,plain,
% 2.23/2.46 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(s(elem!1))))),
% 2.23/2.46 inference(monotonicity,[status(thm)],[1101])).
% 2.23/2.46 tff(12435,plain,
% 2.23/2.46 ((s(s(z)) = elem!1) <=> (s(s(s(elem!1))) = s(s(z)))),
% 2.23/2.46 inference(transitivity,[status(thm)],[12434, 4268])).
% 2.23/2.46 tff(12436,plain,
% 2.23/2.46 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 2.23/2.46 inference(symmetry,[status(thm)],[12435])).
% 2.23/2.46 tff(12437,plain,
% 2.23/2.46 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 2.23/2.46 inference(monotonicity,[status(thm)],[12436])).
% 2.23/2.46 tff(12438,plain,
% 2.23/2.46 (~(s(s(z)) = elem!1)),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[283, 12437])).
% 2.23/2.46 tff(12439,plain,
% 2.23/2.46 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[10399, 323, 424])).
% 2.23/2.46 tff(12440,plain,
% 2.23/2.46 (~r(s(s(z)), elem!1)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[1107, 12439, 307])).
% 2.23/2.46 tff(12441,plain,
% 2.23/2.46 (b(s(s(z)), elem!1)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[370, 12440, 12438])).
% 2.23/2.46 tff(12442,plain,
% 2.23/2.46 (~b(s(z), elem!1)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12280, 12441, 1412, 8794, 297, 12433])).
% 2.23/2.46 tff(12443,plain,
% 2.23/2.46 (~r(elem!1, s(s(z)))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[7464, 323, 11841, 307])).
% 2.23/2.46 tff(12444,plain,
% 2.23/2.46 ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[8803, 45, 424])).
% 2.23/2.46 tff(12445,plain,
% 2.23/2.46 (~r(s(s(s(s(s(s(z)))))), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12444, 1197])).
% 2.23/2.46 tff(12446,plain,
% 2.23/2.46 (b(s(s(s(s(s(s(z)))))), z)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[1022, 21, 1019, 12445])).
% 2.23/2.46 tff(12447,plain,
% 2.23/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(12448,plain,
% 2.23/2.46 (((~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(s(s(z))))))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(12449,plain,
% 2.23/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(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(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))))),
% 2.23/2.46 inference(monotonicity,[status(thm)],[12448])).
% 2.23/2.46 tff(12450,plain,
% 2.23/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(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(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 2.23/2.46 inference(transitivity,[status(thm)],[12449, 12447])).
% 2.23/2.46 tff(12451,plain,
% 2.23/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 2.23/2.46 inference(quant_inst,[status(thm)],[])).
% 2.23/2.46 tff(12452,plain,
% 2.23/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[12451, 12450])).
% 2.23/2.46 tff(12453,plain,
% 2.23/2.46 ((~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12452, 45, 323])).
% 2.23/2.46 tff(12454,plain,
% 2.23/2.46 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12453, 1197])).
% 2.23/2.46 tff(12455,plain,
% 2.23/2.46 (b(s(z), s(s(s(s(s(s(z)))))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[1041, 21, 1038, 12454])).
% 2.23/2.46 tff(12456,plain,
% 2.23/2.46 (((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z))))))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(12457,plain,
% 2.23/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z))))))))))),
% 2.23/2.46 inference(monotonicity,[status(thm)],[12456])).
% 2.23/2.46 tff(12458,plain,
% 2.23/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 2.23/2.46 inference(transitivity,[status(thm)],[12457, 9822])).
% 2.23/2.46 tff(12459,plain,
% 2.23/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 2.23/2.46 inference(quant_inst,[status(thm)],[])).
% 2.23/2.46 tff(12460,plain,
% 2.23/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z))))))))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[12459, 12458])).
% 2.23/2.46 tff(12461,plain,
% 2.23/2.46 ($false),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12460, 128, 550, 3527, 12455, 12446])).
% 2.23/2.46 tff(12462,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.46 tff(12463,plain,
% 2.23/2.46 ((~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12462, 7825])).
% 2.23/2.46 tff(12464,plain,
% 2.23/2.46 (~r(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12463, 323, 424, 11833])).
% 2.23/2.46 tff(12465,plain,
% 2.23/2.46 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[1098, 12464, 307])).
% 2.23/2.46 tff(12466,plain,
% 2.23/2.46 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[1055, 12465, 8794])).
% 2.23/2.46 tff(12467,plain,
% 2.23/2.46 (~r(s(z), elem!1)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[8761, 12466, 11833, 1090, 696, 12433, 12440, 12443])).
% 2.23/2.46 tff(12468,plain,
% 2.23/2.46 ($false),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[665, 12467, 12442, 12432])).
% 2.23/2.46 tff(12469,plain,((~r(s(z), s(s(s(elem!1))))) | (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.46 tff(12470,plain,
% 2.23/2.46 (~r(s(z), s(s(s(elem!1))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12469, 12426, 12399, 12376, 12390])).
% 2.23/2.46 tff(12471,plain,
% 2.23/2.46 (b(s(z), s(s(s(elem!1))))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[339, 12470])).
% 2.23/2.46 tff(12472,plain,
% 2.23/2.46 (b(s(z), elem!1)),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[12471, 12402])).
% 2.23/2.46 tff(12473,plain,
% 2.23/2.46 (~b(s(s(z)), elem!1)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[12280, 12472, 12400, 12384, 12399, 12391])).
% 2.23/2.46 tff(12474,plain,
% 2.23/2.46 (r(s(s(z)), elem!1)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[370, 12473, 12396])).
% 2.23/2.46 tff(12475,plain,
% 2.23/2.46 (~r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[1451, 12474, 12391])).
% 2.23/2.46 tff(12476,plain,
% 2.23/2.46 (b(s(s(s(s(s(s(z)))))), elem!1)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[1055, 12475, 12384])).
% 2.23/2.46 tff(12477,plain,
% 2.23/2.46 (b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 2.23/2.46 inference(modus_ponens,[status(thm)],[12476, 12383])).
% 2.23/2.46 tff(12478,plain,
% 2.23/2.46 (~r(s(s(s(s(z)))), elem!1)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[1469, 12474, 12391])).
% 2.23/2.46 tff(12479,plain,
% 2.23/2.46 (b(s(s(s(s(z)))), elem!1)),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[632, 12478, 12400])).
% 2.23/2.46 tff(12480,plain,
% 2.23/2.46 (b(s(s(s(s(s(s(z)))))), s(z))),
% 2.23/2.46 inference(unit_resolution,[status(thm)],[10614, 12476, 12399, 12472, 12479])).
% 2.23/2.46 tff(12481,plain,
% 2.23/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(12482,plain,
% 2.23/2.46 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 2.23/2.46 inference(rewrite,[status(thm)],[])).
% 2.23/2.46 tff(12483,plain,
% 2.23/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))))),
% 2.23/2.46 inference(monotonicity,[status(thm)],[12482])).
% 2.23/2.46 tff(12484,plain,
% 2.23/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))))),
% 2.23/2.47 inference(transitivity,[status(thm)],[12483, 12481])).
% 2.23/2.47 tff(12485,plain,
% 2.23/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 2.23/2.47 inference(quant_inst,[status(thm)],[])).
% 2.23/2.47 tff(12486,plain,
% 2.23/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1)))))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[12485, 12484])).
% 2.23/2.47 tff(12487,plain,
% 2.23/2.47 (~b(s(s(s(s(s(s(z)))))), s(s(s(elem!1))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[12486, 128, 12471, 12365, 12480])).
% 2.23/2.47 tff(12488,plain,
% 2.23/2.47 ($false),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[12487, 12477])).
% 2.23/2.47 tff(12489,plain,(s(s(elem!1)) = s(s(z))), inference(lemma,lemma(discharge,[]))).
% 2.23/2.47 tff(12490,plain,
% 2.23/2.47 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[12489])).
% 2.23/2.47 tff(12491,plain,
% 2.23/2.47 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.23/2.47 inference(symmetry,[status(thm)],[12490])).
% 2.23/2.47 tff(12492,plain,
% 2.23/2.47 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[12491])).
% 2.23/2.47 tff(12493,plain,
% 2.23/2.47 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(z))))),
% 2.23/2.47 inference(symmetry,[status(thm)],[12492])).
% 2.23/2.47 tff(12494,plain,
% 2.23/2.47 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[12489])).
% 2.23/2.47 tff(12495,plain,
% 2.23/2.47 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(z))))),
% 2.23/2.47 inference(transitivity,[status(thm)],[12494, 12493])).
% 2.23/2.47 tff(12496,plain,
% 2.23/2.47 (s(s(z)) = s(s(elem!1))),
% 2.23/2.47 inference(symmetry,[status(thm)],[12489])).
% 2.23/2.47 tff(12497,plain,
% 2.23/2.47 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[12496])).
% 2.23/2.47 tff(12498,plain,
% 2.23/2.47 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 2.23/2.47 inference(transitivity,[status(thm)],[12497, 799])).
% 2.23/2.47 tff(12499,plain,
% 2.23/2.47 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[12498])).
% 2.23/2.47 tff(12500,plain,
% 2.23/2.47 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[283, 12499])).
% 2.23/2.47 tff(12501,plain,
% 2.23/2.47 (r(s(s(elem!1)), s(z)) <=> r(s(s(z)), s(z))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[12489])).
% 2.23/2.47 tff(12502,plain,
% 2.23/2.47 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(z))),
% 2.23/2.47 inference(symmetry,[status(thm)],[12501])).
% 2.23/2.47 tff(12503,plain,
% 2.23/2.47 (r(s(s(elem!1)), s(z))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[11848, 12502])).
% 2.23/2.47 tff(12504,plain,
% 2.23/2.47 (r(s(s(z)), s(s(elem!1))) <=> r(s(s(z)), s(s(z)))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[12489])).
% 2.23/2.47 tff(12505,plain,
% 2.23/2.47 (r(s(s(z)), s(s(z))) <=> r(s(s(z)), s(s(elem!1)))),
% 2.23/2.47 inference(symmetry,[status(thm)],[12504])).
% 2.23/2.47 tff(12506,plain,
% 2.23/2.47 ((~r(s(s(z)), s(s(z)))) <=> (~r(s(s(z)), s(s(elem!1))))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[12505])).
% 2.23/2.47 tff(12507,plain,
% 2.23/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(z)))))),
% 2.23/2.47 inference(rewrite,[status(thm)],[])).
% 2.23/2.47 tff(12508,plain,
% 2.23/2.47 (((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(z)))))),
% 2.23/2.47 inference(rewrite,[status(thm)],[])).
% 2.23/2.47 tff(12509,plain,
% 2.23/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(z))))))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[12508])).
% 2.23/2.47 tff(12510,plain,
% 2.23/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(z)))))),
% 2.23/2.47 inference(transitivity,[status(thm)],[12509, 12507])).
% 2.23/2.47 tff(12511,plain,
% 2.23/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(z)))))),
% 2.23/2.47 inference(quant_inst,[status(thm)],[])).
% 2.23/2.47 tff(12512,plain,
% 2.23/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(z))))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[12511, 12510])).
% 2.23/2.47 tff(12513,plain,
% 2.23/2.47 (~r(s(s(z)), s(s(z)))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[12512, 45, 11848])).
% 2.23/2.47 tff(12514,plain,
% 2.23/2.47 (~r(s(s(z)), s(s(elem!1)))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[12513, 12506])).
% 2.23/2.47 tff(12515,plain,
% 2.23/2.47 (r(s(s(elem!1)), s(s(z))) <=> r(s(s(z)), s(s(z)))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[12489])).
% 2.23/2.47 tff(12516,plain,
% 2.23/2.47 (r(s(s(z)), s(s(z))) <=> r(s(s(elem!1)), s(s(z)))),
% 2.23/2.47 inference(symmetry,[status(thm)],[12515])).
% 2.23/2.47 tff(12517,plain,
% 2.23/2.47 ((~r(s(s(z)), s(s(z)))) <=> (~r(s(s(elem!1)), s(s(z))))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[12516])).
% 2.23/2.47 tff(12518,plain,
% 2.23/2.47 (~r(s(s(elem!1)), s(s(z)))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[12513, 12517])).
% 2.23/2.47 tff(12519,plain,
% 2.23/2.47 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[12496])).
% 2.23/2.47 tff(12520,plain,
% 2.23/2.47 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[12519])).
% 2.23/2.47 tff(12521,plain,
% 2.23/2.47 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[239, 12520])).
% 2.23/2.47 tff(12522,plain,
% 2.23/2.47 ((s(s(elem!1)) = elem!1) <=> (s(s(z)) = elem!1)),
% 2.23/2.47 inference(monotonicity,[status(thm)],[12489])).
% 2.23/2.47 tff(12523,plain,
% 2.23/2.47 ((s(s(z)) = elem!1) <=> (s(s(elem!1)) = elem!1)),
% 2.23/2.47 inference(symmetry,[status(thm)],[12522])).
% 2.23/2.47 tff(12524,plain,
% 2.23/2.47 (z = elem!1),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[4260, 12489])).
% 2.23/2.47 tff(12525,plain,
% 2.23/2.47 ((s(s(z)) = z) <=> (s(s(z)) = elem!1)),
% 2.23/2.47 inference(monotonicity,[status(thm)],[12524])).
% 2.23/2.47 tff(12526,plain,
% 2.23/2.47 ((s(s(z)) = z) <=> (s(s(elem!1)) = elem!1)),
% 2.23/2.47 inference(transitivity,[status(thm)],[12525, 12523])).
% 2.23/2.47 tff(12527,plain,
% 2.23/2.47 ((~(s(s(z)) = z)) <=> (~(s(s(elem!1)) = elem!1))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[12526])).
% 2.23/2.47 tff(12528,plain,
% 2.23/2.47 (~(s(s(elem!1)) = elem!1)),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[11, 12527])).
% 2.23/2.47 tff(12529,plain,
% 2.23/2.47 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(z)))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[12489])).
% 2.23/2.47 tff(12530,plain,
% 2.23/2.47 (r(s(z), s(s(z))) <=> r(s(z), s(s(elem!1)))),
% 2.23/2.47 inference(symmetry,[status(thm)],[12529])).
% 2.23/2.47 tff(12531,plain,
% 2.23/2.47 (r(s(z), s(s(elem!1)))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[11841, 12530])).
% 2.23/2.47 tff(12532,plain,
% 2.23/2.47 ((~(s(s(elem!1)) = s(s(z)))) | (~r(s(s(z)), s(z))) | r(s(s(s(s(s(s(z)))))), elem!1) | (~r(s(z), s(s(elem!1)))) | (s(s(elem!1)) = elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[11643, 10906])).
% 2.23/2.47 tff(12533,plain,
% 2.23/2.47 (r(s(s(s(s(s(s(z)))))), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[12532, 12531, 12489, 11848, 12528])).
% 2.23/2.47 tff(12534,plain,
% 2.23/2.47 (~b(s(s(s(elem!1))), s(z))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[11930, 12533, 11833, 12521, 12518, 12503, 12514])).
% 2.23/2.47 tff(12535,plain,
% 2.23/2.47 (r(s(s(s(elem!1))), s(z))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[196, 12534])).
% 2.23/2.47 tff(12536,plain,
% 2.23/2.47 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[393, 12535, 12503])).
% 2.23/2.47 tff(12537,plain,
% 2.23/2.47 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[321, 12536, 12500])).
% 2.23/2.47 tff(12538,plain,
% 2.23/2.47 (b(s(s(z)), s(s(s(z))))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[12537, 12495])).
% 2.23/2.47 tff(12539,plain,
% 2.23/2.47 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 2.23/2.47 inference(monotonicity,[status(thm)],[12491])).
% 2.23/2.47 tff(12540,plain,
% 2.23/2.47 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), elem!1)),
% 2.23/2.47 inference(symmetry,[status(thm)],[12539])).
% 2.23/2.47 tff(12541,plain,
% 2.23/2.47 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 2.23/2.47 inference(monotonicity,[status(thm)],[12524])).
% 2.23/2.47 tff(12542,plain,
% 2.23/2.47 ((s(s(s(elem!1))) = z) <=> (elem!1 = s(s(s(elem!1))))),
% 2.23/2.47 inference(transitivity,[status(thm)],[12541, 705])).
% 2.23/2.47 tff(12543,plain,
% 2.23/2.47 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 2.23/2.47 inference(transitivity,[status(thm)],[12542, 982])).
% 2.23/2.47 tff(12544,plain,
% 2.23/2.47 ((~(s(s(s(elem!1))) = z)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[12543])).
% 2.23/2.47 tff(12545,plain,
% 2.23/2.47 (~(s(s(s(elem!1))) = elem!1)),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[382, 12544])).
% 2.23/2.47 tff(12546,plain,
% 2.23/2.47 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[693, 12500])).
% 2.23/2.47 tff(12547,plain,
% 2.23/2.47 ((~(s(s(elem!1)) = s(s(z)))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(z)))))), elem!1)) | (~r(s(s(s(elem!1))), z)) | (~b(z, s(z)))),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[11901, 10906])).
% 2.23/2.47 tff(12548,plain,
% 2.23/2.47 (~r(s(s(s(elem!1))), z)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[12547, 12546, 11833, 12489, 12533])).
% 2.23/2.47 tff(12549,plain,
% 2.23/2.47 (~r(s(s(s(elem!1))), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[2453, 12548, 12524])).
% 2.23/2.47 tff(12550,plain,
% 2.23/2.47 (b(s(s(s(elem!1))), elem!1)),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[742, 12549, 12545])).
% 2.23/2.47 tff(12551,plain,
% 2.23/2.47 (b(s(s(s(z))), elem!1)),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[12550, 12540])).
% 2.23/2.47 tff(12552,plain,
% 2.23/2.47 (b(s(s(z)), z) <=> b(s(s(z)), elem!1)),
% 2.23/2.47 inference(monotonicity,[status(thm)],[12524])).
% 2.23/2.47 tff(12553,plain,
% 2.23/2.47 (b(s(s(z)), elem!1)),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[10906, 12552])).
% 2.23/2.47 tff(12554,plain,
% 2.23/2.47 (b(s(z), z) <=> b(s(z), elem!1)),
% 2.23/2.47 inference(monotonicity,[status(thm)],[12524])).
% 2.23/2.47 tff(12555,plain,
% 2.23/2.47 (b(s(z), elem!1)),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[7825, 12554])).
% 2.23/2.47 tff(12556,plain,
% 2.23/2.47 (b(z, s(z)) <=> b(elem!1, s(z))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[12524])).
% 2.23/2.47 tff(12557,plain,
% 2.23/2.47 (b(elem!1, s(z))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[11833, 12556])).
% 2.23/2.47 tff(12558,plain,
% 2.23/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, 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(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.23/2.47 inference(rewrite,[status(thm)],[])).
% 2.23/2.47 tff(12559,plain,
% 2.23/2.47 (((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, 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(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.23/2.47 inference(rewrite,[status(thm)],[])).
% 2.23/2.47 tff(12560,plain,
% 2.23/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(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(X0, 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(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 2.23/2.47 inference(monotonicity,[status(thm)],[12559])).
% 2.23/2.47 tff(12561,plain,
% 2.23/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(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(X0, 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(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 2.23/2.47 inference(transitivity,[status(thm)],[12560, 12558])).
% 2.23/2.47 tff(12562,plain,
% 2.23/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))))),
% 2.23/2.47 inference(quant_inst,[status(thm)],[])).
% 2.23/2.47 tff(12563,plain,
% 2.23/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 2.23/2.47 inference(modus_ponens,[status(thm)],[12562, 12561])).
% 2.23/2.47 tff(12564,plain,
% 2.23/2.47 ($false),
% 2.23/2.47 inference(unit_resolution,[status(thm)],[12563, 128, 12557, 12555, 12553, 12551, 12538])).
% 2.23/2.47 % SZS output end Proof
% 2.23/2.47 % E exiting
%------------------------------------------------------------------------------