%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRA136-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 06:33:47 PM UTC 2026
% Result : Unsatisfiable 1.12s 1.31s
% Output : Proof 2.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRA136-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.13/0.31 % Computer : n013.cluster.edu
% 0.13/0.31 % Model : x86_64 x86_64
% 0.13/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.31 % Memory : 8042.1875MB
% 0.13/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.31 % CPULimit : 300
% 0.13/0.31 % WCLimit : 300
% 0.13/0.31 % DateTime : Mon May 4 23:02:27 EDT 2026
% 0.13/0.31 % CPUTime :
% 1.12/1.31 % SZS status Unsatisfiable
% 1.12/1.31 % SZS output start Proof
% 1.12/1.31 tff(r_type, type, (
% 1.12/1.31 r: ( $i * $i ) > $o)).
% 1.12/1.31 tff(s_type, type, (
% 1.12/1.31 s: $i > $i)).
% 1.12/1.31 tff(z_type, type, (
% 1.12/1.31 z: $i)).
% 1.12/1.31 tff(elem_1_type, type, (
% 1.12/1.31 elem_1: $i)).
% 1.12/1.31 tff(b_type, type, (
% 1.12/1.31 b: ( $i * $i ) > $o)).
% 1.12/1.31 tff(inj_0_type, type, (
% 1.12/1.31 inj_0: $i > $i)).
% 1.12/1.31 tff(1,assumption,(~b(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.12/1.31 tff(2,plain,
% 1.12/1.31 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.12/1.31 inference(rewrite,[status(thm)],[])).
% 1.12/1.31 tff(3,plain,
% 1.12/1.31 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.12/1.31 inference(rewrite,[status(thm)],[])).
% 1.12/1.31 tff(4,plain,
% 1.12/1.31 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.12/1.31 inference(rewrite,[status(thm)],[])).
% 1.12/1.31 tff(5,axiom,(![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sinj')).
% 1.12/1.31 tff(6,plain,
% 1.12/1.31 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.12/1.31 inference(modus_ponens,[status(thm)],[5, 4])).
% 1.12/1.31 tff(7,plain,(
% 1.12/1.31 ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.12/1.31 inference(skolemize,[status(sab)],[6])).
% 1.12/1.31 tff(8,plain,
% 1.12/1.31 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.12/1.31 inference(modus_ponens,[status(thm)],[7, 3])).
% 1.12/1.31 tff(9,plain,
% 1.12/1.31 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.12/1.31 inference(modus_ponens,[status(thm)],[8, 2])).
% 1.12/1.31 tff(10,plain,
% 1.12/1.31 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.12/1.31 inference(quant_inst,[status(thm)],[])).
% 1.12/1.31 tff(11,plain,
% 1.12/1.31 (inj_0(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.12/1.31 inference(unit_resolution,[status(thm)],[10, 9])).
% 1.12/1.31 tff(12,assumption,(~r(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 1.12/1.31 tff(13,assumption,(~r(z, elem!1)), introduced(assumption)).
% 1.12/1.31 tff(14,assumption,(~b(elem!1, s(z))), introduced(assumption)).
% 1.12/1.31 tff(15,assumption,(~(s(s(z)) = elem!1)), introduced(assumption)).
% 1.12/1.31 tff(16,assumption,(~(s(s(s(z))) = s(s(elem!1)))), introduced(assumption)).
% 1.12/1.31 tff(17,assumption,(elem!1 = s(z)), introduced(assumption)).
% 1.12/1.31 tff(18,plain,
% 1.12/1.31 (s(elem!1) = s(s(z))),
% 1.12/1.31 inference(monotonicity,[status(thm)],[17])).
% 1.12/1.31 tff(19,plain,
% 1.12/1.31 (s(s(elem!1)) = s(s(s(z)))),
% 1.12/1.31 inference(monotonicity,[status(thm)],[18])).
% 1.12/1.31 tff(20,plain,
% 1.12/1.31 (s(s(s(z))) = s(s(elem!1))),
% 1.12/1.31 inference(symmetry,[status(thm)],[19])).
% 1.12/1.31 tff(21,plain,
% 1.12/1.31 (b(s(s(s(z))), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.12/1.31 inference(monotonicity,[status(thm)],[20])).
% 1.12/1.31 tff(22,plain,
% 1.12/1.31 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(s(z))), s(s(s(z))))),
% 1.12/1.31 inference(symmetry,[status(thm)],[21])).
% 1.12/1.31 tff(23,plain,
% 1.12/1.31 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.12/1.31 inference(monotonicity,[status(thm)],[20, 19])).
% 1.12/1.31 tff(24,plain,
% 1.12/1.31 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(s(z))))),
% 1.12/1.31 inference(monotonicity,[status(thm)],[19])).
% 1.12/1.31 tff(25,plain,
% 1.12/1.31 (r(s(s(s(z))), s(s(s(z)))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 1.12/1.31 inference(symmetry,[status(thm)],[24])).
% 1.12/1.31 tff(26,plain,
% 1.12/1.31 ((~r(s(s(s(z))), s(s(s(z))))) <=> (~r(s(s(s(z))), s(s(elem!1))))),
% 1.12/1.31 inference(monotonicity,[status(thm)],[25])).
% 1.12/1.31 tff(27,assumption,(r(s(s(s(z))), s(s(elem!1)))), introduced(assumption)).
% 1.12/1.31 tff(28,plain,
% 1.12/1.31 (^[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))))),
% 1.12/1.31 inference(bind,[status(th)],[])).
% 1.12/1.31 tff(29,plain,
% 1.12/1.31 (![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)))),
% 1.12/1.31 inference(quant_intro,[status(thm)],[28])).
% 1.12/1.31 tff(30,plain,
% 1.12/1.31 (![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)))),
% 1.12/1.31 inference(rewrite,[status(thm)],[])).
% 1.12/1.31 tff(31,plain,
% 1.12/1.31 (^[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)))))),
% 1.12/1.32 inference(bind,[status(th)],[])).
% 1.12/1.32 tff(32,plain,
% 1.12/1.32 (![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)))),
% 1.12/1.32 inference(quant_intro,[status(thm)],[31])).
% 1.12/1.32 tff(33,axiom,(![X0: $i, X3: $i, X2: $i, X1: $i] : ((((~r(X0, X1)) | (~r(X1, X2))) | (~r(X0, X3))) | (~r(X1, X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axr')).
% 1.12/1.32 tff(34,plain,
% 1.12/1.32 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 1.12/1.32 inference(modus_ponens,[status(thm)],[33, 32])).
% 1.12/1.32 tff(35,plain,
% 1.12/1.32 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 1.12/1.32 inference(modus_ponens,[status(thm)],[34, 30])).
% 1.12/1.32 tff(36,plain,(
% 1.12/1.32 ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 1.12/1.32 inference(skolemize,[status(sab)],[35])).
% 1.12/1.32 tff(37,plain,
% 1.12/1.32 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 1.12/1.32 inference(modus_ponens,[status(thm)],[36, 29])).
% 1.12/1.32 tff(38,plain,
% 1.12/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.12/1.32 inference(rewrite,[status(thm)],[])).
% 1.12/1.32 tff(39,plain,
% 1.12/1.32 (((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.12/1.32 inference(rewrite,[status(thm)],[])).
% 1.12/1.32 tff(40,plain,
% 1.12/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1))))))),
% 1.12/1.32 inference(monotonicity,[status(thm)],[39])).
% 1.12/1.32 tff(41,plain,
% 1.12/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.12/1.32 inference(transitivity,[status(thm)],[40, 38])).
% 1.12/1.32 tff(42,plain,
% 1.12/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(z))))))),
% 1.12/1.32 inference(quant_inst,[status(thm)],[])).
% 1.12/1.32 tff(43,plain,
% 1.12/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1))))),
% 1.12/1.32 inference(modus_ponens,[status(thm)],[42, 41])).
% 1.12/1.32 tff(44,plain,
% 1.12/1.32 (~r(s(s(s(z))), s(s(s(z))))),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[43, 37, 27])).
% 1.12/1.32 tff(45,plain,
% 1.12/1.32 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.12/1.32 inference(modus_ponens,[status(thm)],[44, 26])).
% 1.12/1.32 tff(46,plain,
% 1.12/1.32 ($false),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[27, 45])).
% 1.12/1.32 tff(47,plain,((~(elem!1 = s(z))) | (~r(s(s(s(z))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.12/1.32 tff(48,plain,
% 1.12/1.32 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[47, 17])).
% 1.12/1.32 tff(49,plain,
% 1.12/1.32 (^[Y: $i, X: $i] : refl(((X = Y) | b(X, Y) | r(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 1.12/1.32 inference(bind,[status(th)],[])).
% 1.12/1.32 tff(50,plain,
% 1.12/1.32 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.12/1.32 inference(quant_intro,[status(thm)],[49])).
% 1.12/1.32 tff(51,plain,
% 1.12/1.32 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.12/1.32 inference(rewrite,[status(thm)],[])).
% 1.12/1.32 tff(52,plain,
% 1.12/1.32 (^[Y: $i, X: $i] : rewrite((((X = Y) | r(X, Y)) | b(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 1.12/1.32 inference(bind,[status(th)],[])).
% 1.12/1.32 tff(53,plain,
% 1.12/1.32 (![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.12/1.32 inference(quant_intro,[status(thm)],[52])).
% 1.12/1.32 tff(54,axiom,(![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rb')).
% 1.12/1.32 tff(55,plain,
% 1.12/1.32 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.12/1.32 inference(modus_ponens,[status(thm)],[54, 53])).
% 1.12/1.32 tff(56,plain,
% 1.12/1.32 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.12/1.32 inference(modus_ponens,[status(thm)],[55, 51])).
% 1.12/1.32 tff(57,plain,(
% 1.12/1.32 ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.12/1.32 inference(skolemize,[status(sab)],[56])).
% 1.12/1.32 tff(58,plain,
% 1.12/1.32 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.12/1.32 inference(modus_ponens,[status(thm)],[57, 50])).
% 1.12/1.32 tff(59,plain,
% 1.12/1.32 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1))) | r(s(s(s(z))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1))) | r(s(s(s(z))), s(s(elem!1))))),
% 1.12/1.32 inference(rewrite,[status(thm)],[])).
% 1.12/1.32 tff(60,plain,
% 1.12/1.32 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1))) | r(s(s(s(z))), s(s(elem!1))))),
% 1.12/1.32 inference(quant_inst,[status(thm)],[])).
% 1.12/1.32 tff(61,plain,
% 1.12/1.32 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1))) | r(s(s(s(z))), s(s(elem!1)))),
% 1.12/1.32 inference(modus_ponens,[status(thm)],[60, 59])).
% 1.12/1.32 tff(62,plain,
% 1.12/1.32 ((s(s(s(z))) = s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1))) | r(s(s(s(z))), s(s(elem!1)))),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[61, 58])).
% 1.12/1.32 tff(63,plain,
% 1.12/1.32 (b(s(s(s(z))), s(s(elem!1)))),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[62, 48, 16])).
% 1.12/1.32 tff(64,plain,
% 1.12/1.32 (b(s(s(elem!1)), s(s(s(z))))),
% 1.12/1.32 inference(modus_ponens,[status(thm)],[63, 23])).
% 1.12/1.32 tff(65,plain,
% 1.12/1.32 (b(s(s(s(z))), s(s(s(z))))),
% 1.12/1.32 inference(modus_ponens,[status(thm)],[64, 22])).
% 1.12/1.32 tff(66,plain,
% 1.12/1.32 (^[X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : refl(((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))))),
% 1.12/1.32 inference(bind,[status(th)],[])).
% 1.12/1.32 tff(67,plain,
% 1.12/1.32 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.12/1.32 inference(quant_intro,[status(thm)],[66])).
% 1.12/1.32 tff(68,plain,
% 1.12/1.32 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.12/1.32 inference(rewrite,[status(thm)],[])).
% 1.12/1.32 tff(69,plain,
% 1.12/1.32 (^[X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(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(X1, X4))) <=> (((~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X1, X4))))), rewrite((((~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X1, X4))) <=> ((~b(X1, 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(X1, X4))) <=> ((~b(X1, 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(X1, X4))) | (~b(X3, X4))) <=> (((~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X3, X4))))), rewrite((((~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X3, X4))) <=> ((~b(X3, X4)) | (~b(X1, 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(X1, X4))) | (~b(X3, X4))) <=> ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))))),
% 1.12/1.32 inference(bind,[status(th)],[])).
% 1.12/1.32 tff(70,plain,
% 1.12/1.32 (![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(X1, X4))) | (~b(X3, X4))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.12/1.32 inference(quant_intro,[status(thm)],[69])).
% 1.12/1.32 tff(71,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(X1, X4))) | (~b(X3, X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axb')).
% 1.12/1.32 tff(72,plain,
% 1.12/1.32 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.12/1.32 inference(modus_ponens,[status(thm)],[71, 70])).
% 1.12/1.32 tff(73,plain,
% 1.12/1.32 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.12/1.32 inference(modus_ponens,[status(thm)],[72, 68])).
% 1.12/1.32 tff(74,plain,(
% 1.12/1.32 ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.12/1.32 inference(skolemize,[status(sab)],[73])).
% 1.12/1.32 tff(75,plain,
% 1.12/1.32 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.12/1.32 inference(modus_ponens,[status(thm)],[74, 67])).
% 1.12/1.32 tff(76,plain,
% 1.12/1.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(z))))))),
% 1.12/1.32 inference(rewrite,[status(thm)],[])).
% 1.12/1.32 tff(77,plain,
% 1.12/1.32 (((~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(z)))))) <=> (~b(s(s(s(z))), s(s(s(z)))))),
% 1.12/1.32 inference(rewrite,[status(thm)],[])).
% 1.12/1.32 tff(78,plain,
% 1.12/1.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(z))))))),
% 1.12/1.32 inference(monotonicity,[status(thm)],[77])).
% 1.12/1.32 tff(79,plain,
% 1.12/1.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(z))))))),
% 1.12/1.32 inference(transitivity,[status(thm)],[78, 76])).
% 1.12/1.32 tff(80,plain,
% 1.12/1.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(z))))))),
% 1.12/1.32 inference(quant_inst,[status(thm)],[])).
% 1.12/1.32 tff(81,plain,
% 1.12/1.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(z)))))),
% 1.12/1.32 inference(modus_ponens,[status(thm)],[80, 79])).
% 1.12/1.32 tff(82,plain,
% 1.12/1.32 (~b(s(s(s(z))), s(s(s(z))))),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[81, 75])).
% 1.12/1.32 tff(83,plain,
% 1.12/1.32 ($false),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[82, 65])).
% 1.12/1.32 tff(84,plain,((~(elem!1 = s(z))) | (s(s(s(z))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.12/1.32 tff(85,plain,
% 1.12/1.32 (~(elem!1 = s(z))),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[84, 16])).
% 1.12/1.32 tff(86,plain,
% 1.12/1.32 (((~![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)))),
% 1.12/1.32 inference(rewrite,[status(thm)],[])).
% 1.12/1.32 tff(87,plain,
% 1.12/1.32 ((~![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)))),
% 1.12/1.32 inference(quant_inst,[status(thm)],[])).
% 1.12/1.32 tff(88,plain,
% 1.12/1.32 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z))),
% 1.12/1.32 inference(modus_ponens,[status(thm)],[87, 86])).
% 1.12/1.32 tff(89,plain,
% 1.12/1.32 ((elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z))),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[88, 58])).
% 1.12/1.32 tff(90,plain,
% 1.12/1.32 (r(elem!1, s(z))),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[89, 85, 14])).
% 1.12/1.32 tff(91,plain,
% 1.12/1.32 ((elem!1 = s(z)) <=> (s(z) = elem!1)),
% 1.12/1.32 inference(commutativity,[status(thm)],[])).
% 1.12/1.32 tff(92,plain,
% 1.12/1.32 ((s(z) = elem!1) <=> (elem!1 = s(z))),
% 1.12/1.32 inference(symmetry,[status(thm)],[91])).
% 1.12/1.32 tff(93,assumption,(s(z) = elem!1), introduced(assumption)).
% 1.12/1.32 tff(94,plain,
% 1.12/1.32 (elem!1 = s(z)),
% 1.12/1.32 inference(modus_ponens,[status(thm)],[93, 92])).
% 1.12/1.32 tff(95,assumption,(~(elem!1 = s(z))), introduced(assumption)).
% 1.12/1.32 tff(96,plain,
% 1.12/1.32 ($false),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[95, 94])).
% 1.12/1.32 tff(97,plain,((~(s(z) = elem!1)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.12/1.32 tff(98,plain,
% 1.12/1.32 (~(s(z) = elem!1)),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[97, 85])).
% 1.12/1.32 tff(99,assumption,(~b(s(s(z)), elem!1)), introduced(assumption)).
% 1.12/1.32 tff(100,assumption,(~b(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.12/1.32 tff(101,plain,
% 1.12/1.32 (((~![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))),
% 1.12/1.32 inference(rewrite,[status(thm)],[])).
% 1.12/1.32 tff(102,plain,
% 1.12/1.32 ((~![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))),
% 1.12/1.32 inference(quant_inst,[status(thm)],[])).
% 1.12/1.32 tff(103,plain,
% 1.12/1.32 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1)),
% 1.12/1.32 inference(modus_ponens,[status(thm)],[102, 101])).
% 1.12/1.32 tff(104,plain,
% 1.12/1.32 ((s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1)),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[103, 58])).
% 1.12/1.32 tff(105,plain,
% 1.12/1.32 (r(s(s(z)), elem!1)),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[104, 99, 15])).
% 1.12/1.32 tff(106,assumption,(r(s(s(z)), elem!1)), introduced(assumption)).
% 1.12/1.32 tff(107,assumption,(b(s(z), elem!1)), introduced(assumption)).
% 1.12/1.32 tff(108,assumption,(~(s(z) = elem!1)), introduced(assumption)).
% 1.12/1.32 tff(109,plain,
% 1.12/1.32 (s(z) = elem!1),
% 1.12/1.32 inference(modus_ponens,[status(thm)],[17, 91])).
% 1.12/1.32 tff(110,plain,
% 1.12/1.32 ($false),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[108, 109])).
% 1.12/1.32 tff(111,plain,((~(elem!1 = s(z))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.12/1.32 tff(112,plain,
% 1.12/1.32 (~(elem!1 = s(z))),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[111, 108])).
% 1.12/1.32 tff(113,plain,
% 1.12/1.32 (r(elem!1, s(z))),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[89, 112, 14])).
% 1.12/1.32 tff(114,assumption,(r(elem!1, s(z))), introduced(assumption)).
% 1.12/1.32 tff(115,assumption,(r(s(s(z)), s(z))), introduced(assumption)).
% 1.12/1.32 tff(116,plain,
% 1.12/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(z)), 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)), s(z))) | (~r(s(s(z)), elem!1)))),
% 1.12/1.32 inference(rewrite,[status(thm)],[])).
% 1.12/1.32 tff(117,plain,
% 1.12/1.32 (((~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)), s(z))) | (~r(s(s(z)), elem!1)))),
% 1.12/1.32 inference(rewrite,[status(thm)],[])).
% 1.12/1.32 tff(118,plain,
% 1.12/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(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)), s(z))) | (~r(s(s(z)), elem!1))))),
% 1.12/1.32 inference(monotonicity,[status(thm)],[117])).
% 1.12/1.32 tff(119,plain,
% 1.12/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(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)), s(z))) | (~r(s(s(z)), elem!1)))),
% 1.12/1.32 inference(transitivity,[status(thm)],[118, 116])).
% 1.12/1.32 tff(120,plain,
% 1.12/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)))),
% 1.12/1.32 inference(quant_inst,[status(thm)],[])).
% 1.12/1.32 tff(121,plain,
% 1.12/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1))),
% 1.12/1.32 inference(modus_ponens,[status(thm)],[120, 119])).
% 1.12/1.32 tff(122,plain,
% 1.12/1.32 ($false),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[121, 37, 114, 106, 115])).
% 1.12/1.32 tff(123,plain,((~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.12/1.32 tff(124,plain,
% 1.12/1.32 (~r(s(s(z)), s(z))),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[123, 114, 106])).
% 1.12/1.32 tff(125,plain,
% 1.12/1.32 ((s(z) = s(s(z))) <=> (s(s(z)) = s(z))),
% 1.12/1.32 inference(commutativity,[status(thm)],[])).
% 1.12/1.32 tff(126,plain,
% 1.12/1.32 ((~(s(z) = s(s(z)))) <=> (~(s(s(z)) = s(z)))),
% 1.12/1.32 inference(monotonicity,[status(thm)],[125])).
% 1.12/1.32 tff(127,plain,
% 1.12/1.32 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(z)) = z)),
% 1.12/1.32 inference(quant_inst,[status(thm)],[])).
% 1.12/1.32 tff(128,plain,
% 1.12/1.32 (inj_0(s(z)) = z),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[127, 9])).
% 1.12/1.32 tff(129,assumption,(s(z) = s(s(z))), introduced(assumption)).
% 1.12/1.32 tff(130,plain,
% 1.12/1.32 (inj_0(s(z)) = inj_0(s(s(z)))),
% 1.12/1.32 inference(monotonicity,[status(thm)],[129])).
% 1.12/1.32 tff(131,plain,
% 1.12/1.32 (inj_0(s(s(z))) = inj_0(s(z))),
% 1.12/1.32 inference(symmetry,[status(thm)],[130])).
% 1.12/1.32 tff(132,plain,
% 1.12/1.32 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(z))) = s(z))),
% 1.12/1.32 inference(quant_inst,[status(thm)],[])).
% 1.12/1.32 tff(133,plain,
% 1.12/1.32 (inj_0(s(s(z))) = s(z)),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[132, 9])).
% 1.12/1.32 tff(134,plain,
% 1.12/1.32 (s(z) = inj_0(s(s(z)))),
% 1.12/1.32 inference(symmetry,[status(thm)],[133])).
% 1.12/1.32 tff(135,plain,
% 1.12/1.32 (s(s(z)) = s(z)),
% 1.12/1.32 inference(symmetry,[status(thm)],[129])).
% 1.12/1.32 tff(136,plain,
% 1.12/1.32 (s(s(z)) = z),
% 1.12/1.32 inference(transitivity,[status(thm)],[135, 134, 131, 128])).
% 1.12/1.32 tff(137,plain,
% 1.12/1.32 (^[X: $i] : refl((~(s(X) = z)) <=> (~(s(X) = z)))),
% 1.12/1.32 inference(bind,[status(th)],[])).
% 1.12/1.32 tff(138,plain,
% 1.12/1.32 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 1.12/1.32 inference(quant_intro,[status(thm)],[137])).
% 1.12/1.32 tff(139,plain,
% 1.12/1.32 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 1.12/1.32 inference(rewrite,[status(thm)],[])).
% 1.12/1.32 tff(140,axiom,(![X: $i] : (~(s(X) = z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','snz')).
% 1.12/1.32 tff(141,plain,
% 1.12/1.32 (![X: $i] : (~(s(X) = z))),
% 1.12/1.32 inference(modus_ponens,[status(thm)],[140, 139])).
% 1.12/1.32 tff(142,plain,(
% 1.12/1.32 ![X: $i] : (~(s(X) = z))),
% 1.12/1.32 inference(skolemize,[status(sab)],[141])).
% 1.12/1.32 tff(143,plain,
% 1.12/1.32 (![X: $i] : (~(s(X) = z))),
% 1.12/1.32 inference(modus_ponens,[status(thm)],[142, 138])).
% 1.12/1.32 tff(144,plain,
% 1.12/1.32 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(z)) = z))),
% 1.12/1.32 inference(quant_inst,[status(thm)],[])).
% 1.12/1.32 tff(145,plain,
% 1.12/1.32 (~(s(s(z)) = z)),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[144, 143])).
% 1.12/1.32 tff(146,plain,
% 1.12/1.32 ($false),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[145, 136])).
% 1.12/1.32 tff(147,plain,(~(s(z) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.12/1.32 tff(148,plain,
% 1.12/1.32 (~(s(s(z)) = s(z))),
% 1.12/1.32 inference(modus_ponens,[status(thm)],[147, 126])).
% 1.12/1.32 tff(149,plain,
% 1.12/1.32 (((~![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)))),
% 1.12/1.32 inference(rewrite,[status(thm)],[])).
% 1.12/1.32 tff(150,plain,
% 1.12/1.32 ((~![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)))),
% 1.12/1.32 inference(quant_inst,[status(thm)],[])).
% 1.12/1.32 tff(151,plain,
% 1.12/1.32 ((~![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))),
% 1.12/1.32 inference(modus_ponens,[status(thm)],[150, 149])).
% 1.12/1.32 tff(152,plain,
% 1.12/1.32 ((s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z))),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[151, 58])).
% 1.12/1.32 tff(153,plain,
% 1.12/1.32 (b(s(s(z)), s(z)) | r(s(s(z)), s(z))),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[152, 148])).
% 1.12/1.32 tff(154,plain,
% 1.12/1.32 (b(s(s(z)), s(z))),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[153, 124])).
% 1.12/1.32 tff(155,assumption,(r(elem!1, z)), introduced(assumption)).
% 1.12/1.32 tff(156,plain,
% 1.12/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~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(elem!1, s(z))) | (~r(s(z), z)) | (~r(elem!1, z)))),
% 1.12/1.33 inference(rewrite,[status(thm)],[])).
% 1.12/1.33 tff(157,plain,
% 1.12/1.33 (((~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(elem!1, z)))),
% 1.12/1.33 inference(rewrite,[status(thm)],[])).
% 1.12/1.33 tff(158,plain,
% 1.12/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(elem!1, z))))),
% 1.12/1.33 inference(monotonicity,[status(thm)],[157])).
% 1.12/1.33 tff(159,plain,
% 1.12/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(elem!1, z)))),
% 1.12/1.33 inference(transitivity,[status(thm)],[158, 156])).
% 1.12/1.33 tff(160,plain,
% 1.12/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z))))),
% 1.12/1.33 inference(quant_inst,[status(thm)],[])).
% 1.12/1.33 tff(161,plain,
% 1.12/1.33 ((~![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(z), z)) | (~r(elem!1, z))),
% 1.12/1.33 inference(modus_ponens,[status(thm)],[160, 159])).
% 1.12/1.33 tff(162,plain,
% 1.12/1.33 ((~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(elem!1, z))),
% 1.12/1.33 inference(unit_resolution,[status(thm)],[161, 37])).
% 1.12/1.33 tff(163,plain,
% 1.12/1.33 (~r(s(z), z)),
% 1.12/1.33 inference(unit_resolution,[status(thm)],[162, 155, 114])).
% 1.12/1.33 tff(164,plain,
% 1.12/1.33 ((~![X: $i] : (~(s(X) = z))) | (~(s(z) = z))),
% 1.12/1.33 inference(quant_inst,[status(thm)],[])).
% 1.12/1.33 tff(165,plain,
% 1.12/1.33 (~(s(z) = z)),
% 1.12/1.33 inference(unit_resolution,[status(thm)],[164, 143])).
% 1.12/1.33 tff(166,plain,
% 1.12/1.33 (((~![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))),
% 1.12/1.33 inference(rewrite,[status(thm)],[])).
% 1.12/1.33 tff(167,plain,
% 1.12/1.33 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = z) | b(s(z), z) | r(s(z), z))),
% 1.12/1.33 inference(quant_inst,[status(thm)],[])).
% 1.12/1.33 tff(168,plain,
% 1.12/1.33 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = z) | b(s(z), z) | r(s(z), z)),
% 1.12/1.33 inference(modus_ponens,[status(thm)],[167, 166])).
% 1.12/1.33 tff(169,plain,
% 1.12/1.33 (b(s(z), z) | r(s(z), z)),
% 1.12/1.33 inference(unit_resolution,[status(thm)],[168, 58, 165])).
% 1.12/1.33 tff(170,plain,
% 1.12/1.33 (b(s(z), z)),
% 1.12/1.33 inference(unit_resolution,[status(thm)],[169, 163])).
% 1.12/1.33 tff(171,plain,
% 1.12/1.33 (((~![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, z)) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, z)) | (~r(z, s(z))))),
% 1.12/1.33 inference(rewrite,[status(thm)],[])).
% 1.12/1.33 tff(172,plain,
% 1.12/1.33 (((~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z))) <=> ((~r(elem!1, s(z))) | (~r(elem!1, z)) | (~r(z, s(z))))),
% 1.12/1.33 inference(rewrite,[status(thm)],[])).
% 1.12/1.33 tff(173,plain,
% 1.12/1.33 (((~![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(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(elem!1, z)) | (~r(z, s(z)))))),
% 1.12/1.33 inference(monotonicity,[status(thm)],[172])).
% 1.12/1.33 tff(174,plain,
% 1.12/1.33 (((~![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(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, z)) | (~r(z, s(z))))),
% 1.12/1.33 inference(transitivity,[status(thm)],[173, 171])).
% 1.12/1.33 tff(175,plain,
% 1.12/1.33 ((~![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(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z)))),
% 1.12/1.33 inference(quant_inst,[status(thm)],[])).
% 1.12/1.33 tff(176,plain,
% 1.12/1.33 ((~![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, z)) | (~r(z, s(z)))),
% 1.12/1.33 inference(modus_ponens,[status(thm)],[175, 174])).
% 1.12/1.33 tff(177,plain,
% 1.12/1.33 ((~r(elem!1, s(z))) | (~r(elem!1, z)) | (~r(z, s(z)))),
% 1.12/1.33 inference(unit_resolution,[status(thm)],[176, 37])).
% 1.12/1.33 tff(178,plain,
% 1.12/1.33 (~r(z, s(z))),
% 1.12/1.33 inference(unit_resolution,[status(thm)],[177, 155, 114])).
% 1.12/1.33 tff(179,plain,
% 1.12/1.33 ((z = s(z)) <=> (s(z) = z)),
% 1.12/1.33 inference(commutativity,[status(thm)],[])).
% 1.12/1.33 tff(180,plain,
% 1.12/1.33 ((s(z) = z) <=> (z = s(z))),
% 1.12/1.33 inference(symmetry,[status(thm)],[179])).
% 1.12/1.33 tff(181,plain,
% 1.12/1.33 ((~(s(z) = z)) <=> (~(z = s(z)))),
% 1.12/1.33 inference(monotonicity,[status(thm)],[180])).
% 1.12/1.33 tff(182,plain,
% 1.12/1.33 (~(z = s(z))),
% 1.12/1.33 inference(modus_ponens,[status(thm)],[165, 181])).
% 1.12/1.33 tff(183,plain,
% 1.12/1.33 (((~![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)))),
% 1.12/1.33 inference(rewrite,[status(thm)],[])).
% 1.12/1.33 tff(184,plain,
% 1.12/1.33 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(z)) | b(z, s(z)) | r(z, s(z)))),
% 1.12/1.33 inference(quant_inst,[status(thm)],[])).
% 1.12/1.33 tff(185,plain,
% 1.12/1.33 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 1.12/1.33 inference(modus_ponens,[status(thm)],[184, 183])).
% 1.12/1.33 tff(186,plain,
% 1.12/1.33 ((z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 1.12/1.33 inference(unit_resolution,[status(thm)],[185, 58])).
% 1.12/1.33 tff(187,plain,
% 1.12/1.33 (b(z, s(z)) | r(z, s(z))),
% 1.12/1.33 inference(unit_resolution,[status(thm)],[186, 182])).
% 1.12/1.33 tff(188,plain,
% 1.12/1.33 (b(z, s(z))),
% 1.12/1.33 inference(unit_resolution,[status(thm)],[187, 178])).
% 1.12/1.33 tff(189,plain,
% 1.12/1.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(X1, 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))))),
% 1.12/1.33 inference(rewrite,[status(thm)],[])).
% 1.12/1.33 tff(190,plain,
% 1.12/1.33 (((~b(z, s(z))) | (~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))))),
% 1.12/1.33 inference(rewrite,[status(thm)],[])).
% 1.12/1.33 tff(191,plain,
% 1.12/1.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), 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(X1, 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)))))),
% 1.12/1.33 inference(monotonicity,[status(thm)],[190])).
% 1.12/1.33 tff(192,plain,
% 1.12/1.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), 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(X1, 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))))),
% 1.12/1.33 inference(transitivity,[status(thm)],[191, 189])).
% 1.12/1.33 tff(193,plain,
% 1.12/1.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.12/1.33 inference(quant_inst,[status(thm)],[])).
% 1.12/1.33 tff(194,plain,
% 1.12/1.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))),
% 1.12/1.33 inference(modus_ponens,[status(thm)],[193, 192])).
% 1.12/1.33 tff(195,plain,
% 1.12/1.33 (~b(s(s(z)), z)),
% 1.12/1.33 inference(unit_resolution,[status(thm)],[194, 75, 188, 170, 154])).
% 1.12/1.33 tff(196,assumption,(~r(s(s(z)), z)), introduced(assumption)).
% 1.12/1.33 tff(197,assumption,(~b(s(s(z)), z)), introduced(assumption)).
% 1.12/1.33 tff(198,plain,
% 1.12/1.33 (((~![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))),
% 1.12/1.33 inference(rewrite,[status(thm)],[])).
% 1.12/1.33 tff(199,plain,
% 1.12/1.33 ((~![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))),
% 1.12/1.33 inference(quant_inst,[status(thm)],[])).
% 1.12/1.33 tff(200,plain,
% 1.12/1.33 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z)),
% 1.12/1.33 inference(modus_ponens,[status(thm)],[199, 198])).
% 1.12/1.33 tff(201,plain,
% 1.12/1.33 ($false),
% 1.12/1.33 inference(unit_resolution,[status(thm)],[200, 58, 145, 197, 196])).
% 1.12/1.33 tff(202,plain,(r(s(s(z)), z) | b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 1.12/1.33 tff(203,plain,
% 1.12/1.33 (r(s(s(z)), z)),
% 1.12/1.33 inference(unit_resolution,[status(thm)],[202, 195])).
% 1.12/1.33 tff(204,plain,
% 1.12/1.33 (((~![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(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)), z)) | (~r(s(s(z)), elem!1)))),
% 1.12/1.33 inference(rewrite,[status(thm)],[])).
% 1.12/1.33 tff(205,plain,
% 1.12/1.33 (((~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)), z)) | (~r(s(s(z)), elem!1)))),
% 1.12/1.33 inference(rewrite,[status(thm)],[])).
% 1.12/1.33 tff(206,plain,
% 1.12/1.33 (((~![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)), z)) | (~r(s(s(z)), elem!1))))),
% 1.12/1.33 inference(monotonicity,[status(thm)],[205])).
% 1.12/1.33 tff(207,plain,
% 1.12/1.33 (((~![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)), z)) | (~r(s(s(z)), elem!1)))),
% 1.12/1.33 inference(transitivity,[status(thm)],[206, 204])).
% 1.12/1.33 tff(208,plain,
% 1.12/1.33 ((~![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)))),
% 1.12/1.33 inference(quant_inst,[status(thm)],[])).
% 1.12/1.33 tff(209,plain,
% 1.12/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1))),
% 1.12/1.33 inference(modus_ponens,[status(thm)],[208, 207])).
% 1.12/1.33 tff(210,plain,
% 1.12/1.33 ($false),
% 1.12/1.33 inference(unit_resolution,[status(thm)],[209, 37, 155, 106, 203])).
% 1.12/1.33 tff(211,plain,((~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.12/1.33 tff(212,plain,
% 1.12/1.33 (~r(elem!1, z)),
% 1.12/1.33 inference(unit_resolution,[status(thm)],[211, 113, 106])).
% 1.12/1.33 tff(213,assumption,(s(s(s(z))) = elem!1), introduced(assumption)).
% 1.12/1.33 tff(214,plain,
% 1.12/1.33 (s(s(s(s(z)))) = s(elem!1)),
% 1.12/1.33 inference(monotonicity,[status(thm)],[213])).
% 1.12/1.33 tff(215,plain,
% 1.12/1.33 (b(s(z), s(s(s(s(z))))) <=> b(s(z), s(elem!1))),
% 1.12/1.33 inference(monotonicity,[status(thm)],[214])).
% 1.12/1.33 tff(216,plain,
% 1.12/1.33 ((elem!1 = z) <=> (z = elem!1)),
% 1.12/1.33 inference(commutativity,[status(thm)],[])).
% 1.12/1.33 tff(217,plain,
% 1.12/1.33 ((s(s(s(z))) = z) <=> (elem!1 = z)),
% 1.12/1.33 inference(monotonicity,[status(thm)],[213])).
% 1.12/1.33 tff(218,plain,
% 1.12/1.33 ((s(s(s(z))) = z) <=> (z = elem!1)),
% 1.12/1.33 inference(transitivity,[status(thm)],[217, 216])).
% 1.12/1.33 tff(219,plain,
% 1.12/1.33 ((~(s(s(s(z))) = z)) <=> (~(z = elem!1))),
% 1.12/1.33 inference(monotonicity,[status(thm)],[218])).
% 1.12/1.33 tff(220,plain,
% 1.12/1.33 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(z))) = z))),
% 1.12/1.33 inference(quant_inst,[status(thm)],[])).
% 1.12/1.33 tff(221,plain,
% 1.12/1.33 (~(s(s(s(z))) = z)),
% 1.12/1.33 inference(unit_resolution,[status(thm)],[220, 143])).
% 1.12/1.33 tff(222,plain,
% 1.12/1.33 (~(z = elem!1)),
% 1.12/1.33 inference(modus_ponens,[status(thm)],[221, 219])).
% 1.12/1.33 tff(223,plain,
% 1.12/1.33 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(elem!1)) = elem!1)),
% 1.12/1.33 inference(quant_inst,[status(thm)],[])).
% 1.12/1.33 tff(224,plain,
% 1.12/1.33 (inj_0(s(elem!1)) = elem!1),
% 1.12/1.33 inference(unit_resolution,[status(thm)],[223, 9])).
% 1.12/1.33 tff(225,assumption,(s(s(elem!1)) = s(s(z))), introduced(assumption)).
% 1.12/1.33 tff(226,plain,
% 1.12/1.33 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 1.12/1.33 inference(monotonicity,[status(thm)],[225])).
% 1.12/1.33 tff(227,plain,
% 1.12/1.33 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(elem!1))) = s(elem!1))),
% 1.12/1.33 inference(quant_inst,[status(thm)],[])).
% 1.12/1.33 tff(228,plain,
% 1.12/1.33 (inj_0(s(s(elem!1))) = s(elem!1)),
% 1.12/1.33 inference(unit_resolution,[status(thm)],[227, 9])).
% 1.12/1.33 tff(229,plain,
% 1.12/1.33 (s(elem!1) = inj_0(s(s(elem!1)))),
% 1.12/1.33 inference(symmetry,[status(thm)],[228])).
% 1.12/1.33 tff(230,plain,
% 1.12/1.33 (s(elem!1) = s(z)),
% 1.12/1.33 inference(transitivity,[status(thm)],[229, 226, 133])).
% 1.12/1.33 tff(231,plain,
% 1.12/1.33 (inj_0(s(elem!1)) = inj_0(s(z))),
% 1.12/1.33 inference(monotonicity,[status(thm)],[230])).
% 1.12/1.33 tff(232,plain,
% 1.12/1.33 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.12/1.33 inference(symmetry,[status(thm)],[231])).
% 1.12/1.33 tff(233,plain,
% 1.12/1.33 (z = inj_0(s(z))),
% 1.12/1.33 inference(symmetry,[status(thm)],[128])).
% 1.12/1.33 tff(234,plain,
% 1.12/1.33 (z = elem!1),
% 1.12/1.33 inference(transitivity,[status(thm)],[233, 232, 224])).
% 1.12/1.33 tff(235,assumption,(~(z = elem!1)), introduced(assumption)).
% 1.12/1.33 tff(236,plain,
% 1.12/1.33 ($false),
% 1.12/1.33 inference(unit_resolution,[status(thm)],[235, 234])).
% 1.12/1.33 tff(237,plain,((~(s(s(elem!1)) = s(s(z)))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.12/1.33 tff(238,plain,
% 1.12/1.33 (~(s(s(elem!1)) = s(s(z)))),
% 1.12/1.33 inference(unit_resolution,[status(thm)],[237, 222])).
% 1.12/1.33 tff(239,plain,
% 1.12/1.33 ((s(s(s(s(z)))) = elem!1) <=> (elem!1 = s(s(s(s(z)))))),
% 1.12/1.33 inference(commutativity,[status(thm)],[])).
% 1.12/1.33 tff(240,plain,
% 1.12/1.33 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 1.12/1.33 inference(symmetry,[status(thm)],[239])).
% 1.12/1.33 tff(241,plain,
% 1.12/1.33 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(s(z)))) = elem!1)),
% 1.12/1.33 inference(monotonicity,[status(thm)],[213])).
% 1.12/1.33 tff(242,plain,
% 1.12/1.33 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (elem!1 = s(s(s(s(z)))))),
% 1.12/1.33 inference(transitivity,[status(thm)],[241, 239])).
% 1.12/1.33 tff(243,plain,
% 1.12/1.33 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(s(z)))) = elem!1)),
% 1.12/1.33 inference(transitivity,[status(thm)],[242, 240])).
% 1.12/1.33 tff(244,plain,
% 1.12/1.33 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 1.12/1.33 inference(monotonicity,[status(thm)],[243])).
% 1.12/1.33 tff(245,plain,
% 1.12/1.33 ((s(s(s(z))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 1.12/1.33 inference(commutativity,[status(thm)],[])).
% 1.12/1.33 tff(246,plain,
% 1.12/1.33 ((~(s(s(s(z))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(s(z)))))),
% 1.12/1.33 inference(monotonicity,[status(thm)],[245])).
% 1.12/1.33 tff(247,plain,
% 1.12/1.33 ((s(s(s(s(z)))) = s(z)) <=> (s(z) = s(s(s(s(z)))))),
% 1.12/1.33 inference(commutativity,[status(thm)],[])).
% 1.12/1.33 tff(248,assumption,(s(s(s(z))) = s(s(s(s(z))))), introduced(assumption)).
% 1.12/1.33 tff(249,plain,
% 1.12/1.33 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(z))))) = s(s(s(z))))),
% 1.12/1.33 inference(quant_inst,[status(thm)],[])).
% 1.12/1.33 tff(250,plain,
% 1.12/1.33 (inj_0(s(s(s(s(z))))) = s(s(s(z)))),
% 1.12/1.33 inference(unit_resolution,[status(thm)],[249, 9])).
% 1.12/1.33 tff(251,plain,
% 1.12/1.33 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(z)))))),
% 1.12/1.33 inference(monotonicity,[status(thm)],[248])).
% 1.12/1.33 tff(252,plain,
% 1.12/1.33 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(z)))) = s(s(z)))),
% 1.12/1.33 inference(quant_inst,[status(thm)],[])).
% 1.12/1.33 tff(253,plain,
% 1.12/1.33 (inj_0(s(s(s(z)))) = s(s(z))),
% 1.12/1.33 inference(unit_resolution,[status(thm)],[252, 9])).
% 1.12/1.33 tff(254,plain,
% 1.12/1.33 (s(s(z)) = inj_0(s(s(s(z))))),
% 1.12/1.33 inference(symmetry,[status(thm)],[253])).
% 1.12/1.33 tff(255,plain,
% 1.12/1.33 (s(s(z)) = s(s(s(s(z))))),
% 1.12/1.33 inference(transitivity,[status(thm)],[254, 251, 250, 248])).
% 1.12/1.33 tff(256,plain,
% 1.12/1.33 ((s(s(z)) = s(z)) <=> (s(s(s(s(z)))) = s(z))),
% 1.12/1.33 inference(monotonicity,[status(thm)],[255])).
% 1.12/1.33 tff(257,plain,
% 1.12/1.33 ((s(s(z)) = s(z)) <=> (s(z) = s(s(s(s(z)))))),
% 1.12/1.33 inference(transitivity,[status(thm)],[256, 247])).
% 1.12/1.33 tff(258,plain,
% 1.12/1.33 ((s(z) = s(s(s(s(z))))) <=> (s(s(z)) = s(z))),
% 1.12/1.33 inference(symmetry,[status(thm)],[257])).
% 1.12/1.33 tff(259,plain,
% 1.12/1.33 (inj_0(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 1.12/1.33 inference(monotonicity,[status(thm)],[255])).
% 1.12/1.33 tff(260,plain,
% 1.12/1.33 (s(z) = s(s(s(s(z))))),
% 1.12/1.33 inference(transitivity,[status(thm)],[134, 259, 250, 248])).
% 1.12/1.33 tff(261,plain,
% 1.12/1.33 (s(s(z)) = s(z)),
% 1.12/1.33 inference(modus_ponens,[status(thm)],[260, 258])).
% 1.12/1.33 tff(262,plain,
% 1.12/1.33 ($false),
% 1.12/1.33 inference(unit_resolution,[status(thm)],[148, 261])).
% 1.12/1.33 tff(263,plain,(~(s(s(s(z))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.12/1.33 tff(264,plain,
% 1.12/1.33 (~(s(s(s(s(z)))) = s(s(s(z))))),
% 1.12/1.33 inference(modus_ponens,[status(thm)],[263, 246])).
% 1.12/1.33 tff(265,plain,
% 1.12/1.33 (~(s(s(s(s(z)))) = elem!1)),
% 1.12/1.33 inference(modus_ponens,[status(thm)],[264, 244])).
% 1.12/1.33 tff(266,assumption,(~(s(s(elem!1)) = s(s(z)))), introduced(assumption)).
% 1.12/1.33 tff(267,assumption,(~(s(s(s(s(z)))) = elem!1)), introduced(assumption)).
% 1.12/1.33 tff(268,assumption,(~r(elem!1, s(s(s(s(z)))))), introduced(assumption)).
% 1.12/1.33 tff(269,plain,
% 1.12/1.33 ((s(s(s(s(s(s(s(z))))))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.12/1.33 inference(commutativity,[status(thm)],[])).
% 1.12/1.33 tff(270,assumption,(elem!1 = s(s(s(s(z))))), introduced(assumption)).
% 1.12/1.33 tff(271,plain,
% 1.12/1.33 (s(s(s(s(z)))) = elem!1),
% 1.12/1.33 inference(modus_ponens,[status(thm)],[270, 240])).
% 1.12/1.33 tff(272,plain,
% 1.12/1.33 ($false),
% 1.12/1.33 inference(unit_resolution,[status(thm)],[267, 271])).
% 1.12/1.33 tff(273,plain,((~(elem!1 = s(s(s(s(z)))))) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.12/1.33 tff(274,plain,
% 1.12/1.33 (~(elem!1 = s(s(s(s(z)))))),
% 1.12/1.33 inference(unit_resolution,[status(thm)],[273, 267])).
% 1.12/1.33 tff(275,plain,
% 1.12/1.33 (((~![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))))))),
% 1.12/1.33 inference(rewrite,[status(thm)],[])).
% 1.12/1.33 tff(276,plain,
% 1.12/1.33 ((~![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))))))),
% 1.12/1.33 inference(quant_inst,[status(thm)],[])).
% 1.12/1.33 tff(277,plain,
% 1.12/1.33 ((~![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)))))),
% 1.12/1.33 inference(modus_ponens,[status(thm)],[276, 275])).
% 1.12/1.33 tff(278,plain,
% 1.12/1.33 ((elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z)))))),
% 1.12/1.33 inference(unit_resolution,[status(thm)],[277, 58])).
% 1.12/1.33 tff(279,plain,
% 1.12/1.33 (b(elem!1, s(s(s(s(z)))))),
% 1.12/1.33 inference(unit_resolution,[status(thm)],[278, 268, 274])).
% 1.12/1.33 tff(280,plain,
% 1.12/1.33 (((~![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))),
% 1.12/1.33 inference(rewrite,[status(thm)],[])).
% 1.12/1.33 tff(281,plain,
% 1.12/1.33 ((~![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))),
% 1.12/1.34 inference(quant_inst,[status(thm)],[])).
% 1.12/1.34 tff(282,plain,
% 1.12/1.34 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1)),
% 1.12/1.34 inference(modus_ponens,[status(thm)],[281, 280])).
% 1.12/1.34 tff(283,plain,
% 1.12/1.34 ((s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1)),
% 1.12/1.34 inference(unit_resolution,[status(thm)],[282, 58])).
% 1.12/1.34 tff(284,plain,
% 1.12/1.34 (b(s(s(s(s(z)))), elem!1)),
% 1.12/1.34 inference(unit_resolution,[status(thm)],[283, 12, 267])).
% 1.12/1.34 tff(285,assumption,(~b(z, elem!1)), introduced(assumption)).
% 1.12/1.34 tff(286,assumption,(b(elem!1, s(s(s(s(z)))))), introduced(assumption)).
% 1.12/1.34 tff(287,assumption,(b(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 1.12/1.34 tff(288,assumption,(z = elem!1), introduced(assumption)).
% 1.12/1.34 tff(289,plain,
% 1.12/1.34 (s(z) = s(elem!1)),
% 1.12/1.34 inference(monotonicity,[status(thm)],[288])).
% 1.12/1.34 tff(290,plain,
% 1.12/1.34 (s(s(z)) = s(s(elem!1))),
% 1.12/1.34 inference(monotonicity,[status(thm)],[289])).
% 1.12/1.34 tff(291,plain,
% 1.12/1.34 (s(s(elem!1)) = s(s(z))),
% 1.12/1.34 inference(symmetry,[status(thm)],[290])).
% 1.12/1.34 tff(292,plain,
% 1.12/1.34 ($false),
% 1.12/1.34 inference(unit_resolution,[status(thm)],[266, 291])).
% 1.12/1.34 tff(293,plain,((~(z = elem!1)) | (s(s(elem!1)) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.12/1.34 tff(294,plain,
% 1.12/1.34 (~(z = elem!1)),
% 1.12/1.34 inference(unit_resolution,[status(thm)],[293, 266])).
% 1.12/1.34 tff(295,plain,
% 1.12/1.34 (((~![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))),
% 1.12/1.34 inference(rewrite,[status(thm)],[])).
% 1.12/1.34 tff(296,plain,
% 1.12/1.34 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = elem!1) | b(z, elem!1) | r(z, elem!1))),
% 1.12/1.34 inference(quant_inst,[status(thm)],[])).
% 1.12/1.34 tff(297,plain,
% 1.12/1.34 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = elem!1) | b(z, elem!1) | r(z, elem!1)),
% 1.12/1.34 inference(modus_ponens,[status(thm)],[296, 295])).
% 1.12/1.34 tff(298,plain,
% 1.12/1.34 ((z = elem!1) | b(z, elem!1) | r(z, elem!1)),
% 1.12/1.34 inference(unit_resolution,[status(thm)],[297, 58])).
% 1.12/1.34 tff(299,plain,
% 1.12/1.34 (r(z, elem!1)),
% 1.12/1.34 inference(unit_resolution,[status(thm)],[298, 285, 294])).
% 1.12/1.34 tff(300,assumption,(r(z, elem!1)), introduced(assumption)).
% 1.12/1.34 tff(301,assumption,(elem!1 = z), introduced(assumption)).
% 1.12/1.34 tff(302,plain,
% 1.12/1.34 (z = elem!1),
% 1.12/1.34 inference(modus_ponens,[status(thm)],[301, 216])).
% 1.12/1.34 tff(303,plain,
% 1.12/1.34 ($false),
% 1.12/1.34 inference(unit_resolution,[status(thm)],[235, 302])).
% 1.12/1.34 tff(304,plain,((~(elem!1 = z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.12/1.34 tff(305,plain,
% 1.12/1.34 (~(elem!1 = z)),
% 1.12/1.34 inference(unit_resolution,[status(thm)],[304, 294])).
% 1.12/1.34 tff(306,plain,
% 1.12/1.34 ((elem!1 = s(s(z))) <=> (s(s(z)) = elem!1)),
% 1.12/1.34 inference(commutativity,[status(thm)],[])).
% 1.12/1.34 tff(307,plain,
% 1.12/1.34 ((s(s(z)) = elem!1) <=> (elem!1 = s(s(z)))),
% 1.12/1.34 inference(symmetry,[status(thm)],[306])).
% 1.12/1.34 tff(308,plain,
% 1.12/1.34 ((~(s(s(z)) = elem!1)) <=> (~(elem!1 = s(s(z))))),
% 1.12/1.34 inference(monotonicity,[status(thm)],[307])).
% 1.12/1.34 tff(309,assumption,(b(s(s(z)), s(z))), introduced(assumption)).
% 1.12/1.34 tff(310,assumption,(s(s(z)) = elem!1), introduced(assumption)).
% 1.12/1.34 tff(311,plain,
% 1.12/1.34 (b(s(s(z)), s(z)) <=> b(elem!1, s(z))),
% 1.12/1.34 inference(monotonicity,[status(thm)],[310])).
% 1.12/1.34 tff(312,plain,
% 1.12/1.34 (b(elem!1, s(z)) <=> b(s(s(z)), s(z))),
% 1.12/1.34 inference(symmetry,[status(thm)],[311])).
% 1.12/1.34 tff(313,plain,
% 1.12/1.34 ((~b(elem!1, s(z))) <=> (~b(s(s(z)), s(z)))),
% 1.12/1.34 inference(monotonicity,[status(thm)],[312])).
% 1.12/1.34 tff(314,plain,
% 1.12/1.34 (~b(s(s(z)), s(z))),
% 1.12/1.34 inference(modus_ponens,[status(thm)],[14, 313])).
% 1.12/1.34 tff(315,plain,
% 1.12/1.34 ($false),
% 1.12/1.34 inference(unit_resolution,[status(thm)],[309, 314])).
% 1.12/1.34 tff(316,plain,((~(s(s(z)) = elem!1)) | (~b(s(s(z)), s(z))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.12/1.34 tff(317,plain,
% 1.12/1.34 (~(s(s(z)) = elem!1)),
% 1.12/1.34 inference(unit_resolution,[status(thm)],[316, 309, 14])).
% 1.12/1.34 tff(318,plain,
% 1.12/1.34 (~(elem!1 = s(s(z)))),
% 1.12/1.34 inference(modus_ponens,[status(thm)],[317, 308])).
% 1.12/1.34 tff(319,plain,
% 1.12/1.34 (r(s(s(z)), elem!1)),
% 1.12/1.34 inference(unit_resolution,[status(thm)],[104, 317, 99])).
% 1.12/1.34 tff(320,assumption,(r(s(s(z)), z)), introduced(assumption)).
% 1.12/1.34 tff(321,plain,
% 1.12/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), 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(s(s(z)), z)) | (~r(s(s(z)), elem!1)))),
% 1.12/1.34 inference(rewrite,[status(thm)],[])).
% 1.12/1.34 tff(322,plain,
% 1.12/1.34 (((~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)), z)) | (~r(s(s(z)), elem!1)))),
% 1.12/1.34 inference(rewrite,[status(thm)],[])).
% 1.12/1.34 tff(323,plain,
% 1.12/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(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)), z)) | (~r(s(s(z)), elem!1))))),
% 1.12/1.34 inference(monotonicity,[status(thm)],[322])).
% 1.12/1.34 tff(324,plain,
% 1.12/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(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)), z)) | (~r(s(s(z)), elem!1)))),
% 1.12/1.34 inference(transitivity,[status(thm)],[323, 321])).
% 1.12/1.34 tff(325,plain,
% 1.12/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(z)), z)))),
% 1.12/1.34 inference(quant_inst,[status(thm)],[])).
% 1.12/1.34 tff(326,plain,
% 1.12/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1))),
% 1.12/1.34 inference(modus_ponens,[status(thm)],[325, 324])).
% 1.12/1.34 tff(327,plain,
% 1.12/1.34 ($false),
% 1.12/1.34 inference(unit_resolution,[status(thm)],[326, 37, 300, 106, 320])).
% 1.12/1.34 tff(328,plain,((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.12/1.34 tff(329,plain,
% 1.12/1.34 (~r(s(s(z)), z)),
% 1.12/1.34 inference(unit_resolution,[status(thm)],[328, 319, 300])).
% 1.12/1.34 tff(330,plain,
% 1.12/1.34 (b(s(s(z)), z)),
% 1.12/1.34 inference(unit_resolution,[status(thm)],[202, 329])).
% 1.12/1.34 tff(331,assumption,(r(z, s(s(z)))), introduced(assumption)).
% 1.12/1.34 tff(332,plain,
% 1.12/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(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)))),
% 1.12/1.34 inference(rewrite,[status(thm)],[])).
% 1.12/1.34 tff(333,plain,
% 1.12/1.34 (((~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)))),
% 1.12/1.34 inference(rewrite,[status(thm)],[])).
% 1.12/1.34 tff(334,plain,
% 1.12/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), 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))))),
% 1.12/1.34 inference(monotonicity,[status(thm)],[333])).
% 1.12/1.34 tff(335,plain,
% 1.12/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), 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)))),
% 1.12/1.34 inference(transitivity,[status(thm)],[334, 332])).
% 1.12/1.34 tff(336,plain,
% 1.12/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))))),
% 1.12/1.34 inference(quant_inst,[status(thm)],[])).
% 1.12/1.34 tff(337,plain,
% 1.12/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(z)))) | (~r(s(s(z)), elem!1))),
% 1.12/1.34 inference(modus_ponens,[status(thm)],[336, 335])).
% 1.12/1.34 tff(338,plain,
% 1.12/1.34 ($false),
% 1.12/1.34 inference(unit_resolution,[status(thm)],[337, 37, 300, 106, 331])).
% 1.12/1.34 tff(339,plain,((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.12/1.34 tff(340,plain,
% 1.12/1.34 (~r(z, s(s(z)))),
% 1.12/1.34 inference(unit_resolution,[status(thm)],[339, 319, 300])).
% 1.12/1.34 tff(341,assumption,(z = s(s(z))), introduced(assumption)).
% 1.12/1.34 tff(342,plain,
% 1.12/1.34 (s(s(z)) = z),
% 1.12/1.34 inference(symmetry,[status(thm)],[341])).
% 1.12/1.34 tff(343,plain,
% 1.12/1.34 ($false),
% 1.12/1.34 inference(unit_resolution,[status(thm)],[145, 342])).
% 1.12/1.34 tff(344,plain,(~(z = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.12/1.34 tff(345,assumption,(~r(z, s(s(z)))), introduced(assumption)).
% 1.12/1.34 tff(346,assumption,(~b(z, s(s(z)))), introduced(assumption)).
% 1.12/1.34 tff(347,plain,
% 1.12/1.34 (((~![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))))),
% 1.12/1.34 inference(rewrite,[status(thm)],[])).
% 1.12/1.34 tff(348,plain,
% 1.12/1.34 ((~![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))))),
% 1.12/1.34 inference(quant_inst,[status(thm)],[])).
% 1.12/1.34 tff(349,plain,
% 1.12/1.34 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z)))),
% 1.12/1.34 inference(modus_ponens,[status(thm)],[348, 347])).
% 1.12/1.34 tff(350,plain,
% 1.12/1.34 ($false),
% 1.12/1.34 inference(unit_resolution,[status(thm)],[349, 58, 346, 345, 344])).
% 1.12/1.34 tff(351,plain,(r(z, s(s(z))) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.12/1.34 tff(352,plain,
% 1.12/1.34 (b(z, s(s(z)))),
% 1.12/1.34 inference(unit_resolution,[status(thm)],[351, 340])).
% 1.12/1.34 tff(353,assumption,(~(elem!1 = z)), introduced(assumption)).
% 1.12/1.34 tff(354,plain,
% 1.12/1.34 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(z))),
% 1.12/1.34 inference(monotonicity,[status(thm)],[17])).
% 1.12/1.34 tff(355,plain,
% 1.12/1.34 (b(s(s(z)), s(z)) <=> b(s(s(z)), elem!1)),
% 1.12/1.34 inference(symmetry,[status(thm)],[354])).
% 1.12/1.34 tff(356,plain,
% 1.12/1.34 (b(s(s(z)), elem!1)),
% 1.12/1.34 inference(modus_ponens,[status(thm)],[309, 355])).
% 1.12/1.34 tff(357,plain,
% 1.12/1.34 ($false),
% 1.12/1.34 inference(unit_resolution,[status(thm)],[99, 356])).
% 1.12/1.34 tff(358,plain,((~(elem!1 = s(z))) | b(s(s(z)), elem!1) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.12/1.34 tff(359,plain,
% 1.12/1.34 (~(elem!1 = s(z))),
% 1.12/1.34 inference(unit_resolution,[status(thm)],[358, 309, 99])).
% 1.12/1.34 tff(360,plain,
% 1.12/1.34 (r(elem!1, s(z))),
% 1.12/1.34 inference(unit_resolution,[status(thm)],[89, 359, 14])).
% 1.12/1.34 tff(361,plain,
% 1.12/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(z, s(z))))),
% 1.12/1.34 inference(rewrite,[status(thm)],[])).
% 1.12/1.34 tff(362,plain,
% 1.12/1.34 (((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(z, s(z))))),
% 1.12/1.34 inference(rewrite,[status(thm)],[])).
% 1.12/1.34 tff(363,plain,
% 1.12/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(z, s(z)))))),
% 1.12/1.34 inference(monotonicity,[status(thm)],[362])).
% 1.12/1.34 tff(364,plain,
% 1.12/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(z, s(z))))),
% 1.12/1.34 inference(transitivity,[status(thm)],[363, 361])).
% 1.12/1.34 tff(365,plain,
% 1.12/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, elem!1)))),
% 1.12/1.34 inference(quant_inst,[status(thm)],[])).
% 1.12/1.34 tff(366,plain,
% 1.12/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(z, s(z)))),
% 1.12/1.34 inference(modus_ponens,[status(thm)],[365, 364])).
% 1.12/1.34 tff(367,plain,
% 1.12/1.34 ((~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(z, s(z)))),
% 1.12/1.34 inference(unit_resolution,[status(thm)],[366, 37])).
% 1.12/1.34 tff(368,plain,
% 1.12/1.34 (~r(z, s(z))),
% 1.12/1.34 inference(unit_resolution,[status(thm)],[367, 360, 300])).
% 1.12/1.34 tff(369,plain,
% 1.12/1.34 (b(z, s(z))),
% 1.12/1.34 inference(unit_resolution,[status(thm)],[187, 368])).
% 1.12/1.34 tff(370,assumption,(b(z, s(s(z)))), introduced(assumption)).
% 1.12/1.34 tff(371,assumption,(b(s(z), z)), introduced(assumption)).
% 1.12/1.34 tff(372,assumption,(b(z, s(z))), introduced(assumption)).
% 1.12/1.34 tff(373,plain,
% 1.12/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(s(z)), s(z))))),
% 1.12/1.34 inference(rewrite,[status(thm)],[])).
% 1.12/1.34 tff(374,plain,
% 1.12/1.34 (((~b(z, s(z))) | (~b(s(s(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(z, s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.12/1.34 inference(rewrite,[status(thm)],[])).
% 1.12/1.34 tff(375,plain,
% 1.12/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z)))) | (~b(s(s(z)), s(z)))))),
% 1.12/1.34 inference(monotonicity,[status(thm)],[374])).
% 1.12/1.34 tff(376,plain,
% 1.12/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z)))) | (~b(s(s(z)), s(z))))),
% 1.12/1.34 inference(transitivity,[status(thm)],[375, 373])).
% 1.12/1.34 tff(377,plain,
% 1.12/1.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))),
% 1.12/1.34 inference(quant_inst,[status(thm)],[])).
% 1.12/1.34 tff(378,plain,
% 1.12/1.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z)))),
% 1.12/1.34 inference(modus_ponens,[status(thm)],[377, 376])).
% 1.12/1.34 tff(379,plain,
% 1.12/1.34 ($false),
% 1.12/1.34 inference(unit_resolution,[status(thm)],[378, 75, 372, 371, 309, 370])).
% 1.12/1.34 tff(380,plain,((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.12/1.34 tff(381,plain,
% 1.12/1.34 (~b(s(z), z)),
% 1.12/1.34 inference(unit_resolution,[status(thm)],[380, 369, 309, 352])).
% 1.12/1.34 tff(382,plain,
% 1.12/1.34 (r(s(z), z)),
% 1.12/1.34 inference(unit_resolution,[status(thm)],[169, 381])).
% 1.12/1.34 tff(383,plain,
% 1.12/1.34 (~r(elem!1, z)),
% 1.12/1.34 inference(unit_resolution,[status(thm)],[162, 382, 360])).
% 1.12/1.34 tff(384,plain,
% 1.12/1.34 (((~![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))),
% 1.12/1.34 inference(rewrite,[status(thm)],[])).
% 1.12/1.34 tff(385,plain,
% 1.12/1.34 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = z) | b(elem!1, z) | r(elem!1, z))),
% 1.12/1.34 inference(quant_inst,[status(thm)],[])).
% 1.12/1.34 tff(386,plain,
% 1.12/1.34 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = z) | b(elem!1, z) | r(elem!1, z)),
% 1.12/1.34 inference(modus_ponens,[status(thm)],[385, 384])).
% 1.12/1.34 tff(387,plain,
% 1.12/1.34 ((elem!1 = z) | b(elem!1, z) | r(elem!1, z)),
% 1.12/1.34 inference(unit_resolution,[status(thm)],[386, 58])).
% 1.12/1.34 tff(388,plain,
% 1.12/1.34 (b(elem!1, z)),
% 1.12/1.34 inference(unit_resolution,[status(thm)],[387, 383, 353])).
% 1.12/1.34 tff(389,plain,
% 1.12/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))))),
% 1.12/1.34 inference(rewrite,[status(thm)],[])).
% 1.12/1.34 tff(390,plain,
% 1.12/1.34 (((~b(s(s(z)), z)) | (~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(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))))),
% 1.12/1.34 inference(rewrite,[status(thm)],[])).
% 1.12/1.34 tff(391,plain,
% 1.12/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z))))))),
% 1.12/1.34 inference(monotonicity,[status(thm)],[390])).
% 1.12/1.34 tff(392,plain,
% 1.12/1.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))))),
% 1.12/1.34 inference(transitivity,[status(thm)],[391, 389])).
% 1.12/1.34 tff(393,plain,
% 1.12/1.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))))),
% 1.12/1.34 inference(quant_inst,[status(thm)],[])).
% 1.12/1.34 tff(394,plain,
% 1.12/1.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(z))))),
% 1.12/1.34 inference(modus_ponens,[status(thm)],[393, 392])).
% 1.12/1.34 tff(395,plain,
% 1.12/1.34 (~b(elem!1, s(s(z)))),
% 1.12/1.34 inference(unit_resolution,[status(thm)],[394, 75, 388, 352, 330])).
% 1.12/1.34 tff(396,plain,
% 1.12/1.34 (((~![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))))),
% 1.12/1.34 inference(rewrite,[status(thm)],[])).
% 1.12/1.34 tff(397,plain,
% 1.12/1.34 ((~![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))))),
% 1.12/1.35 inference(quant_inst,[status(thm)],[])).
% 1.12/1.35 tff(398,plain,
% 1.12/1.35 ((~![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)))),
% 1.12/1.35 inference(modus_ponens,[status(thm)],[397, 396])).
% 1.12/1.35 tff(399,plain,
% 1.12/1.35 ((elem!1 = s(s(z))) | r(elem!1, s(s(z)))),
% 1.12/1.35 inference(unit_resolution,[status(thm)],[398, 58, 395])).
% 1.12/1.35 tff(400,plain,
% 1.12/1.35 (r(elem!1, s(s(z)))),
% 1.12/1.35 inference(unit_resolution,[status(thm)],[399, 318])).
% 1.12/1.35 tff(401,assumption,(b(s(s(z)), z)), introduced(assumption)).
% 1.12/1.35 tff(402,assumption,(b(s(z), s(s(z)))), introduced(assumption)).
% 1.12/1.35 tff(403,plain,
% 1.12/1.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 1.12/1.35 inference(rewrite,[status(thm)],[])).
% 1.12/1.35 tff(404,plain,
% 1.12/1.35 (((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 1.12/1.35 inference(rewrite,[status(thm)],[])).
% 1.12/1.35 tff(405,plain,
% 1.12/1.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))))),
% 1.12/1.35 inference(monotonicity,[status(thm)],[404])).
% 1.12/1.35 tff(406,plain,
% 1.12/1.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 1.12/1.35 inference(transitivity,[status(thm)],[405, 403])).
% 1.12/1.35 tff(407,plain,
% 1.12/1.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))),
% 1.12/1.35 inference(quant_inst,[status(thm)],[])).
% 1.12/1.35 tff(408,plain,
% 1.12/1.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))),
% 1.12/1.35 inference(modus_ponens,[status(thm)],[407, 406])).
% 1.12/1.35 tff(409,plain,
% 1.12/1.35 ($false),
% 1.12/1.35 inference(unit_resolution,[status(thm)],[408, 75, 372, 402, 370, 401])).
% 1.12/1.35 tff(410,plain,((~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.12/1.35 tff(411,plain,
% 1.12/1.35 (~b(s(z), s(s(z)))),
% 1.12/1.35 inference(unit_resolution,[status(thm)],[410, 330, 352, 369])).
% 1.12/1.35 tff(412,plain,
% 1.12/1.35 (((~![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))))),
% 1.12/1.35 inference(rewrite,[status(thm)],[])).
% 1.12/1.35 tff(413,plain,
% 1.12/1.35 ((~![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))))),
% 1.12/1.35 inference(quant_inst,[status(thm)],[])).
% 1.12/1.35 tff(414,plain,
% 1.12/1.35 ((~![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)))),
% 1.12/1.35 inference(modus_ponens,[status(thm)],[413, 412])).
% 1.12/1.35 tff(415,plain,
% 1.12/1.35 ((s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z)))),
% 1.12/1.35 inference(unit_resolution,[status(thm)],[414, 58])).
% 1.12/1.35 tff(416,plain,
% 1.12/1.35 (b(s(z), s(s(z))) | r(s(z), s(s(z)))),
% 1.12/1.35 inference(unit_resolution,[status(thm)],[415, 147])).
% 1.12/1.35 tff(417,plain,
% 1.12/1.35 (r(s(z), s(s(z)))),
% 1.12/1.35 inference(unit_resolution,[status(thm)],[416, 411])).
% 1.12/1.35 tff(418,plain,
% 1.12/1.35 (((~![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(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))))),
% 1.12/1.35 inference(rewrite,[status(thm)],[])).
% 1.12/1.35 tff(419,plain,
% 1.12/1.35 (((~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(z), z)) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))))),
% 1.12/1.35 inference(rewrite,[status(thm)],[])).
% 1.12/1.35 tff(420,plain,
% 1.12/1.35 (((~![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(elem!1, s(s(z)))) | (~r(s(z), z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z))))))),
% 1.12/1.35 inference(monotonicity,[status(thm)],[419])).
% 1.12/1.35 tff(421,plain,
% 1.12/1.35 (((~![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(elem!1, s(s(z)))) | (~r(s(z), z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))))),
% 1.12/1.35 inference(transitivity,[status(thm)],[420, 418])).
% 1.12/1.35 tff(422,plain,
% 1.12/1.35 ((~![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(elem!1, s(s(z)))) | (~r(s(z), z)) | (~r(elem!1, s(z))))),
% 1.12/1.35 inference(quant_inst,[status(thm)],[])).
% 1.12/1.35 tff(423,plain,
% 1.12/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z))))),
% 1.12/1.35 inference(modus_ponens,[status(thm)],[422, 421])).
% 1.12/1.35 tff(424,plain,
% 1.12/1.35 ($false),
% 1.12/1.35 inference(unit_resolution,[status(thm)],[423, 37, 382, 360, 417, 400])).
% 1.12/1.35 tff(425,plain,((~b(s(s(z)), s(z))) | (elem!1 = z) | (~r(z, elem!1)) | b(elem!1, s(z)) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.12/1.35 tff(426,plain,
% 1.12/1.35 (~b(s(s(z)), s(z))),
% 1.12/1.35 inference(unit_resolution,[status(thm)],[425, 14, 300, 305, 99])).
% 1.12/1.35 tff(427,plain,
% 1.12/1.35 (r(s(s(z)), s(z))),
% 1.12/1.35 inference(unit_resolution,[status(thm)],[153, 426])).
% 1.12/1.35 tff(428,assumption,(~b(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 1.12/1.35 tff(429,plain,
% 1.12/1.35 (b(s(s(z)), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.12/1.35 inference(monotonicity,[status(thm)],[310])).
% 1.12/1.35 tff(430,plain,
% 1.12/1.35 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 1.12/1.35 inference(symmetry,[status(thm)],[429])).
% 1.12/1.35 tff(431,plain,
% 1.12/1.35 (b(s(s(z)), s(s(s(s(z)))))),
% 1.12/1.35 inference(modus_ponens,[status(thm)],[286, 430])).
% 1.12/1.35 tff(432,plain,
% 1.12/1.35 ($false),
% 1.12/1.35 inference(unit_resolution,[status(thm)],[428, 431])).
% 1.12/1.35 tff(433,plain,((~(s(s(z)) = elem!1)) | b(s(s(z)), s(s(s(s(z))))) | (~b(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.12/1.35 tff(434,plain,
% 1.12/1.35 (~(s(s(z)) = elem!1)),
% 1.12/1.35 inference(unit_resolution,[status(thm)],[433, 428, 286])).
% 1.12/1.35 tff(435,plain,
% 1.12/1.35 (r(s(s(z)), elem!1)),
% 1.12/1.35 inference(unit_resolution,[status(thm)],[104, 434, 99])).
% 1.12/1.35 tff(436,plain,
% 1.12/1.35 (~r(elem!1, s(z))),
% 1.12/1.35 inference(unit_resolution,[status(thm)],[123, 435, 427])).
% 1.12/1.35 tff(437,plain,
% 1.12/1.35 (elem!1 = s(z)),
% 1.12/1.35 inference(unit_resolution,[status(thm)],[89, 436, 14])).
% 1.12/1.35 tff(438,plain,
% 1.12/1.35 (s(elem!1) = s(s(z))),
% 1.12/1.35 inference(monotonicity,[status(thm)],[437])).
% 1.12/1.35 tff(439,plain,
% 1.12/1.35 (s(s(elem!1)) = s(s(s(z)))),
% 1.12/1.35 inference(monotonicity,[status(thm)],[438])).
% 1.12/1.35 tff(440,plain,
% 1.12/1.35 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 1.12/1.35 inference(monotonicity,[status(thm)],[439])).
% 1.12/1.35 tff(441,plain,
% 1.12/1.35 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.12/1.35 inference(symmetry,[status(thm)],[440])).
% 1.12/1.35 tff(442,plain,
% 1.12/1.35 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.12/1.35 inference(monotonicity,[status(thm)],[439])).
% 1.12/1.35 tff(443,plain,
% 1.12/1.35 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 1.12/1.35 inference(monotonicity,[status(thm)],[442])).
% 1.12/1.35 tff(444,plain,
% 1.12/1.35 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 1.12/1.35 inference(symmetry,[status(thm)],[443])).
% 1.12/1.35 tff(445,plain,
% 1.12/1.35 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.12/1.35 inference(transitivity,[status(thm)],[444, 441])).
% 1.12/1.35 tff(446,plain,
% 1.12/1.35 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(z))),
% 1.12/1.35 inference(monotonicity,[status(thm)],[437])).
% 1.12/1.35 tff(447,plain,
% 1.12/1.35 (b(s(s(s(s(z)))), s(z))),
% 1.12/1.35 inference(modus_ponens,[status(thm)],[287, 446])).
% 1.12/1.35 tff(448,assumption,(s(s(z)) = s(s(s(s(z))))), introduced(assumption)).
% 1.12/1.35 tff(449,plain,
% 1.12/1.35 (inj_0(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 1.12/1.35 inference(monotonicity,[status(thm)],[448])).
% 1.12/1.35 tff(450,plain,
% 1.12/1.35 (inj_0(s(s(s(s(z))))) = inj_0(s(s(z)))),
% 1.12/1.35 inference(symmetry,[status(thm)],[449])).
% 1.12/1.35 tff(451,plain,
% 1.12/1.35 (s(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 1.12/1.35 inference(symmetry,[status(thm)],[250])).
% 1.12/1.35 tff(452,plain,
% 1.12/1.35 (s(s(s(z))) = s(z)),
% 1.12/1.35 inference(transitivity,[status(thm)],[451, 450, 133])).
% 1.12/1.35 tff(453,assumption,(s(s(s(z))) = s(z)), introduced(assumption)).
% 1.12/1.35 tff(454,plain,
% 1.12/1.35 (inj_0(s(s(s(z)))) = inj_0(s(z))),
% 1.12/1.35 inference(monotonicity,[status(thm)],[453])).
% 1.12/1.35 tff(455,plain,
% 1.12/1.35 (s(s(z)) = z),
% 1.12/1.35 inference(transitivity,[status(thm)],[254, 454, 128])).
% 1.12/1.35 tff(456,plain,
% 1.12/1.35 ($false),
% 1.12/1.35 inference(unit_resolution,[status(thm)],[145, 455])).
% 1.12/1.35 tff(457,plain,(~(s(s(s(z))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.12/1.35 tff(458,plain,
% 1.12/1.35 ($false),
% 1.12/1.35 inference(unit_resolution,[status(thm)],[457, 452])).
% 1.12/1.35 tff(459,plain,(~(s(s(z)) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.12/1.35 tff(460,assumption,(~r(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 1.12/1.35 tff(461,plain,
% 1.12/1.35 (((~![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))))))),
% 1.12/1.35 inference(rewrite,[status(thm)],[])).
% 1.12/1.35 tff(462,plain,
% 1.12/1.35 ((~![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))))))),
% 1.12/1.35 inference(quant_inst,[status(thm)],[])).
% 1.12/1.35 tff(463,plain,
% 1.12/1.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z)))))),
% 1.12/1.35 inference(modus_ponens,[status(thm)],[462, 461])).
% 1.12/1.35 tff(464,plain,
% 1.12/1.35 ($false),
% 1.12/1.35 inference(unit_resolution,[status(thm)],[463, 58, 428, 460, 459])).
% 1.12/1.35 tff(465,plain,(r(s(s(z)), s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.12/1.35 tff(466,plain,
% 1.12/1.35 (r(s(s(z)), s(s(s(s(z)))))),
% 1.12/1.35 inference(unit_resolution,[status(thm)],[465, 428])).
% 1.12/1.35 tff(467,assumption,(r(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 1.12/1.35 tff(468,assumption,(r(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 1.12/1.35 tff(469,plain,
% 1.12/1.35 (((~![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(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.12/1.35 inference(rewrite,[status(thm)],[])).
% 1.12/1.35 tff(470,plain,
% 1.12/1.35 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.12/1.35 inference(rewrite,[status(thm)],[])).
% 1.12/1.35 tff(471,plain,
% 1.12/1.35 (((~![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(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z))))))))),
% 1.12/1.35 inference(monotonicity,[status(thm)],[470])).
% 1.12/1.35 tff(472,plain,
% 1.12/1.35 (((~![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(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.12/1.35 inference(transitivity,[status(thm)],[471, 469])).
% 1.12/1.35 tff(473,plain,
% 1.12/1.35 ((~![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(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))),
% 1.12/1.35 inference(quant_inst,[status(thm)],[])).
% 1.12/1.35 tff(474,plain,
% 1.12/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z))))))),
% 1.12/1.35 inference(modus_ponens,[status(thm)],[473, 472])).
% 1.12/1.35 tff(475,plain,
% 1.12/1.35 ($false),
% 1.12/1.35 inference(unit_resolution,[status(thm)],[474, 37, 115, 468, 467])).
% 1.12/1.35 tff(476,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.12/1.35 tff(477,plain,
% 1.12/1.35 (~r(s(z), s(s(s(s(z)))))),
% 1.12/1.35 inference(unit_resolution,[status(thm)],[476, 466, 427])).
% 1.12/1.35 tff(478,plain,
% 1.12/1.35 ((~(s(s(s(s(z)))) = s(z))) <=> (~(s(z) = s(s(s(s(z))))))),
% 1.12/1.35 inference(monotonicity,[status(thm)],[247])).
% 1.12/1.35 tff(479,assumption,(s(s(s(s(z)))) = s(z)), introduced(assumption)).
% 1.12/1.35 tff(480,plain,
% 1.12/1.35 (inj_0(s(s(s(s(z))))) = inj_0(s(z))),
% 1.12/1.35 inference(monotonicity,[status(thm)],[479])).
% 1.12/1.35 tff(481,plain,
% 1.12/1.35 (s(s(s(z))) = z),
% 1.12/1.35 inference(transitivity,[status(thm)],[451, 480, 128])).
% 1.12/1.35 tff(482,plain,
% 1.12/1.35 ($false),
% 1.12/1.35 inference(unit_resolution,[status(thm)],[221, 481])).
% 1.12/1.35 tff(483,plain,(~(s(s(s(s(z)))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.12/1.35 tff(484,plain,
% 1.12/1.35 (~(s(z) = s(s(s(s(z)))))),
% 1.12/1.35 inference(modus_ponens,[status(thm)],[483, 478])).
% 1.12/1.35 tff(485,plain,
% 1.12/1.35 (((~![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))))))),
% 1.12/1.35 inference(rewrite,[status(thm)],[])).
% 1.12/1.35 tff(486,plain,
% 1.12/1.35 ((~![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))))))),
% 1.12/1.35 inference(quant_inst,[status(thm)],[])).
% 1.12/1.35 tff(487,plain,
% 1.12/1.35 ((~![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)))))),
% 1.12/1.35 inference(modus_ponens,[status(thm)],[486, 485])).
% 1.12/1.35 tff(488,plain,
% 1.12/1.35 ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 1.12/1.35 inference(unit_resolution,[status(thm)],[487, 58])).
% 1.12/1.35 tff(489,plain,
% 1.12/1.35 (b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 1.12/1.35 inference(unit_resolution,[status(thm)],[488, 484])).
% 1.12/1.35 tff(490,plain,
% 1.12/1.35 (b(s(z), s(s(s(s(z)))))),
% 1.12/1.35 inference(unit_resolution,[status(thm)],[489, 477])).
% 1.12/1.35 tff(491,plain,
% 1.12/1.35 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(z))), s(z))),
% 1.12/1.35 inference(monotonicity,[status(thm)],[439])).
% 1.12/1.35 tff(492,plain,
% 1.12/1.35 (r(z, elem!1) <=> r(z, s(z))),
% 1.12/1.35 inference(monotonicity,[status(thm)],[437])).
% 1.12/1.35 tff(493,plain,
% 1.12/1.35 (r(z, s(z))),
% 1.12/1.35 inference(modus_ponens,[status(thm)],[300, 492])).
% 1.12/1.36 tff(494,assumption,(r(s(s(elem!1)), s(z))), introduced(assumption)).
% 1.12/1.36 tff(495,plain,
% 1.12/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), 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)))))),
% 1.12/1.36 inference(rewrite,[status(thm)],[])).
% 1.12/1.36 tff(496,plain,
% 1.12/1.36 (((~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)))))),
% 1.12/1.36 inference(rewrite,[status(thm)],[])).
% 1.12/1.36 tff(497,plain,
% 1.12/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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))))))),
% 1.12/1.36 inference(monotonicity,[status(thm)],[496])).
% 1.12/1.36 tff(498,plain,
% 1.12/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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)))))),
% 1.12/1.36 inference(transitivity,[status(thm)],[497, 495])).
% 1.12/1.36 tff(499,plain,
% 1.12/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.12/1.36 inference(quant_inst,[status(thm)],[])).
% 1.12/1.36 tff(500,plain,
% 1.12/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z))))),
% 1.12/1.36 inference(modus_ponens,[status(thm)],[499, 498])).
% 1.12/1.36 tff(501,plain,
% 1.12/1.36 (~r(s(s(elem!1)), s(s(z)))),
% 1.12/1.36 inference(unit_resolution,[status(thm)],[500, 37, 494, 115])).
% 1.12/1.36 tff(502,plain,
% 1.12/1.36 (((~![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))))),
% 1.12/1.36 inference(rewrite,[status(thm)],[])).
% 1.12/1.36 tff(503,plain,
% 1.12/1.36 ((~![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))))),
% 1.12/1.36 inference(quant_inst,[status(thm)],[])).
% 1.12/1.36 tff(504,plain,
% 1.12/1.36 ((~![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)))),
% 1.12/1.36 inference(modus_ponens,[status(thm)],[503, 502])).
% 1.12/1.36 tff(505,plain,
% 1.12/1.36 (b(s(s(elem!1)), s(s(z)))),
% 1.12/1.36 inference(unit_resolution,[status(thm)],[504, 58, 266, 501])).
% 1.12/1.36 tff(506,assumption,(r(z, s(z))), introduced(assumption)).
% 1.12/1.36 tff(507,plain,
% 1.12/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(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, elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)))),
% 1.12/1.36 inference(rewrite,[status(thm)],[])).
% 1.12/1.36 tff(508,plain,
% 1.12/1.36 (((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z))) <=> ((~r(z, elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)))),
% 1.12/1.36 inference(rewrite,[status(thm)],[])).
% 1.12/1.36 tff(509,plain,
% 1.12/1.36 (((~![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(s(s(elem!1)), s(z))) | (~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)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z))))),
% 1.12/1.36 inference(monotonicity,[status(thm)],[508])).
% 1.12/1.36 tff(510,plain,
% 1.12/1.36 (((~![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(s(s(elem!1)), s(z))) | (~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)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)))),
% 1.12/1.36 inference(transitivity,[status(thm)],[509, 507])).
% 1.12/1.36 tff(511,plain,
% 1.12/1.36 ((~![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(s(s(elem!1)), s(z))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)))),
% 1.12/1.36 inference(quant_inst,[status(thm)],[])).
% 1.12/1.36 tff(512,plain,
% 1.12/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z))),
% 1.12/1.36 inference(modus_ponens,[status(thm)],[511, 510])).
% 1.12/1.36 tff(513,plain,
% 1.12/1.36 (~r(s(s(elem!1)), z)),
% 1.12/1.36 inference(unit_resolution,[status(thm)],[512, 37, 300, 494, 506])).
% 1.12/1.36 tff(514,plain,
% 1.12/1.36 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(elem!1)) = z))),
% 1.12/1.36 inference(quant_inst,[status(thm)],[])).
% 1.12/1.36 tff(515,plain,
% 1.12/1.36 (~(s(s(elem!1)) = z)),
% 1.12/1.36 inference(unit_resolution,[status(thm)],[514, 143])).
% 1.12/1.36 tff(516,plain,
% 1.12/1.36 (((~![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))),
% 1.12/1.36 inference(rewrite,[status(thm)],[])).
% 1.12/1.36 tff(517,plain,
% 1.12/1.36 ((~![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))),
% 1.12/1.36 inference(quant_inst,[status(thm)],[])).
% 1.12/1.36 tff(518,plain,
% 1.12/1.36 ((~![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)),
% 1.12/1.36 inference(modus_ponens,[status(thm)],[517, 516])).
% 1.12/1.36 tff(519,plain,
% 1.12/1.36 (b(s(s(elem!1)), z)),
% 1.12/1.36 inference(unit_resolution,[status(thm)],[518, 58, 515, 513])).
% 1.12/1.36 tff(520,plain,
% 1.12/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 1.12/1.36 inference(rewrite,[status(thm)],[])).
% 1.12/1.36 tff(521,plain,
% 1.12/1.36 (((~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)), z)) | (~r(s(s(z)), s(z))))),
% 1.12/1.36 inference(rewrite,[status(thm)],[])).
% 1.12/1.36 tff(522,plain,
% 1.12/1.36 (((~![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(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)), z)) | (~r(s(s(z)), s(z)))))),
% 1.12/1.36 inference(monotonicity,[status(thm)],[521])).
% 1.12/1.36 tff(523,plain,
% 1.12/1.36 (((~![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(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)), z)) | (~r(s(s(z)), s(z))))),
% 1.12/1.36 inference(transitivity,[status(thm)],[522, 520])).
% 1.12/1.36 tff(524,plain,
% 1.12/1.36 ((~![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(s(s(z)), s(z))) | (~r(z, elem!1)) | (~r(s(s(z)), z)))),
% 1.12/1.36 inference(quant_inst,[status(thm)],[])).
% 1.12/1.36 tff(525,plain,
% 1.12/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))),
% 1.12/1.36 inference(modus_ponens,[status(thm)],[524, 523])).
% 1.12/1.36 tff(526,plain,
% 1.12/1.36 (~r(s(s(z)), z)),
% 1.12/1.36 inference(unit_resolution,[status(thm)],[525, 37, 300, 506, 115])).
% 1.12/1.36 tff(527,plain,
% 1.12/1.36 (b(s(s(z)), z)),
% 1.12/1.36 inference(unit_resolution,[status(thm)],[200, 58, 145, 526])).
% 1.12/1.36 tff(528,plain,
% 1.12/1.36 ((z = s(s(z))) <=> (s(s(z)) = z)),
% 1.12/1.36 inference(commutativity,[status(thm)],[])).
% 1.12/1.36 tff(529,plain,
% 1.12/1.36 ((s(s(z)) = z) <=> (z = s(s(z)))),
% 1.12/1.36 inference(symmetry,[status(thm)],[528])).
% 1.12/1.36 tff(530,plain,
% 1.12/1.36 ((~(s(s(z)) = z)) <=> (~(z = s(s(z))))),
% 1.12/1.36 inference(monotonicity,[status(thm)],[529])).
% 1.12/1.36 tff(531,plain,
% 1.12/1.36 (~(z = s(s(z)))),
% 1.12/1.36 inference(modus_ponens,[status(thm)],[145, 530])).
% 1.12/1.36 tff(532,plain,
% 1.12/1.36 (((~![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(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))))),
% 1.12/1.36 inference(rewrite,[status(thm)],[])).
% 1.12/1.36 tff(533,plain,
% 1.12/1.36 (((~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))))),
% 1.12/1.36 inference(rewrite,[status(thm)],[])).
% 1.12/1.36 tff(534,plain,
% 1.12/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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)))))),
% 1.12/1.36 inference(monotonicity,[status(thm)],[533])).
% 1.12/1.36 tff(535,plain,
% 1.12/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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))))),
% 1.12/1.36 inference(transitivity,[status(thm)],[534, 532])).
% 1.12/1.36 tff(536,plain,
% 1.12/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))),
% 1.12/1.36 inference(quant_inst,[status(thm)],[])).
% 1.12/1.36 tff(537,plain,
% 1.12/1.36 ((~![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(z, s(s(z)))) | (~r(s(s(z)), s(z)))),
% 1.12/1.36 inference(modus_ponens,[status(thm)],[536, 535])).
% 1.12/1.36 tff(538,plain,
% 1.12/1.36 (~r(z, s(s(z)))),
% 1.12/1.36 inference(unit_resolution,[status(thm)],[537, 37, 506, 115])).
% 1.12/1.36 tff(539,plain,
% 1.12/1.36 ((z = s(s(z))) | b(z, s(s(z)))),
% 1.12/1.36 inference(unit_resolution,[status(thm)],[349, 58, 538])).
% 1.12/1.36 tff(540,plain,
% 1.12/1.36 (b(z, s(s(z)))),
% 1.12/1.36 inference(unit_resolution,[status(thm)],[539, 531])).
% 1.12/1.36 tff(541,plain,
% 1.12/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.12/1.36 inference(rewrite,[status(thm)],[])).
% 1.12/1.36 tff(542,plain,
% 1.12/1.36 (((~b(s(s(z)), z)) | (~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(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.12/1.36 inference(rewrite,[status(thm)],[])).
% 1.12/1.36 tff(543,plain,
% 1.12/1.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z))))))),
% 1.12/1.37 inference(monotonicity,[status(thm)],[542])).
% 1.12/1.37 tff(544,plain,
% 1.12/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.12/1.37 inference(transitivity,[status(thm)],[543, 541])).
% 1.12/1.37 tff(545,plain,
% 1.12/1.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))))),
% 1.12/1.37 inference(quant_inst,[status(thm)],[])).
% 1.12/1.37 tff(546,plain,
% 1.12/1.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z))))),
% 1.12/1.37 inference(modus_ponens,[status(thm)],[545, 544])).
% 1.12/1.37 tff(547,plain,
% 1.12/1.37 ($false),
% 1.12/1.37 inference(unit_resolution,[status(thm)],[546, 75, 540, 527, 519, 505])).
% 1.12/1.37 tff(548,plain,((~r(s(s(elem!1)), s(z))) | (s(s(elem!1)) = s(s(z))) | (~r(s(s(z)), s(z))) | (~r(z, elem!1)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.12/1.37 tff(549,plain,
% 1.12/1.37 (~r(s(s(elem!1)), s(z))),
% 1.12/1.37 inference(unit_resolution,[status(thm)],[548, 493, 300, 427, 266])).
% 1.12/1.37 tff(550,assumption,(s(s(elem!1)) = s(z)), introduced(assumption)).
% 1.12/1.37 tff(551,plain,
% 1.12/1.37 (inj_0(s(s(elem!1))) = inj_0(s(z))),
% 1.12/1.37 inference(monotonicity,[status(thm)],[550])).
% 1.12/1.37 tff(552,plain,
% 1.12/1.37 (s(elem!1) = z),
% 1.12/1.37 inference(transitivity,[status(thm)],[229, 551, 128])).
% 1.12/1.37 tff(553,plain,
% 1.12/1.37 ((~![X: $i] : (~(s(X) = z))) | (~(s(elem!1) = z))),
% 1.12/1.37 inference(quant_inst,[status(thm)],[])).
% 1.12/1.37 tff(554,plain,
% 1.12/1.37 (~(s(elem!1) = z)),
% 1.12/1.37 inference(unit_resolution,[status(thm)],[553, 143])).
% 1.12/1.37 tff(555,plain,
% 1.12/1.37 ($false),
% 1.12/1.37 inference(unit_resolution,[status(thm)],[554, 552])).
% 1.12/1.37 tff(556,plain,(~(s(s(elem!1)) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.12/1.37 tff(557,plain,
% 1.12/1.37 (((~![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)))),
% 1.12/1.37 inference(rewrite,[status(thm)],[])).
% 1.12/1.37 tff(558,plain,
% 1.12/1.37 ((~![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)))),
% 1.12/1.37 inference(quant_inst,[status(thm)],[])).
% 1.12/1.37 tff(559,plain,
% 1.12/1.37 ((~![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))),
% 1.12/1.37 inference(modus_ponens,[status(thm)],[558, 557])).
% 1.12/1.37 tff(560,plain,
% 1.12/1.37 ((s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z))),
% 1.12/1.37 inference(unit_resolution,[status(thm)],[559, 58])).
% 1.12/1.37 tff(561,plain,
% 1.12/1.37 (b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z))),
% 1.12/1.37 inference(unit_resolution,[status(thm)],[560, 556])).
% 1.12/1.37 tff(562,plain,
% 1.12/1.37 (b(s(s(elem!1)), s(z))),
% 1.12/1.37 inference(unit_resolution,[status(thm)],[561, 549])).
% 1.12/1.37 tff(563,plain,
% 1.12/1.37 (b(s(s(s(z))), s(z))),
% 1.12/1.37 inference(modus_ponens,[status(thm)],[562, 491])).
% 1.12/1.37 tff(564,plain,
% 1.12/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(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(X1, 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(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.12/1.37 inference(rewrite,[status(thm)],[])).
% 1.12/1.37 tff(565,plain,
% 1.12/1.37 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.12/1.37 inference(rewrite,[status(thm)],[])).
% 1.12/1.37 tff(566,plain,
% 1.12/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))))),
% 1.12/1.37 inference(monotonicity,[status(thm)],[565])).
% 1.12/1.37 tff(567,plain,
% 1.12/1.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.12/1.37 inference(transitivity,[status(thm)],[566, 564])).
% 1.12/1.37 tff(568,plain,
% 1.12/1.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.12/1.37 inference(quant_inst,[status(thm)],[])).
% 1.12/1.37 tff(569,plain,
% 1.12/1.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))),
% 1.12/1.37 inference(modus_ponens,[status(thm)],[568, 567])).
% 1.12/1.37 tff(570,plain,
% 1.12/1.37 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.12/1.37 inference(unit_resolution,[status(thm)],[569, 75, 563, 490, 447])).
% 1.12/1.37 tff(571,plain,
% 1.12/1.37 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))))),
% 1.12/1.37 inference(rewrite,[status(thm)],[])).
% 1.12/1.37 tff(572,plain,
% 1.12/1.37 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))))),
% 1.12/1.37 inference(quant_inst,[status(thm)],[])).
% 1.12/1.37 tff(573,plain,
% 1.12/1.37 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 1.12/1.37 inference(modus_ponens,[status(thm)],[572, 571])).
% 1.12/1.37 tff(574,plain,
% 1.12/1.37 ((s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 1.12/1.38 inference(unit_resolution,[status(thm)],[573, 58])).
% 1.12/1.38 tff(575,plain,
% 1.12/1.38 (b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 1.12/1.38 inference(unit_resolution,[status(thm)],[574, 263])).
% 1.12/1.38 tff(576,plain,
% 1.12/1.38 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.12/1.38 inference(unit_resolution,[status(thm)],[575, 570])).
% 1.12/1.38 tff(577,plain,
% 1.12/1.38 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.12/1.38 inference(modus_ponens,[status(thm)],[576, 445])).
% 1.12/1.38 tff(578,assumption,(b(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 1.12/1.38 tff(579,plain,
% 1.12/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.12/1.38 inference(rewrite,[status(thm)],[])).
% 1.12/1.38 tff(580,plain,
% 1.12/1.38 (((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.12/1.38 inference(rewrite,[status(thm)],[])).
% 1.12/1.38 tff(581,plain,
% 1.12/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(s(s(z)))))) | (~b(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(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z))))))))),
% 1.12/1.38 inference(monotonicity,[status(thm)],[580])).
% 1.12/1.38 tff(582,plain,
% 1.12/1.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(s(s(z)))))) | (~b(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(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.12/1.38 inference(transitivity,[status(thm)],[581, 579])).
% 1.12/1.38 tff(583,plain,
% 1.12/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(s(s(z)))))) | (~b(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(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)))),
% 1.12/1.38 inference(quant_inst,[status(thm)],[])).
% 1.12/1.38 tff(584,plain,
% 1.12/1.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z))))))),
% 1.12/1.38 inference(modus_ponens,[status(thm)],[583, 582])).
% 1.12/1.38 tff(585,plain,
% 1.12/1.38 ($false),
% 1.12/1.38 inference(unit_resolution,[status(thm)],[584, 75, 107, 578, 286, 287])).
% 1.12/1.38 tff(586,plain,((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.12/1.38 tff(587,plain,
% 1.12/1.38 (~b(s(z), elem!1)),
% 1.12/1.38 inference(unit_resolution,[status(thm)],[586, 490, 286, 287])).
% 1.12/1.38 tff(588,assumption,(r(s(z), elem!1)), introduced(assumption)).
% 1.12/1.38 tff(589,plain,
% 1.12/1.38 (((~![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(z)), 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(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))),
% 1.12/1.38 inference(rewrite,[status(thm)],[])).
% 1.12/1.38 tff(590,plain,
% 1.12/1.38 (((~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)), s(z))) | (~r(s(s(z)), elem!1)))),
% 1.12/1.38 inference(rewrite,[status(thm)],[])).
% 1.12/1.38 tff(591,plain,
% 1.12/1.38 (((~![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(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)), s(z))) | (~r(s(s(z)), elem!1))))),
% 1.12/1.38 inference(monotonicity,[status(thm)],[590])).
% 1.12/1.38 tff(592,plain,
% 1.12/1.38 (((~![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(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)), s(z))) | (~r(s(s(z)), elem!1)))),
% 1.12/1.38 inference(transitivity,[status(thm)],[591, 589])).
% 1.12/1.38 tff(593,plain,
% 1.12/1.38 ((~![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(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))))),
% 1.12/1.38 inference(quant_inst,[status(thm)],[])).
% 1.12/1.38 tff(594,plain,
% 1.12/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1))),
% 1.12/1.38 inference(modus_ponens,[status(thm)],[593, 592])).
% 1.12/1.38 tff(595,plain,
% 1.12/1.38 ($false),
% 1.12/1.38 inference(unit_resolution,[status(thm)],[594, 37, 588, 106, 115])).
% 1.12/1.38 tff(596,plain,((~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.12/1.38 tff(597,plain,
% 1.12/1.38 (~r(s(z), elem!1)),
% 1.12/1.38 inference(unit_resolution,[status(thm)],[596, 435, 427])).
% 1.12/1.38 tff(598,plain,
% 1.12/1.38 (((~![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))),
% 1.12/1.38 inference(rewrite,[status(thm)],[])).
% 1.12/1.38 tff(599,plain,
% 1.12/1.38 ((~![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))),
% 1.12/1.38 inference(quant_inst,[status(thm)],[])).
% 1.12/1.38 tff(600,plain,
% 1.12/1.38 ((~![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)),
% 1.12/1.38 inference(modus_ponens,[status(thm)],[599, 598])).
% 1.12/1.38 tff(601,plain,
% 1.12/1.38 ((s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1)),
% 1.12/1.38 inference(unit_resolution,[status(thm)],[600, 58])).
% 1.12/1.38 tff(602,plain,
% 1.12/1.38 (s(z) = elem!1),
% 1.12/1.38 inference(unit_resolution,[status(thm)],[601, 597, 587])).
% 1.12/1.38 tff(603,plain,
% 1.12/1.38 (b(elem!1, s(s(s(elem!1)))) <=> b(s(z), s(s(s(s(z)))))),
% 1.12/1.38 inference(monotonicity,[status(thm)],[437, 442])).
% 1.12/1.38 tff(604,plain,
% 1.12/1.38 (b(s(z), s(s(s(s(z))))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.12/1.38 inference(symmetry,[status(thm)],[603])).
% 1.12/1.38 tff(605,plain,
% 1.12/1.38 (b(elem!1, s(s(s(elem!1))))),
% 1.12/1.38 inference(modus_ponens,[status(thm)],[490, 604])).
% 1.12/1.38 tff(606,plain,
% 1.12/1.38 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(z))),
% 1.12/1.38 inference(monotonicity,[status(thm)],[437])).
% 1.12/1.38 tff(607,plain,
% 1.12/1.38 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 1.12/1.38 inference(symmetry,[status(thm)],[606])).
% 1.12/1.38 tff(608,plain,
% 1.12/1.38 (b(s(s(elem!1)), elem!1)),
% 1.12/1.38 inference(modus_ponens,[status(thm)],[562, 607])).
% 1.12/1.38 tff(609,plain,
% 1.12/1.38 (s(s(z)) = s(elem!1)),
% 1.12/1.38 inference(monotonicity,[status(thm)],[93])).
% 1.12/1.38 tff(610,plain,
% 1.12/1.38 (s(s(s(z))) = s(s(elem!1))),
% 1.12/1.38 inference(monotonicity,[status(thm)],[609])).
% 1.12/1.38 tff(611,plain,
% 1.12/1.38 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.12/1.38 inference(monotonicity,[status(thm)],[610])).
% 1.12/1.38 tff(612,plain,
% 1.12/1.38 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.12/1.38 inference(symmetry,[status(thm)],[611])).
% 1.12/1.38 tff(613,plain,
% 1.12/1.38 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 1.12/1.38 inference(monotonicity,[status(thm)],[612])).
% 1.12/1.38 tff(614,plain,
% 1.12/1.38 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 1.12/1.38 inference(symmetry,[status(thm)],[613])).
% 1.12/1.38 tff(615,plain,
% 1.12/1.38 ((s(z) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(z)))))),
% 1.12/1.38 inference(monotonicity,[status(thm)],[93])).
% 1.12/1.38 tff(616,plain,
% 1.12/1.38 ((s(z) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 1.12/1.38 inference(transitivity,[status(thm)],[615, 240])).
% 1.12/1.38 tff(617,plain,
% 1.12/1.38 ((~(s(z) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 1.12/1.38 inference(monotonicity,[status(thm)],[616])).
% 1.12/1.38 tff(618,plain,
% 1.12/1.38 (~(s(s(s(s(z)))) = elem!1)),
% 1.12/1.38 inference(modus_ponens,[status(thm)],[484, 617])).
% 1.12/1.38 tff(619,plain,
% 1.12/1.38 (s(elem!1) = s(s(z))),
% 1.12/1.38 inference(symmetry,[status(thm)],[609])).
% 1.12/1.38 tff(620,plain,
% 1.12/1.38 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 1.12/1.38 inference(monotonicity,[status(thm)],[619, 612])).
% 1.12/1.38 tff(621,plain,
% 1.12/1.38 ((s(s(z)) = s(s(s(s(z))))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.12/1.38 inference(symmetry,[status(thm)],[620])).
% 1.12/1.38 tff(622,plain,
% 1.12/1.38 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 1.12/1.38 inference(monotonicity,[status(thm)],[621])).
% 1.12/1.38 tff(623,plain,
% 1.12/1.38 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.12/1.38 inference(modus_ponens,[status(thm)],[459, 622])).
% 1.12/1.38 tff(624,assumption,(r(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.12/1.38 tff(625,plain,
% 1.12/1.38 (r(s(elem!1), elem!1) <=> r(s(s(z)), elem!1)),
% 1.12/1.38 inference(monotonicity,[status(thm)],[619])).
% 1.12/1.38 tff(626,plain,
% 1.12/1.38 (r(s(s(z)), elem!1) <=> r(s(elem!1), elem!1)),
% 1.12/1.38 inference(symmetry,[status(thm)],[625])).
% 1.12/1.38 tff(627,plain,
% 1.12/1.38 (r(s(elem!1), elem!1)),
% 1.12/1.38 inference(modus_ponens,[status(thm)],[106, 626])).
% 1.12/1.38 tff(628,plain,
% 1.12/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(elem!1), s(s(s(elem!1))))))),
% 1.12/1.38 inference(rewrite,[status(thm)],[])).
% 1.12/1.38 tff(629,plain,
% 1.12/1.38 (((~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(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.12/1.38 inference(rewrite,[status(thm)],[])).
% 1.12/1.38 tff(630,plain,
% 1.12/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1)))))))),
% 1.12/1.38 inference(monotonicity,[status(thm)],[629])).
% 1.12/1.38 tff(631,plain,
% 1.12/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.12/1.38 inference(transitivity,[status(thm)],[630, 628])).
% 1.12/1.38 tff(632,plain,
% 1.12/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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))))))),
% 1.12/1.38 inference(quant_inst,[status(thm)],[])).
% 1.12/1.38 tff(633,plain,
% 1.12/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 1.12/1.39 inference(modus_ponens,[status(thm)],[632, 631])).
% 1.12/1.39 tff(634,plain,
% 1.12/1.39 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.12/1.39 inference(unit_resolution,[status(thm)],[633, 37, 627, 624])).
% 1.12/1.39 tff(635,plain,
% 1.12/1.39 (((~![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)))))),
% 1.12/1.39 inference(rewrite,[status(thm)],[])).
% 1.12/1.39 tff(636,plain,
% 1.12/1.39 ((~![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)))))),
% 1.12/1.39 inference(quant_inst,[status(thm)],[])).
% 1.12/1.39 tff(637,plain,
% 1.12/1.39 ((~![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))))),
% 1.12/1.39 inference(modus_ponens,[status(thm)],[636, 635])).
% 1.12/1.39 tff(638,plain,
% 1.12/1.39 ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1))))),
% 1.12/1.39 inference(unit_resolution,[status(thm)],[637, 58, 634])).
% 1.12/1.39 tff(639,plain,
% 1.12/1.39 (b(s(elem!1), s(s(s(elem!1))))),
% 1.12/1.39 inference(unit_resolution,[status(thm)],[638, 623])).
% 1.12/1.39 tff(640,plain,
% 1.12/1.39 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 1.12/1.39 inference(commutativity,[status(thm)],[])).
% 1.12/1.39 tff(641,plain,
% 1.12/1.39 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(z)))),
% 1.12/1.39 inference(monotonicity,[status(thm)],[612, 619])).
% 1.12/1.39 tff(642,plain,
% 1.12/1.39 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(z)) = s(s(s(s(z)))))),
% 1.12/1.39 inference(transitivity,[status(thm)],[641, 640])).
% 1.12/1.39 tff(643,plain,
% 1.12/1.39 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.12/1.39 inference(symmetry,[status(thm)],[642])).
% 1.12/1.39 tff(644,plain,
% 1.12/1.39 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 1.12/1.39 inference(monotonicity,[status(thm)],[643])).
% 1.12/1.39 tff(645,plain,
% 1.12/1.39 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.12/1.39 inference(modus_ponens,[status(thm)],[459, 644])).
% 1.12/1.39 tff(646,plain,
% 1.12/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.12/1.39 inference(rewrite,[status(thm)],[])).
% 1.12/1.39 tff(647,plain,
% 1.12/1.39 (((~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(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.12/1.39 inference(rewrite,[status(thm)],[])).
% 1.12/1.39 tff(648,plain,
% 1.12/1.39 (((~![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(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(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1)))))),
% 1.12/1.39 inference(monotonicity,[status(thm)],[647])).
% 1.12/1.39 tff(649,plain,
% 1.12/1.39 (((~![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(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(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.12/1.39 inference(transitivity,[status(thm)],[648, 646])).
% 1.12/1.39 tff(650,plain,
% 1.12/1.39 ((~![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(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.12/1.39 inference(quant_inst,[status(thm)],[])).
% 1.12/1.39 tff(651,plain,
% 1.12/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 1.12/1.39 inference(modus_ponens,[status(thm)],[650, 649])).
% 1.12/1.39 tff(652,plain,
% 1.12/1.39 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.12/1.39 inference(unit_resolution,[status(thm)],[651, 37, 627, 624])).
% 1.12/1.39 tff(653,plain,
% 1.12/1.39 (((~![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)))),
% 1.12/1.39 inference(rewrite,[status(thm)],[])).
% 1.12/1.39 tff(654,plain,
% 1.12/1.39 ((~![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)))),
% 1.12/1.39 inference(quant_inst,[status(thm)],[])).
% 1.12/1.39 tff(655,plain,
% 1.12/1.39 ((~![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))),
% 1.12/1.39 inference(modus_ponens,[status(thm)],[654, 653])).
% 1.12/1.39 tff(656,plain,
% 1.12/1.39 ((s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1))),
% 1.12/1.39 inference(unit_resolution,[status(thm)],[655, 58, 652])).
% 1.12/1.39 tff(657,plain,
% 1.12/1.39 (b(s(s(s(elem!1))), s(elem!1))),
% 1.12/1.39 inference(unit_resolution,[status(thm)],[656, 645])).
% 1.12/1.39 tff(658,plain,
% 1.12/1.39 ((z = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = z)),
% 1.12/1.39 inference(commutativity,[status(thm)],[])).
% 1.12/1.39 tff(659,plain,
% 1.12/1.39 ((s(s(s(elem!1))) = z) <=> (z = s(s(s(elem!1))))),
% 1.12/1.39 inference(symmetry,[status(thm)],[658])).
% 1.12/1.39 tff(660,plain,
% 1.12/1.39 ((~(s(s(s(elem!1))) = z)) <=> (~(z = s(s(s(elem!1)))))),
% 1.12/1.39 inference(monotonicity,[status(thm)],[659])).
% 1.12/1.39 tff(661,plain,
% 1.12/1.39 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(elem!1))) = z))),
% 1.12/1.39 inference(quant_inst,[status(thm)],[])).
% 1.12/1.39 tff(662,plain,
% 1.12/1.39 (~(s(s(s(elem!1))) = z)),
% 1.12/1.39 inference(unit_resolution,[status(thm)],[661, 143])).
% 1.12/1.39 tff(663,plain,
% 1.12/1.39 (~(z = s(s(s(elem!1))))),
% 1.12/1.39 inference(modus_ponens,[status(thm)],[662, 660])).
% 1.12/1.39 tff(664,plain,
% 1.12/1.39 (((~![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, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))))),
% 1.12/1.39 inference(rewrite,[status(thm)],[])).
% 1.12/1.39 tff(665,plain,
% 1.12/1.39 (((~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(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))))),
% 1.12/1.39 inference(rewrite,[status(thm)],[])).
% 1.12/1.39 tff(666,plain,
% 1.12/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1)))))))),
% 1.12/1.39 inference(monotonicity,[status(thm)],[665])).
% 1.12/1.39 tff(667,plain,
% 1.12/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))))),
% 1.12/1.39 inference(transitivity,[status(thm)],[666, 664])).
% 1.12/1.39 tff(668,plain,
% 1.12/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1))))))),
% 1.12/1.39 inference(quant_inst,[status(thm)],[])).
% 1.12/1.39 tff(669,plain,
% 1.12/1.39 ((~![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, s(s(s(elem!1)))))),
% 1.12/1.39 inference(modus_ponens,[status(thm)],[668, 667])).
% 1.12/1.39 tff(670,plain,
% 1.12/1.39 ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, s(s(s(elem!1)))))),
% 1.12/1.39 inference(unit_resolution,[status(thm)],[669, 37, 300])).
% 1.12/1.39 tff(671,plain,
% 1.12/1.39 (~r(z, s(s(s(elem!1))))),
% 1.12/1.39 inference(unit_resolution,[status(thm)],[670, 624])).
% 1.12/1.39 tff(672,plain,
% 1.12/1.39 (((~![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)))))),
% 1.12/1.39 inference(rewrite,[status(thm)],[])).
% 1.12/1.39 tff(673,plain,
% 1.12/1.39 ((~![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)))))),
% 1.12/1.39 inference(quant_inst,[status(thm)],[])).
% 1.12/1.39 tff(674,plain,
% 1.12/1.39 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1))))),
% 1.12/1.39 inference(modus_ponens,[status(thm)],[673, 672])).
% 1.12/1.39 tff(675,plain,
% 1.12/1.39 ((z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1))))),
% 1.12/1.39 inference(unit_resolution,[status(thm)],[674, 58, 671])).
% 1.12/1.39 tff(676,plain,
% 1.12/1.39 (b(z, s(s(s(elem!1))))),
% 1.12/1.39 inference(unit_resolution,[status(thm)],[675, 663])).
% 1.12/1.39 tff(677,plain,
% 1.12/1.39 (~r(z, s(s(z)))),
% 1.12/1.39 inference(unit_resolution,[status(thm)],[339, 106, 300])).
% 1.12/1.39 tff(678,plain,
% 1.12/1.39 (b(z, s(s(z)))),
% 1.12/1.39 inference(unit_resolution,[status(thm)],[351, 677])).
% 1.12/1.39 tff(679,plain,
% 1.12/1.39 (b(z, s(s(z))) <=> b(z, s(elem!1))),
% 1.12/1.39 inference(monotonicity,[status(thm)],[609])).
% 1.12/1.39 tff(680,plain,
% 1.12/1.39 (b(z, s(elem!1)) <=> b(z, s(s(z)))),
% 1.12/1.39 inference(symmetry,[status(thm)],[679])).
% 1.12/1.39 tff(681,plain,
% 1.12/1.39 ((~b(z, s(elem!1))) <=> (~b(z, s(s(z))))),
% 1.12/1.39 inference(monotonicity,[status(thm)],[680])).
% 1.12/1.39 tff(682,assumption,(~b(z, s(elem!1))), introduced(assumption)).
% 1.12/1.39 tff(683,plain,
% 1.12/1.39 (~b(z, s(s(z)))),
% 1.12/1.39 inference(modus_ponens,[status(thm)],[682, 681])).
% 1.12/1.39 tff(684,plain,
% 1.12/1.39 ($false),
% 1.12/1.39 inference(unit_resolution,[status(thm)],[370, 683])).
% 1.12/1.39 tff(685,plain,(b(z, s(elem!1)) | (~b(z, s(s(z)))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.12/1.39 tff(686,plain,
% 1.12/1.39 (b(z, s(elem!1))),
% 1.12/1.39 inference(unit_resolution,[status(thm)],[685, 678, 93])).
% 1.12/1.39 tff(687,plain,
% 1.12/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))))),
% 1.12/1.39 inference(rewrite,[status(thm)],[])).
% 1.12/1.39 tff(688,plain,
% 1.12/1.39 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1)))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))))),
% 1.12/1.39 inference(rewrite,[status(thm)],[])).
% 1.12/1.39 tff(689,plain,
% 1.12/1.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~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(X1, 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(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1)))))))),
% 1.12/1.39 inference(monotonicity,[status(thm)],[688])).
% 1.22/1.40 tff(690,plain,
% 1.22/1.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~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(X1, 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(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))))),
% 1.22/1.40 inference(transitivity,[status(thm)],[689, 687])).
% 1.22/1.40 tff(691,plain,
% 1.22/1.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))))),
% 1.22/1.40 inference(quant_inst,[status(thm)],[])).
% 1.22/1.40 tff(692,plain,
% 1.22/1.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1)))))),
% 1.22/1.40 inference(modus_ponens,[status(thm)],[691, 690])).
% 1.22/1.40 tff(693,plain,
% 1.22/1.40 ($false),
% 1.22/1.40 inference(unit_resolution,[status(thm)],[692, 75, 686, 676, 657, 639])).
% 1.22/1.40 tff(694,plain,((~r(s(s(z)), elem!1)) | (~(s(z) = elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.40 tff(695,plain,
% 1.22/1.40 (~r(s(s(s(elem!1))), elem!1)),
% 1.22/1.40 inference(unit_resolution,[status(thm)],[694, 106, 300, 93])).
% 1.22/1.40 tff(696,plain,
% 1.22/1.40 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 1.22/1.40 inference(monotonicity,[status(thm)],[612])).
% 1.22/1.40 tff(697,plain,
% 1.22/1.40 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 1.22/1.40 inference(symmetry,[status(thm)],[696])).
% 1.22/1.40 tff(698,assumption,(r(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 1.22/1.40 tff(699,plain,
% 1.22/1.40 (r(s(s(s(elem!1))), elem!1)),
% 1.22/1.40 inference(modus_ponens,[status(thm)],[698, 697])).
% 1.22/1.40 tff(700,assumption,(~r(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.22/1.40 tff(701,plain,
% 1.22/1.40 ($false),
% 1.22/1.40 inference(unit_resolution,[status(thm)],[700, 699])).
% 1.22/1.40 tff(702,plain,((~r(s(s(s(s(z)))), elem!1)) | r(s(s(s(elem!1))), elem!1) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.40 tff(703,plain,
% 1.22/1.40 (~r(s(s(s(s(z)))), elem!1)),
% 1.22/1.40 inference(unit_resolution,[status(thm)],[702, 695, 93])).
% 1.22/1.40 tff(704,plain,
% 1.22/1.40 (b(s(s(s(s(z)))), elem!1)),
% 1.22/1.40 inference(unit_resolution,[status(thm)],[283, 703, 618])).
% 1.22/1.40 tff(705,plain,
% 1.22/1.40 (b(s(s(s(elem!1))), elem!1)),
% 1.22/1.40 inference(modus_ponens,[status(thm)],[704, 614])).
% 1.22/1.40 tff(706,assumption,(b(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 1.22/1.40 tff(707,assumption,(b(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.22/1.40 tff(708,plain,
% 1.22/1.40 (elem!1 = s(z)),
% 1.22/1.40 inference(symmetry,[status(thm)],[93])).
% 1.22/1.40 tff(709,assumption,(s(s(s(s(s(s(s(z))))))) = elem!1), introduced(assumption)).
% 1.22/1.40 tff(710,plain,
% 1.22/1.40 (s(s(s(s(s(s(s(z))))))) = s(z)),
% 1.22/1.40 inference(transitivity,[status(thm)],[709, 708])).
% 1.22/1.40 tff(711,plain,
% 1.22/1.40 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(z))),
% 1.22/1.40 inference(monotonicity,[status(thm)],[710])).
% 1.22/1.40 tff(712,plain,
% 1.22/1.40 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(s(s(z)))))))),
% 1.22/1.40 inference(quant_inst,[status(thm)],[])).
% 1.22/1.40 tff(713,plain,
% 1.22/1.40 (inj_0(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(s(s(z))))))),
% 1.22/1.40 inference(unit_resolution,[status(thm)],[712, 9])).
% 1.22/1.40 tff(714,plain,
% 1.22/1.40 (s(s(s(s(s(s(z)))))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 1.22/1.40 inference(symmetry,[status(thm)],[713])).
% 1.22/1.40 tff(715,plain,
% 1.22/1.40 (s(s(s(s(s(s(z)))))) = z),
% 1.22/1.40 inference(transitivity,[status(thm)],[714, 711, 128])).
% 1.22/1.40 tff(716,plain,
% 1.22/1.40 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(s(z)))))) = z))),
% 1.22/1.40 inference(quant_inst,[status(thm)],[])).
% 1.22/1.40 tff(717,plain,
% 1.22/1.40 (~(s(s(s(s(s(s(z)))))) = z)),
% 1.22/1.40 inference(unit_resolution,[status(thm)],[716, 143])).
% 1.22/1.40 tff(718,plain,
% 1.22/1.40 ($false),
% 1.22/1.40 inference(unit_resolution,[status(thm)],[717, 715])).
% 1.22/1.40 tff(719,plain,((~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.40 tff(720,plain,
% 1.22/1.40 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.22/1.40 inference(unit_resolution,[status(thm)],[719, 93])).
% 1.22/1.40 tff(721,assumption,(s(elem!1) = s(s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.22/1.40 tff(722,plain,
% 1.22/1.40 (s(s(s(s(s(s(s(z))))))) = s(elem!1)),
% 1.22/1.40 inference(symmetry,[status(thm)],[721])).
% 1.22/1.40 tff(723,plain,
% 1.22/1.40 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(elem!1))),
% 1.22/1.40 inference(monotonicity,[status(thm)],[722])).
% 1.22/1.40 tff(724,plain,
% 1.22/1.40 (inj_0(s(elem!1)) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 1.22/1.40 inference(symmetry,[status(thm)],[723])).
% 1.22/1.40 tff(725,plain,
% 1.22/1.40 (elem!1 = inj_0(s(elem!1))),
% 1.22/1.40 inference(symmetry,[status(thm)],[224])).
% 1.22/1.40 tff(726,plain,
% 1.22/1.40 (s(z) = s(s(s(s(s(s(z))))))),
% 1.22/1.40 inference(transitivity,[status(thm)],[93, 725, 724, 713])).
% 1.22/1.40 tff(727,plain,
% 1.22/1.40 (inj_0(s(z)) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.22/1.40 inference(monotonicity,[status(thm)],[726])).
% 1.22/1.40 tff(728,plain,
% 1.22/1.40 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(z))),
% 1.22/1.40 inference(symmetry,[status(thm)],[727])).
% 1.22/1.40 tff(729,plain,
% 1.22/1.40 ((~![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))))))),
% 1.22/1.40 inference(quant_inst,[status(thm)],[])).
% 1.22/1.40 tff(730,plain,
% 1.22/1.40 (inj_0(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))),
% 1.22/1.40 inference(unit_resolution,[status(thm)],[729, 9])).
% 1.22/1.40 tff(731,plain,
% 1.22/1.40 (s(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.22/1.40 inference(symmetry,[status(thm)],[730])).
% 1.22/1.40 tff(732,plain,
% 1.22/1.40 (s(s(s(s(s(z))))) = z),
% 1.22/1.40 inference(transitivity,[status(thm)],[731, 728, 128])).
% 1.22/1.40 tff(733,plain,
% 1.22/1.40 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(z))))) = z))),
% 1.22/1.40 inference(quant_inst,[status(thm)],[])).
% 1.22/1.40 tff(734,plain,
% 1.22/1.40 (~(s(s(s(s(s(z))))) = z)),
% 1.22/1.40 inference(unit_resolution,[status(thm)],[733, 143])).
% 1.22/1.40 tff(735,plain,
% 1.22/1.40 ($false),
% 1.22/1.40 inference(unit_resolution,[status(thm)],[734, 732])).
% 1.22/1.40 tff(736,plain,((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.40 tff(737,plain,
% 1.22/1.40 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.22/1.40 inference(unit_resolution,[status(thm)],[736, 93])).
% 1.22/1.40 tff(738,assumption,(r(s(s(s(s(s(s(s(z))))))), elem!1)), introduced(assumption)).
% 1.22/1.40 tff(739,plain,
% 1.22/1.40 (((~![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(s(z))))))), z)) | (~r(s(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(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.22/1.40 inference(rewrite,[status(thm)],[])).
% 1.22/1.40 tff(740,plain,
% 1.22/1.40 (((~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z))) <=> ((~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.22/1.40 inference(rewrite,[status(thm)],[])).
% 1.22/1.40 tff(741,plain,
% 1.22/1.40 (((~![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(s(z))))))), elem!1)) | (~r(z, elem!1)) | (~r(s(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(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 1.22/1.40 inference(monotonicity,[status(thm)],[740])).
% 1.22/1.40 tff(742,plain,
% 1.22/1.40 (((~![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(s(z))))))), elem!1)) | (~r(z, elem!1)) | (~r(s(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(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.22/1.40 inference(transitivity,[status(thm)],[741, 739])).
% 1.22/1.40 tff(743,plain,
% 1.22/1.40 ((~![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(s(z))))))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 1.22/1.40 inference(quant_inst,[status(thm)],[])).
% 1.22/1.40 tff(744,plain,
% 1.22/1.40 ((~![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(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 1.22/1.40 inference(modus_ponens,[status(thm)],[743, 742])).
% 1.22/1.40 tff(745,plain,
% 1.22/1.40 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 1.22/1.40 inference(unit_resolution,[status(thm)],[744, 37, 300, 738])).
% 1.22/1.40 tff(746,plain,
% 1.22/1.40 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(s(s(z))))))) = z))),
% 1.22/1.40 inference(quant_inst,[status(thm)],[])).
% 1.22/1.40 tff(747,plain,
% 1.22/1.40 (~(s(s(s(s(s(s(s(z))))))) = z)),
% 1.22/1.40 inference(unit_resolution,[status(thm)],[746, 143])).
% 1.22/1.40 tff(748,plain,
% 1.22/1.40 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = z) | b(s(s(s(s(s(s(s(z))))))), z) | r(s(s(s(s(s(s(s(z))))))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = z) | b(s(s(s(s(s(s(s(z))))))), z) | r(s(s(s(s(s(s(s(z))))))), z))),
% 1.22/1.40 inference(rewrite,[status(thm)],[])).
% 1.22/1.40 tff(749,plain,
% 1.22/1.40 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = z) | b(s(s(s(s(s(s(s(z))))))), z) | r(s(s(s(s(s(s(s(z))))))), z))),
% 1.22/1.40 inference(quant_inst,[status(thm)],[])).
% 1.22/1.40 tff(750,plain,
% 1.22/1.40 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = z) | b(s(s(s(s(s(s(s(z))))))), z) | r(s(s(s(s(s(s(s(z))))))), z)),
% 1.22/1.40 inference(modus_ponens,[status(thm)],[749, 748])).
% 1.22/1.40 tff(751,plain,
% 1.22/1.40 (b(s(s(s(s(s(s(s(z))))))), z)),
% 1.22/1.40 inference(unit_resolution,[status(thm)],[750, 58, 747, 745])).
% 1.22/1.40 tff(752,assumption,(r(s(elem!1), elem!1)), introduced(assumption)).
% 1.22/1.40 tff(753,plain,
% 1.22/1.40 (((~![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)))),
% 1.22/1.40 inference(rewrite,[status(thm)],[])).
% 1.22/1.40 tff(754,plain,
% 1.22/1.40 (((~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)))),
% 1.22/1.40 inference(rewrite,[status(thm)],[])).
% 1.22/1.40 tff(755,plain,
% 1.22/1.40 (((~![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))))),
% 1.22/1.40 inference(monotonicity,[status(thm)],[754])).
% 1.22/1.40 tff(756,plain,
% 1.22/1.40 (((~![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)))),
% 1.22/1.40 inference(transitivity,[status(thm)],[755, 753])).
% 1.22/1.40 tff(757,plain,
% 1.22/1.40 ((~![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)))),
% 1.22/1.40 inference(quant_inst,[status(thm)],[])).
% 1.22/1.40 tff(758,plain,
% 1.22/1.40 ((~![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))),
% 1.22/1.40 inference(modus_ponens,[status(thm)],[757, 756])).
% 1.22/1.40 tff(759,plain,
% 1.22/1.40 (~r(s(elem!1), z)),
% 1.22/1.40 inference(unit_resolution,[status(thm)],[758, 37, 300, 752])).
% 1.22/1.40 tff(760,assumption,(~r(s(elem!1), z)), introduced(assumption)).
% 1.22/1.40 tff(761,assumption,(~b(s(elem!1), z)), introduced(assumption)).
% 1.22/1.41 tff(762,plain,
% 1.22/1.41 (((~![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))),
% 1.22/1.41 inference(rewrite,[status(thm)],[])).
% 1.22/1.41 tff(763,plain,
% 1.22/1.41 ((~![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))),
% 1.22/1.41 inference(quant_inst,[status(thm)],[])).
% 1.22/1.41 tff(764,plain,
% 1.22/1.41 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = z) | b(s(elem!1), z) | r(s(elem!1), z)),
% 1.22/1.41 inference(modus_ponens,[status(thm)],[763, 762])).
% 1.22/1.41 tff(765,plain,
% 1.22/1.41 ($false),
% 1.22/1.41 inference(unit_resolution,[status(thm)],[764, 58, 554, 761, 760])).
% 1.22/1.41 tff(766,plain,(b(s(elem!1), z) | r(s(elem!1), z)), inference(lemma,lemma(discharge,[]))).
% 1.22/1.41 tff(767,plain,
% 1.22/1.41 (b(s(elem!1), z)),
% 1.22/1.41 inference(unit_resolution,[status(thm)],[766, 759])).
% 1.22/1.41 tff(768,plain,
% 1.22/1.41 (((~![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(s(z))))))), elem!1)) | (~r(z, s(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(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.22/1.41 inference(rewrite,[status(thm)],[])).
% 1.22/1.41 tff(769,plain,
% 1.22/1.41 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.22/1.41 inference(rewrite,[status(thm)],[])).
% 1.22/1.41 tff(770,plain,
% 1.22/1.41 (((~![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(s(z))))))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(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(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 1.22/1.41 inference(monotonicity,[status(thm)],[769])).
% 1.22/1.41 tff(771,plain,
% 1.22/1.41 (((~![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(s(z))))))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(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(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.22/1.41 inference(transitivity,[status(thm)],[770, 768])).
% 1.22/1.41 tff(772,plain,
% 1.22/1.41 ((~![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(s(z))))))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.22/1.41 inference(quant_inst,[status(thm)],[])).
% 1.22/1.41 tff(773,plain,
% 1.22/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 1.22/1.41 inference(modus_ponens,[status(thm)],[772, 771])).
% 1.22/1.41 tff(774,plain,
% 1.22/1.41 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 1.22/1.41 inference(unit_resolution,[status(thm)],[773, 37, 300, 738])).
% 1.22/1.41 tff(775,assumption,(z = s(s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.22/1.41 tff(776,plain,
% 1.22/1.41 (s(s(s(s(s(s(s(z))))))) = z),
% 1.22/1.41 inference(symmetry,[status(thm)],[775])).
% 1.22/1.41 tff(777,plain,
% 1.22/1.41 ($false),
% 1.22/1.41 inference(unit_resolution,[status(thm)],[747, 776])).
% 1.22/1.41 tff(778,plain,(~(z = s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.41 tff(779,plain,
% 1.22/1.41 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(s(s(z)))))))) | b(z, s(s(s(s(s(s(s(z)))))))) | r(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(s(s(z)))))))) | b(z, s(s(s(s(s(s(s(z)))))))) | r(z, s(s(s(s(s(s(s(z)))))))))),
% 1.22/1.41 inference(rewrite,[status(thm)],[])).
% 1.22/1.41 tff(780,plain,
% 1.22/1.41 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(s(s(z)))))))) | b(z, s(s(s(s(s(s(s(z)))))))) | r(z, s(s(s(s(s(s(s(z)))))))))),
% 1.22/1.41 inference(quant_inst,[status(thm)],[])).
% 1.22/1.41 tff(781,plain,
% 1.22/1.41 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(s(s(z)))))))) | b(z, s(s(s(s(s(s(s(z)))))))) | r(z, s(s(s(s(s(s(s(z))))))))),
% 1.22/1.41 inference(modus_ponens,[status(thm)],[780, 779])).
% 1.22/1.41 tff(782,plain,
% 1.22/1.41 (b(z, s(s(s(s(s(s(s(z))))))))),
% 1.22/1.41 inference(unit_resolution,[status(thm)],[781, 58, 778, 774])).
% 1.22/1.41 tff(783,plain,
% 1.22/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.22/1.41 inference(rewrite,[status(thm)],[])).
% 1.22/1.41 tff(784,plain,
% 1.22/1.41 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.22/1.41 inference(rewrite,[status(thm)],[])).
% 1.22/1.41 tff(785,plain,
% 1.22/1.41 (((~![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(s(z))))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(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(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 1.22/1.41 inference(monotonicity,[status(thm)],[784])).
% 1.22/1.41 tff(786,plain,
% 1.22/1.41 (((~![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(s(z))))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(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(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.22/1.41 inference(transitivity,[status(thm)],[785, 783])).
% 1.22/1.41 tff(787,plain,
% 1.22/1.41 ((~![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(s(z))))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.22/1.41 inference(quant_inst,[status(thm)],[])).
% 1.22/1.41 tff(788,plain,
% 1.22/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 1.22/1.41 inference(modus_ponens,[status(thm)],[787, 786])).
% 1.22/1.41 tff(789,plain,
% 1.22/1.41 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.22/1.41 inference(unit_resolution,[status(thm)],[788, 37, 738, 752])).
% 1.22/1.41 tff(790,assumption,(~(s(elem!1) = s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.22/1.41 tff(791,plain,
% 1.22/1.41 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(s(s(s(z)))))))) | b(s(elem!1), s(s(s(s(s(s(s(z)))))))) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | b(s(elem!1), s(s(s(s(s(s(s(z)))))))) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 1.22/1.41 inference(rewrite,[status(thm)],[])).
% 1.22/1.41 tff(792,plain,
% 1.22/1.41 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(s(s(s(z)))))))) | b(s(elem!1), s(s(s(s(s(s(s(z)))))))) | r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 1.22/1.41 inference(quant_inst,[status(thm)],[])).
% 1.22/1.41 tff(793,plain,
% 1.22/1.41 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | b(s(elem!1), s(s(s(s(s(s(s(z)))))))) | r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.22/1.41 inference(modus_ponens,[status(thm)],[792, 791])).
% 1.22/1.42 tff(794,plain,
% 1.22/1.42 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.22/1.42 inference(unit_resolution,[status(thm)],[793, 58, 790, 789])).
% 1.22/1.42 tff(795,assumption,(b(s(s(s(s(s(s(s(z))))))), z)), introduced(assumption)).
% 1.22/1.42 tff(796,assumption,(b(s(elem!1), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.22/1.42 tff(797,assumption,(b(z, s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.22/1.42 tff(798,assumption,(b(s(elem!1), z)), introduced(assumption)).
% 1.22/1.42 tff(799,plain,
% 1.22/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.22/1.42 inference(rewrite,[status(thm)],[])).
% 1.22/1.42 tff(800,plain,
% 1.22/1.42 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), z))) <=> ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.22/1.42 inference(rewrite,[status(thm)],[])).
% 1.22/1.42 tff(801,plain,
% 1.22/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 1.22/1.42 inference(monotonicity,[status(thm)],[800])).
% 1.22/1.42 tff(802,plain,
% 1.22/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.22/1.42 inference(transitivity,[status(thm)],[801, 799])).
% 1.22/1.42 tff(803,plain,
% 1.22/1.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), z)))),
% 1.22/1.42 inference(quant_inst,[status(thm)],[])).
% 1.22/1.42 tff(804,plain,
% 1.22/1.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 1.22/1.42 inference(modus_ponens,[status(thm)],[803, 802])).
% 1.22/1.42 tff(805,plain,
% 1.22/1.42 ($false),
% 1.22/1.42 inference(unit_resolution,[status(thm)],[804, 75, 798, 797, 796, 795])).
% 1.22/1.42 tff(806,plain,((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.42 tff(807,plain,
% 1.22/1.42 ($false),
% 1.22/1.42 inference(unit_resolution,[status(thm)],[806, 794, 782, 767, 751])).
% 1.22/1.42 tff(808,plain,((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.42 tff(809,plain,
% 1.22/1.42 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.22/1.42 inference(unit_resolution,[status(thm)],[808, 627, 300, 737])).
% 1.22/1.42 tff(810,plain,
% 1.22/1.42 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = elem!1) | b(s(s(s(s(s(s(s(z))))))), elem!1) | r(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | b(s(s(s(s(s(s(s(z))))))), elem!1) | r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 1.22/1.42 inference(rewrite,[status(thm)],[])).
% 1.22/1.42 tff(811,plain,
% 1.22/1.42 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = elem!1) | b(s(s(s(s(s(s(s(z))))))), elem!1) | r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 1.22/1.42 inference(quant_inst,[status(thm)],[])).
% 1.22/1.42 tff(812,plain,
% 1.22/1.42 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | b(s(s(s(s(s(s(s(z))))))), elem!1) | r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.22/1.42 inference(modus_ponens,[status(thm)],[811, 810])).
% 1.22/1.42 tff(813,plain,
% 1.22/1.42 ((s(s(s(s(s(s(s(z))))))) = elem!1) | b(s(s(s(s(s(s(s(z))))))), elem!1) | r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.22/1.42 inference(unit_resolution,[status(thm)],[812, 58])).
% 1.22/1.42 tff(814,plain,
% 1.22/1.42 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.22/1.42 inference(unit_resolution,[status(thm)],[813, 809, 720])).
% 1.22/1.42 tff(815,plain,
% 1.22/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.22/1.42 inference(rewrite,[status(thm)],[])).
% 1.22/1.42 tff(816,plain,
% 1.22/1.42 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.22/1.42 inference(rewrite,[status(thm)],[])).
% 1.22/1.42 tff(817,plain,
% 1.22/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 1.22/1.42 inference(monotonicity,[status(thm)],[816])).
% 1.22/1.42 tff(818,plain,
% 1.22/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.22/1.42 inference(transitivity,[status(thm)],[817, 815])).
% 1.22/1.42 tff(819,plain,
% 1.22/1.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.22/1.42 inference(quant_inst,[status(thm)],[])).
% 1.22/1.42 tff(820,plain,
% 1.22/1.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 1.22/1.42 inference(modus_ponens,[status(thm)],[819, 818])).
% 1.22/1.42 tff(821,plain,
% 1.22/1.42 (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.22/1.42 inference(unit_resolution,[status(thm)],[820, 75, 814, 707, 706, 705])).
% 1.22/1.42 tff(822,assumption,(s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.22/1.42 tff(823,plain,
% 1.22/1.42 (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))),
% 1.22/1.42 inference(symmetry,[status(thm)],[822])).
% 1.22/1.42 tff(824,plain,
% 1.22/1.42 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(s(elem!1)))),
% 1.22/1.42 inference(monotonicity,[status(thm)],[823])).
% 1.22/1.42 tff(825,plain,
% 1.22/1.42 (s(s(s(s(s(s(z)))))) = s(elem!1)),
% 1.22/1.42 inference(transitivity,[status(thm)],[714, 824, 228])).
% 1.22/1.42 tff(826,plain,
% 1.22/1.42 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(elem!1))),
% 1.22/1.42 inference(monotonicity,[status(thm)],[825])).
% 1.22/1.42 tff(827,plain,
% 1.22/1.42 (inj_0(s(elem!1)) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.22/1.42 inference(symmetry,[status(thm)],[826])).
% 1.22/1.42 tff(828,plain,
% 1.22/1.42 (s(z) = s(s(s(s(s(z)))))),
% 1.22/1.42 inference(transitivity,[status(thm)],[93, 725, 827, 730])).
% 1.22/1.42 tff(829,plain,
% 1.22/1.42 (inj_0(s(z)) = inj_0(s(s(s(s(s(z))))))),
% 1.22/1.42 inference(monotonicity,[status(thm)],[828])).
% 1.22/1.42 tff(830,plain,
% 1.22/1.42 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(z))),
% 1.22/1.42 inference(symmetry,[status(thm)],[829])).
% 1.22/1.42 tff(831,plain,
% 1.22/1.42 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 1.22/1.42 inference(quant_inst,[status(thm)],[])).
% 1.22/1.42 tff(832,plain,
% 1.22/1.42 (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z))))),
% 1.22/1.42 inference(unit_resolution,[status(thm)],[831, 9])).
% 1.22/1.42 tff(833,plain,
% 1.22/1.42 (s(s(s(s(z)))) = inj_0(s(s(s(s(s(z))))))),
% 1.22/1.42 inference(symmetry,[status(thm)],[832])).
% 1.22/1.42 tff(834,plain,
% 1.22/1.42 (s(s(s(elem!1))) = z),
% 1.22/1.42 inference(transitivity,[status(thm)],[612, 833, 830, 128])).
% 1.22/1.42 tff(835,plain,
% 1.22/1.42 ($false),
% 1.22/1.42 inference(unit_resolution,[status(thm)],[662, 834])).
% 1.22/1.42 tff(836,plain,((~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.42 tff(837,plain,
% 1.22/1.42 (~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 1.22/1.42 inference(unit_resolution,[status(thm)],[836, 93])).
% 1.22/1.42 tff(838,plain,
% 1.22/1.42 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))) | b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) | r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))) | b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) | r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 1.22/1.42 inference(rewrite,[status(thm)],[])).
% 1.22/1.42 tff(839,plain,
% 1.22/1.42 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))) | b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) | r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 1.22/1.42 inference(quant_inst,[status(thm)],[])).
% 1.22/1.42 tff(840,plain,
% 1.22/1.42 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))) | b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))) | r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.22/1.42 inference(modus_ponens,[status(thm)],[839, 838])).
% 1.22/1.42 tff(841,plain,
% 1.22/1.42 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.22/1.42 inference(unit_resolution,[status(thm)],[840, 58, 837, 821])).
% 1.22/1.42 tff(842,plain,
% 1.22/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.22/1.42 inference(rewrite,[status(thm)],[])).
% 1.22/1.42 tff(843,plain,
% 1.22/1.42 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.22/1.42 inference(rewrite,[status(thm)],[])).
% 1.22/1.42 tff(844,plain,
% 1.22/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(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(X1, 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(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 1.22/1.42 inference(monotonicity,[status(thm)],[843])).
% 1.22/1.42 tff(845,plain,
% 1.22/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(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(X1, 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(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.22/1.42 inference(transitivity,[status(thm)],[844, 842])).
% 1.22/1.42 tff(846,plain,
% 1.22/1.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 1.22/1.42 inference(quant_inst,[status(thm)],[])).
% 1.22/1.42 tff(847,plain,
% 1.22/1.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 1.22/1.42 inference(modus_ponens,[status(thm)],[846, 845])).
% 1.22/1.42 tff(848,plain,
% 1.22/1.42 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 1.22/1.42 inference(unit_resolution,[status(thm)],[847, 75, 814, 706, 705])).
% 1.22/1.42 tff(849,plain,
% 1.22/1.42 ((~(s(z) = s(s(s(s(z)))))) <=> (~(elem!1 = s(s(s(s(z))))))),
% 1.22/1.42 inference(monotonicity,[status(thm)],[615])).
% 1.22/1.42 tff(850,plain,
% 1.22/1.42 (~(elem!1 = s(s(s(s(z)))))),
% 1.22/1.42 inference(modus_ponens,[status(thm)],[484, 849])).
% 1.22/1.43 tff(851,assumption,(s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.22/1.43 tff(852,plain,
% 1.22/1.43 (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))),
% 1.22/1.43 inference(symmetry,[status(thm)],[851])).
% 1.22/1.43 tff(853,plain,
% 1.22/1.43 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(s(s(elem!1))))),
% 1.22/1.43 inference(monotonicity,[status(thm)],[852])).
% 1.22/1.43 tff(854,plain,
% 1.22/1.43 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 1.22/1.43 inference(transitivity,[status(thm)],[714, 853, 11])).
% 1.22/1.43 tff(855,plain,
% 1.22/1.43 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(elem!1)))),
% 1.22/1.43 inference(monotonicity,[status(thm)],[854])).
% 1.22/1.43 tff(856,plain,
% 1.22/1.43 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.22/1.43 inference(symmetry,[status(thm)],[855])).
% 1.22/1.43 tff(857,plain,
% 1.22/1.43 (s(elem!1) = s(s(s(s(s(z)))))),
% 1.22/1.43 inference(transitivity,[status(thm)],[229, 856, 730])).
% 1.22/1.43 tff(858,plain,
% 1.22/1.43 (inj_0(s(elem!1)) = inj_0(s(s(s(s(s(z))))))),
% 1.22/1.43 inference(monotonicity,[status(thm)],[857])).
% 1.22/1.43 tff(859,plain,
% 1.22/1.43 (elem!1 = s(s(s(s(z))))),
% 1.22/1.43 inference(transitivity,[status(thm)],[725, 858, 832])).
% 1.22/1.43 tff(860,assumption,(~(elem!1 = s(s(s(s(z)))))), introduced(assumption)).
% 1.22/1.43 tff(861,plain,
% 1.22/1.43 ($false),
% 1.22/1.43 inference(unit_resolution,[status(thm)],[860, 859])).
% 1.22/1.43 tff(862,plain,((~(s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))) | (elem!1 = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.43 tff(863,plain,
% 1.22/1.43 (~(s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))),
% 1.22/1.43 inference(unit_resolution,[status(thm)],[862, 850])).
% 1.22/1.43 tff(864,plain,
% 1.22/1.43 ((s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 1.22/1.43 inference(commutativity,[status(thm)],[])).
% 1.22/1.43 tff(865,plain,
% 1.22/1.43 ((s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))),
% 1.22/1.43 inference(symmetry,[status(thm)],[864])).
% 1.22/1.43 tff(866,assumption,(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))), introduced(assumption)).
% 1.22/1.43 tff(867,plain,
% 1.22/1.43 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 1.22/1.43 inference(modus_ponens,[status(thm)],[866, 865])).
% 1.22/1.43 tff(868,assumption,(~(s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.22/1.43 tff(869,plain,
% 1.22/1.43 ($false),
% 1.22/1.43 inference(unit_resolution,[status(thm)],[868, 867])).
% 1.22/1.43 tff(870,plain,((~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.43 tff(871,plain,
% 1.22/1.43 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 1.22/1.43 inference(unit_resolution,[status(thm)],[870, 863])).
% 1.22/1.43 tff(872,plain,
% 1.22/1.43 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 1.22/1.43 inference(rewrite,[status(thm)],[])).
% 1.22/1.43 tff(873,plain,
% 1.22/1.43 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 1.22/1.43 inference(quant_inst,[status(thm)],[])).
% 1.22/1.43 tff(874,plain,
% 1.22/1.43 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 1.22/1.43 inference(modus_ponens,[status(thm)],[873, 872])).
% 1.22/1.43 tff(875,plain,
% 1.22/1.43 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 1.22/1.43 inference(unit_resolution,[status(thm)],[874, 58, 871, 848])).
% 1.22/1.43 tff(876,assumption,(r(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 1.22/1.43 tff(877,plain,
% 1.22/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.22/1.43 inference(rewrite,[status(thm)],[])).
% 1.22/1.43 tff(878,plain,
% 1.22/1.43 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.22/1.43 inference(rewrite,[status(thm)],[])).
% 1.22/1.43 tff(879,plain,
% 1.22/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 1.22/1.43 inference(monotonicity,[status(thm)],[878])).
% 1.22/1.43 tff(880,plain,
% 1.22/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.22/1.43 inference(transitivity,[status(thm)],[879, 877])).
% 1.22/1.43 tff(881,plain,
% 1.22/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.22/1.43 inference(quant_inst,[status(thm)],[])).
% 1.22/1.43 tff(882,plain,
% 1.22/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 1.22/1.43 inference(modus_ponens,[status(thm)],[881, 880])).
% 1.22/1.43 tff(883,plain,
% 1.22/1.43 ($false),
% 1.22/1.43 inference(unit_resolution,[status(thm)],[882, 37, 876, 875, 841])).
% 1.22/1.43 tff(884,plain,((~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.43 tff(885,plain,
% 1.22/1.43 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.22/1.43 inference(unit_resolution,[status(thm)],[884, 608, 435, 605, 300, 602])).
% 1.22/1.43 tff(886,plain,
% 1.22/1.43 ($false),
% 1.22/1.43 inference(unit_resolution,[status(thm)],[885, 577])).
% 1.22/1.43 tff(887,plain,(b(s(s(z)), s(s(s(s(z))))) | (~r(z, elem!1)) | (s(s(elem!1)) = s(s(z))) | (~b(s(s(s(s(z)))), elem!1)) | b(elem!1, s(z)) | b(s(s(z)), elem!1) | (~b(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.43 tff(888,plain,
% 1.22/1.43 (b(s(s(z)), s(s(s(s(z)))))),
% 1.22/1.43 inference(unit_resolution,[status(thm)],[887, 14, 266, 287, 300, 99, 286])).
% 1.22/1.43 tff(889,plain,
% 1.22/1.43 (r(s(s(z)), elem!1)),
% 1.22/1.43 inference(unit_resolution,[status(thm)],[104, 15, 99])).
% 1.22/1.43 tff(890,plain,
% 1.22/1.43 (~r(elem!1, s(z))),
% 1.22/1.43 inference(unit_resolution,[status(thm)],[123, 889, 427])).
% 1.22/1.43 tff(891,plain,
% 1.22/1.43 (elem!1 = s(z)),
% 1.22/1.43 inference(unit_resolution,[status(thm)],[89, 890, 14])).
% 1.22/1.43 tff(892,plain,
% 1.22/1.43 (b(elem!1, s(s(s(s(z))))) <=> b(s(z), s(s(s(s(z)))))),
% 1.22/1.43 inference(monotonicity,[status(thm)],[891])).
% 1.22/1.43 tff(893,plain,
% 1.22/1.43 (b(s(z), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.22/1.43 inference(symmetry,[status(thm)],[892])).
% 1.22/1.43 tff(894,plain,
% 1.22/1.43 ((~b(s(z), s(s(s(s(z)))))) <=> (~b(elem!1, s(s(s(s(z))))))),
% 1.22/1.43 inference(monotonicity,[status(thm)],[893])).
% 1.22/1.43 tff(895,assumption,(b(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 1.22/1.43 tff(896,plain,
% 1.22/1.43 (s(z) = elem!1),
% 1.22/1.43 inference(unit_resolution,[status(thm)],[111, 891])).
% 1.22/1.43 tff(897,plain,
% 1.22/1.43 (r(s(s(elem!1)), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.22/1.43 inference(monotonicity,[status(thm)],[611])).
% 1.22/1.43 tff(898,plain,
% 1.22/1.43 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.22/1.43 inference(monotonicity,[status(thm)],[610])).
% 1.22/1.43 tff(899,plain,
% 1.22/1.43 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.22/1.43 inference(transitivity,[status(thm)],[898, 897])).
% 1.22/1.43 tff(900,plain,
% 1.22/1.43 (b(s(s(s(z))), s(z)) <=> b(s(s(s(z))), elem!1)),
% 1.22/1.43 inference(monotonicity,[status(thm)],[93])).
% 1.22/1.43 tff(901,plain,
% 1.22/1.43 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(z))),
% 1.22/1.43 inference(symmetry,[status(thm)],[900])).
% 1.22/1.43 tff(902,plain,
% 1.22/1.43 (b(s(s(s(z))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.22/1.43 inference(monotonicity,[status(thm)],[610])).
% 1.22/1.43 tff(903,plain,
% 1.22/1.43 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(z))), elem!1)),
% 1.22/1.43 inference(symmetry,[status(thm)],[902])).
% 1.22/1.43 tff(904,plain,
% 1.22/1.43 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 1.22/1.43 inference(monotonicity,[status(thm)],[93])).
% 1.22/1.43 tff(905,plain,
% 1.22/1.43 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(z))), s(z))),
% 1.22/1.43 inference(transitivity,[status(thm)],[904, 903, 901])).
% 1.22/1.43 tff(906,plain,
% 1.22/1.43 (r(z, s(z)) <=> r(z, elem!1)),
% 1.22/1.43 inference(monotonicity,[status(thm)],[93])).
% 1.22/1.43 tff(907,plain,
% 1.22/1.43 (r(z, elem!1) <=> r(z, s(z))),
% 1.22/1.43 inference(symmetry,[status(thm)],[906])).
% 1.22/1.43 tff(908,plain,
% 1.22/1.43 (r(z, s(z))),
% 1.22/1.43 inference(modus_ponens,[status(thm)],[300, 907])).
% 1.22/1.43 tff(909,plain,
% 1.22/1.43 (elem!1 = s(z)),
% 1.22/1.43 inference(unit_resolution,[status(thm)],[97, 93])).
% 1.22/1.43 tff(910,plain,
% 1.22/1.43 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 1.22/1.43 inference(monotonicity,[status(thm)],[612])).
% 1.22/1.43 tff(911,plain,
% 1.22/1.43 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.22/1.43 inference(symmetry,[status(thm)],[910])).
% 1.22/1.43 tff(912,plain,
% 1.22/1.43 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 1.22/1.43 inference(monotonicity,[status(thm)],[609])).
% 1.22/1.43 tff(913,plain,
% 1.22/1.43 (b(s(elem!1), s(s(s(s(z)))))),
% 1.22/1.43 inference(modus_ponens,[status(thm)],[895, 912])).
% 1.22/1.43 tff(914,plain,
% 1.22/1.43 (b(s(elem!1), s(s(s(elem!1))))),
% 1.22/1.43 inference(modus_ponens,[status(thm)],[913, 911])).
% 1.22/1.43 tff(915,plain,
% 1.22/1.43 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.22/1.43 inference(monotonicity,[status(thm)],[612])).
% 1.22/1.43 tff(916,plain,
% 1.22/1.43 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.22/1.43 inference(symmetry,[status(thm)],[915])).
% 1.22/1.43 tff(917,plain,
% 1.22/1.43 (b(s(z), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.22/1.43 inference(monotonicity,[status(thm)],[93])).
% 1.22/1.43 tff(918,plain,
% 1.22/1.43 (b(elem!1, s(s(s(s(z)))))),
% 1.22/1.43 inference(modus_ponens,[status(thm)],[578, 917])).
% 1.22/1.43 tff(919,plain,
% 1.22/1.43 (b(elem!1, s(s(s(elem!1))))),
% 1.22/1.43 inference(modus_ponens,[status(thm)],[918, 916])).
% 1.22/1.43 tff(920,assumption,(b(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 1.22/1.43 tff(921,assumption,(b(s(elem!1), elem!1)), introduced(assumption)).
% 1.22/1.43 tff(922,assumption,(b(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.22/1.43 tff(923,plain,
% 1.22/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), 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(X1, 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), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.22/1.43 inference(rewrite,[status(thm)],[])).
% 1.22/1.43 tff(924,plain,
% 1.22/1.43 (((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), 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), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.22/1.43 inference(rewrite,[status(thm)],[])).
% 1.22/1.43 tff(925,plain,
% 1.22/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(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(X1, 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), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.22/1.43 inference(monotonicity,[status(thm)],[924])).
% 1.22/1.43 tff(926,plain,
% 1.22/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(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(X1, 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), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.22/1.43 inference(transitivity,[status(thm)],[925, 923])).
% 1.22/1.43 tff(927,plain,
% 1.22/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))),
% 1.22/1.43 inference(quant_inst,[status(thm)],[])).
% 1.22/1.43 tff(928,plain,
% 1.22/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.22/1.43 inference(modus_ponens,[status(thm)],[927, 926])).
% 1.22/1.43 tff(929,plain,
% 1.22/1.43 ($false),
% 1.22/1.43 inference(unit_resolution,[status(thm)],[928, 75, 921, 706, 922, 920])).
% 1.22/1.43 tff(930,plain,((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.43 tff(931,plain,
% 1.22/1.43 (~b(s(s(s(elem!1))), elem!1)),
% 1.22/1.43 inference(unit_resolution,[status(thm)],[930, 921, 706, 920])).
% 1.22/1.43 tff(932,plain,
% 1.22/1.43 (b(s(s(s(elem!1))), elem!1)),
% 1.22/1.43 inference(modus_ponens,[status(thm)],[287, 614])).
% 1.22/1.43 tff(933,assumption,(~b(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.22/1.43 tff(934,plain,
% 1.22/1.43 ($false),
% 1.22/1.43 inference(unit_resolution,[status(thm)],[933, 932])).
% 1.22/1.43 tff(935,plain,((~b(s(s(s(s(z)))), elem!1)) | b(s(s(s(elem!1))), elem!1) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.43 tff(936,plain,
% 1.22/1.43 (~b(s(s(s(s(z)))), elem!1)),
% 1.22/1.43 inference(unit_resolution,[status(thm)],[935, 931, 93])).
% 1.22/1.43 tff(937,plain,
% 1.22/1.43 (r(s(s(s(s(z)))), elem!1)),
% 1.22/1.43 inference(unit_resolution,[status(thm)],[283, 936, 618])).
% 1.22/1.43 tff(938,plain,
% 1.22/1.43 (r(s(s(s(elem!1))), elem!1)),
% 1.22/1.43 inference(unit_resolution,[status(thm)],[702, 937, 93])).
% 1.22/1.43 tff(939,plain,
% 1.22/1.43 (((~![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(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))), elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 1.22/1.43 inference(rewrite,[status(thm)],[])).
% 1.22/1.43 tff(940,plain,
% 1.22/1.43 (((~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))), elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 1.22/1.43 inference(rewrite,[status(thm)],[])).
% 1.22/1.43 tff(941,plain,
% 1.22/1.43 (((~![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))), elem!1)) | (~r(s(s(s(elem!1))), z))))),
% 1.22/1.43 inference(monotonicity,[status(thm)],[940])).
% 1.22/1.43 tff(942,plain,
% 1.22/1.43 (((~![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))), elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 1.22/1.43 inference(transitivity,[status(thm)],[941, 939])).
% 1.22/1.43 tff(943,plain,
% 1.22/1.43 ((~![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)))),
% 1.22/1.43 inference(quant_inst,[status(thm)],[])).
% 1.22/1.43 tff(944,plain,
% 1.22/1.43 ((~![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(s(s(s(elem!1))), z))),
% 1.22/1.43 inference(modus_ponens,[status(thm)],[943, 942])).
% 1.22/1.43 tff(945,plain,
% 1.22/1.43 (~r(s(s(s(elem!1))), z)),
% 1.22/1.43 inference(unit_resolution,[status(thm)],[944, 37, 300, 938])).
% 1.22/1.43 tff(946,plain,
% 1.22/1.43 (((~![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))),
% 1.22/1.43 inference(rewrite,[status(thm)],[])).
% 1.22/1.43 tff(947,plain,
% 1.22/1.43 ((~![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))),
% 1.22/1.43 inference(quant_inst,[status(thm)],[])).
% 1.22/1.43 tff(948,plain,
% 1.22/1.43 ((~![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)),
% 1.22/1.43 inference(modus_ponens,[status(thm)],[947, 946])).
% 1.22/1.43 tff(949,plain,
% 1.22/1.43 (b(s(s(s(elem!1))), z)),
% 1.22/1.43 inference(unit_resolution,[status(thm)],[948, 58, 662, 945])).
% 1.22/1.43 tff(950,plain,
% 1.22/1.43 (~r(z, s(s(s(elem!1))))),
% 1.22/1.43 inference(unit_resolution,[status(thm)],[669, 37, 300, 938])).
% 1.22/1.43 tff(951,plain,
% 1.22/1.43 ((z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1))))),
% 1.22/1.43 inference(unit_resolution,[status(thm)],[674, 58, 950])).
% 1.22/1.43 tff(952,plain,
% 1.22/1.43 (b(z, s(s(s(elem!1))))),
% 1.22/1.43 inference(unit_resolution,[status(thm)],[951, 663])).
% 1.22/1.43 tff(953,plain,
% 1.22/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(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(X1, 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), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 1.22/1.43 inference(rewrite,[status(thm)],[])).
% 1.22/1.43 tff(954,plain,
% 1.22/1.43 (((~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(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), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 1.22/1.43 inference(rewrite,[status(thm)],[])).
% 1.22/1.43 tff(955,plain,
% 1.22/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(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(X1, 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), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))))),
% 1.22/1.44 inference(monotonicity,[status(thm)],[954])).
% 1.22/1.44 tff(956,plain,
% 1.22/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(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(X1, 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), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 1.22/1.44 inference(transitivity,[status(thm)],[955, 953])).
% 1.22/1.44 tff(957,plain,
% 1.22/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))),
% 1.22/1.44 inference(quant_inst,[status(thm)],[])).
% 1.22/1.44 tff(958,plain,
% 1.22/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))),
% 1.22/1.44 inference(modus_ponens,[status(thm)],[957, 956])).
% 1.22/1.44 tff(959,plain,
% 1.22/1.44 ($false),
% 1.22/1.44 inference(unit_resolution,[status(thm)],[958, 75, 921, 706, 920, 952, 949])).
% 1.22/1.44 tff(960,plain,((~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~r(z, elem!1)) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.44 tff(961,plain,
% 1.22/1.44 (~b(s(elem!1), elem!1)),
% 1.22/1.44 inference(unit_resolution,[status(thm)],[960, 919, 914, 300, 93])).
% 1.22/1.44 tff(962,plain,
% 1.22/1.44 (b(s(elem!1), elem!1) <=> b(s(s(z)), elem!1)),
% 1.22/1.44 inference(monotonicity,[status(thm)],[619])).
% 1.22/1.44 tff(963,plain,
% 1.22/1.44 (b(s(s(z)), elem!1) <=> b(s(elem!1), elem!1)),
% 1.22/1.44 inference(symmetry,[status(thm)],[962])).
% 1.22/1.44 tff(964,assumption,(b(s(s(z)), elem!1)), introduced(assumption)).
% 1.22/1.44 tff(965,plain,
% 1.22/1.44 (b(s(elem!1), elem!1)),
% 1.22/1.44 inference(modus_ponens,[status(thm)],[964, 963])).
% 1.22/1.44 tff(966,assumption,(~b(s(elem!1), elem!1)), introduced(assumption)).
% 1.22/1.44 tff(967,plain,
% 1.22/1.44 ($false),
% 1.22/1.44 inference(unit_resolution,[status(thm)],[966, 965])).
% 1.22/1.44 tff(968,plain,((~b(s(s(z)), elem!1)) | b(s(elem!1), elem!1) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.44 tff(969,plain,
% 1.22/1.44 (~b(s(s(z)), elem!1)),
% 1.22/1.44 inference(unit_resolution,[status(thm)],[968, 961, 93])).
% 1.22/1.44 tff(970,plain,
% 1.22/1.44 (~b(s(s(z)), s(z))),
% 1.22/1.44 inference(unit_resolution,[status(thm)],[358, 969, 909])).
% 1.22/1.44 tff(971,plain,
% 1.22/1.44 (r(s(s(z)), s(z))),
% 1.22/1.44 inference(unit_resolution,[status(thm)],[153, 970])).
% 1.22/1.44 tff(972,plain,
% 1.22/1.44 (~r(s(s(elem!1)), s(z))),
% 1.22/1.44 inference(unit_resolution,[status(thm)],[548, 971, 908, 300, 266])).
% 1.22/1.44 tff(973,plain,
% 1.22/1.44 (b(s(s(elem!1)), s(z))),
% 1.22/1.44 inference(unit_resolution,[status(thm)],[561, 972])).
% 1.22/1.44 tff(974,plain,
% 1.22/1.44 (b(s(s(s(z))), s(z))),
% 1.22/1.44 inference(modus_ponens,[status(thm)],[973, 905])).
% 1.22/1.44 tff(975,plain,
% 1.22/1.44 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(z)))), elem!1)),
% 1.22/1.44 inference(monotonicity,[status(thm)],[93])).
% 1.22/1.44 tff(976,plain,
% 1.22/1.44 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(z))),
% 1.22/1.44 inference(symmetry,[status(thm)],[975])).
% 1.22/1.44 tff(977,plain,
% 1.22/1.44 (r(s(s(z)), elem!1)),
% 1.22/1.44 inference(unit_resolution,[status(thm)],[104, 969, 15])).
% 1.22/1.44 tff(978,plain,
% 1.22/1.44 (~r(s(s(s(elem!1))), elem!1)),
% 1.22/1.44 inference(unit_resolution,[status(thm)],[694, 977, 300, 93])).
% 1.22/1.44 tff(979,plain,
% 1.22/1.44 (~r(s(s(s(s(z)))), elem!1)),
% 1.22/1.44 inference(unit_resolution,[status(thm)],[702, 978, 93])).
% 1.22/1.44 tff(980,plain,
% 1.22/1.44 (b(s(s(s(s(z)))), elem!1)),
% 1.22/1.44 inference(unit_resolution,[status(thm)],[283, 979, 618])).
% 1.22/1.44 tff(981,plain,
% 1.22/1.44 (b(s(s(s(s(z)))), s(z))),
% 1.22/1.44 inference(modus_ponens,[status(thm)],[980, 976])).
% 1.22/1.44 tff(982,assumption,(b(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.22/1.44 tff(983,assumption,(b(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 1.22/1.44 tff(984,assumption,(b(s(s(s(z))), s(z))), introduced(assumption)).
% 1.22/1.44 tff(985,plain,
% 1.22/1.44 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.22/1.44 inference(rewrite,[status(thm)],[])).
% 1.22/1.44 tff(986,plain,
% 1.22/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))))),
% 1.22/1.44 inference(monotonicity,[status(thm)],[985])).
% 1.22/1.44 tff(987,plain,
% 1.22/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.22/1.44 inference(transitivity,[status(thm)],[986, 564])).
% 1.22/1.44 tff(988,plain,
% 1.22/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 1.22/1.44 inference(quant_inst,[status(thm)],[])).
% 1.22/1.44 tff(989,plain,
% 1.22/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))),
% 1.22/1.44 inference(modus_ponens,[status(thm)],[988, 987])).
% 1.22/1.44 tff(990,plain,
% 1.22/1.44 ($false),
% 1.22/1.44 inference(unit_resolution,[status(thm)],[989, 75, 984, 578, 983, 982])).
% 1.22/1.44 tff(991,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.44 tff(992,plain,
% 1.22/1.44 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.22/1.44 inference(unit_resolution,[status(thm)],[991, 981, 578, 974])).
% 1.22/1.44 tff(993,plain,
% 1.22/1.44 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.22/1.44 inference(unit_resolution,[status(thm)],[575, 992])).
% 1.22/1.44 tff(994,plain,
% 1.22/1.44 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.22/1.44 inference(modus_ponens,[status(thm)],[993, 899])).
% 1.22/1.44 tff(995,plain,
% 1.22/1.44 (b(s(s(elem!1)), elem!1)),
% 1.22/1.44 inference(modus_ponens,[status(thm)],[973, 904])).
% 1.22/1.44 tff(996,plain,
% 1.22/1.44 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.22/1.44 inference(unit_resolution,[status(thm)],[884, 995, 977, 919, 300, 93])).
% 1.22/1.44 tff(997,plain,
% 1.22/1.44 ($false),
% 1.22/1.44 inference(unit_resolution,[status(thm)],[996, 994])).
% 1.22/1.44 tff(998,plain,((~(s(z) = elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~r(z, elem!1)) | (s(s(elem!1)) = s(s(z))) | (s(s(z)) = elem!1) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.44 tff(999,plain,
% 1.22/1.44 (~b(s(z), s(s(s(s(z)))))),
% 1.22/1.44 inference(unit_resolution,[status(thm)],[998, 896, 300, 266, 895, 15])).
% 1.22/1.44 tff(1000,plain,
% 1.22/1.44 (~b(elem!1, s(s(s(s(z)))))),
% 1.22/1.44 inference(modus_ponens,[status(thm)],[999, 894])).
% 1.22/1.44 tff(1001,plain,
% 1.22/1.44 ($false),
% 1.22/1.44 inference(unit_resolution,[status(thm)],[286, 1000])).
% 1.22/1.44 tff(1002,plain,((s(s(z)) = elem!1) | (~b(elem!1, s(s(s(s(z)))))) | (~r(z, elem!1)) | (s(s(elem!1)) = s(s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | b(elem!1, s(z)) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.22/1.44 tff(1003,plain,
% 1.22/1.44 (s(s(z)) = elem!1),
% 1.22/1.44 inference(unit_resolution,[status(thm)],[1002, 888, 300, 266, 286, 14, 99])).
% 1.22/1.44 tff(1004,plain,
% 1.22/1.44 (s(s(s(z))) = s(elem!1)),
% 1.22/1.44 inference(monotonicity,[status(thm)],[1003])).
% 1.22/1.44 tff(1005,plain,
% 1.22/1.44 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 1.22/1.44 inference(monotonicity,[status(thm)],[1004])).
% 1.22/1.44 tff(1006,plain,
% 1.22/1.44 (b(s(s(elem!1)), s(s(z))) <=> b(s(s(elem!1)), elem!1)),
% 1.22/1.44 inference(monotonicity,[status(thm)],[1003])).
% 1.22/1.44 tff(1007,plain,
% 1.22/1.44 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(s(z)))),
% 1.22/1.44 inference(symmetry,[status(thm)],[1006])).
% 1.22/1.44 tff(1008,plain,
% 1.22/1.44 (s(s(s(z))) = s(elem!1)),
% 1.22/1.44 inference(monotonicity,[status(thm)],[310])).
% 1.22/1.44 tff(1009,plain,
% 1.22/1.44 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.22/1.44 inference(monotonicity,[status(thm)],[1008])).
% 1.22/1.44 tff(1010,plain,
% 1.22/1.44 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.22/1.44 inference(symmetry,[status(thm)],[1009])).
% 1.22/1.44 tff(1011,assumption,(~(s(s(elem!1)) = s(s(s(s(z)))))), introduced(assumption)).
% 1.22/1.44 tff(1012,plain,
% 1.22/1.44 ($false),
% 1.22/1.44 inference(unit_resolution,[status(thm)],[1011, 1010])).
% 1.22/1.44 tff(1013,plain,((~(s(s(z)) = elem!1)) | (s(s(elem!1)) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.44 tff(1014,plain,
% 1.22/1.44 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.22/1.44 inference(unit_resolution,[status(thm)],[1013, 1003])).
% 1.22/1.44 tff(1015,plain,
% 1.22/1.44 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 1.22/1.44 inference(monotonicity,[status(thm)],[1014])).
% 1.22/1.44 tff(1016,plain,
% 1.22/1.44 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.22/1.44 inference(symmetry,[status(thm)],[1015])).
% 1.22/1.44 tff(1017,plain,
% 1.22/1.44 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(elem!1)), s(s(z)))),
% 1.22/1.44 inference(transitivity,[status(thm)],[1016, 1007])).
% 1.22/1.44 tff(1018,plain,
% 1.22/1.44 (b(s(s(elem!1)), s(s(z)))),
% 1.22/1.44 inference(modus_ponens,[status(thm)],[287, 1017])).
% 1.22/1.44 tff(1019,plain,
% 1.22/1.44 (s(elem!1) = s(s(s(s(z))))),
% 1.22/1.44 inference(symmetry,[status(thm)],[214])).
% 1.22/1.44 tff(1020,assumption,(s(s(elem!1)) = s(s(s(s(z))))), introduced(assumption)).
% 1.22/1.44 tff(1021,plain,
% 1.22/1.44 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.22/1.44 inference(symmetry,[status(thm)],[1020])).
% 1.22/1.44 tff(1022,plain,
% 1.22/1.44 (s(elem!1) = s(s(elem!1))),
% 1.22/1.44 inference(transitivity,[status(thm)],[1019, 1021])).
% 1.22/1.44 tff(1023,plain,
% 1.22/1.44 (inj_0(s(elem!1)) = inj_0(s(s(elem!1)))),
% 1.22/1.44 inference(monotonicity,[status(thm)],[1022])).
% 1.22/1.44 tff(1024,plain,
% 1.22/1.44 (elem!1 = s(s(s(s(z))))),
% 1.22/1.44 inference(transitivity,[status(thm)],[725, 1023, 228, 1019])).
% 1.22/1.44 tff(1025,plain,
% 1.22/1.44 ($false),
% 1.22/1.44 inference(unit_resolution,[status(thm)],[860, 1024])).
% 1.22/1.44 tff(1026,plain,((~(s(s(elem!1)) = s(s(s(s(z)))))) | (elem!1 = s(s(s(s(z))))) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.44 tff(1027,plain,
% 1.22/1.44 (~(s(s(s(z))) = elem!1)),
% 1.22/1.44 inference(unit_resolution,[status(thm)],[1026, 1014, 860])).
% 1.22/1.44 tff(1028,plain,
% 1.22/1.44 ((elem!1 = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 1.22/1.44 inference(commutativity,[status(thm)],[])).
% 1.22/1.44 tff(1029,assumption,(elem!1 = s(s(s(z)))), introduced(assumption)).
% 1.22/1.44 tff(1030,plain,
% 1.22/1.44 (s(s(s(z))) = elem!1),
% 1.22/1.44 inference(modus_ponens,[status(thm)],[1029, 1028])).
% 1.22/1.44 tff(1031,assumption,(~(s(s(s(z))) = elem!1)), introduced(assumption)).
% 1.22/1.44 tff(1032,plain,
% 1.22/1.44 ($false),
% 1.22/1.44 inference(unit_resolution,[status(thm)],[1031, 1030])).
% 1.22/1.44 tff(1033,plain,((~(elem!1 = s(s(s(z))))) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.22/1.44 tff(1034,plain,
% 1.22/1.44 (~(elem!1 = s(s(s(z))))),
% 1.22/1.44 inference(unit_resolution,[status(thm)],[1033, 1027])).
% 1.22/1.44 tff(1035,plain,
% 1.22/1.44 (r(s(s(z)), s(z)) <=> r(elem!1, s(z))),
% 1.22/1.44 inference(monotonicity,[status(thm)],[1003])).
% 1.22/1.44 tff(1036,plain,
% 1.22/1.44 (r(elem!1, s(z))),
% 1.22/1.44 inference(modus_ponens,[status(thm)],[427, 1035])).
% 1.22/1.44 tff(1037,plain,
% 1.22/1.44 ((s(s(s(s(s(s(s(z))))))) = s(s(z))) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.22/1.44 inference(monotonicity,[status(thm)],[310])).
% 1.22/1.44 tff(1038,plain,
% 1.22/1.44 ((~(s(s(s(s(s(s(s(z))))))) = s(s(z)))) <=> (~(s(s(s(s(s(s(s(z))))))) = elem!1))),
% 1.22/1.44 inference(monotonicity,[status(thm)],[1037])).
% 1.22/1.44 tff(1039,assumption,(s(s(s(s(s(s(s(z))))))) = s(s(z))), introduced(assumption)).
% 1.22/1.44 tff(1040,plain,
% 1.22/1.44 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(s(z)))),
% 1.22/1.44 inference(monotonicity,[status(thm)],[1039])).
% 1.22/1.44 tff(1041,plain,
% 1.22/1.44 (s(s(s(s(s(s(z)))))) = s(z)),
% 1.22/1.44 inference(transitivity,[status(thm)],[714, 1040, 133])).
% 1.22/1.44 tff(1042,plain,
% 1.22/1.44 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(z))),
% 1.22/1.44 inference(monotonicity,[status(thm)],[1041])).
% 1.22/1.44 tff(1043,plain,
% 1.22/1.44 (s(s(s(s(s(z))))) = z),
% 1.22/1.44 inference(transitivity,[status(thm)],[731, 1042, 128])).
% 1.22/1.44 tff(1044,plain,
% 1.22/1.44 ($false),
% 1.22/1.44 inference(unit_resolution,[status(thm)],[734, 1043])).
% 1.22/1.44 tff(1045,plain,(~(s(s(s(s(s(s(s(z))))))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.44 tff(1046,plain,
% 1.22/1.44 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.22/1.44 inference(modus_ponens,[status(thm)],[1045, 1038])).
% 1.22/1.44 tff(1047,plain,
% 1.22/1.44 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.22/1.44 inference(unit_resolution,[status(thm)],[1013, 310])).
% 1.22/1.44 tff(1048,plain,
% 1.22/1.44 (~r(z, s(z))),
% 1.22/1.44 inference(unit_resolution,[status(thm)],[367, 114, 300])).
% 1.22/1.44 tff(1049,plain,
% 1.22/1.44 (b(z, s(z))),
% 1.22/1.44 inference(unit_resolution,[status(thm)],[187, 1048])).
% 1.22/1.44 tff(1050,plain,
% 1.22/1.44 (r(z, s(s(z))) <=> r(z, elem!1)),
% 1.22/1.44 inference(monotonicity,[status(thm)],[310])).
% 1.22/1.44 tff(1051,plain,
% 1.22/1.44 (r(z, elem!1) <=> r(z, s(s(z)))),
% 1.22/1.44 inference(symmetry,[status(thm)],[1050])).
% 1.22/1.44 tff(1052,plain,
% 1.22/1.44 (r(z, s(s(z)))),
% 1.22/1.44 inference(modus_ponens,[status(thm)],[300, 1051])).
% 1.22/1.44 tff(1053,assumption,(b(s(z), s(s(s(z))))), introduced(assumption)).
% 1.22/1.44 tff(1054,plain,
% 1.22/1.44 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(z)))))),
% 1.22/1.44 inference(monotonicity,[status(thm)],[1020])).
% 1.22/1.44 tff(1055,plain,
% 1.22/1.44 (s(elem!1) = s(s(s(z)))),
% 1.22/1.44 inference(transitivity,[status(thm)],[229, 1054, 250])).
% 1.22/1.44 tff(1056,plain,
% 1.22/1.44 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 1.22/1.44 inference(monotonicity,[status(thm)],[1055])).
% 1.22/1.44 tff(1057,plain,
% 1.22/1.44 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.22/1.44 inference(symmetry,[status(thm)],[1056])).
% 1.22/1.44 tff(1058,plain,
% 1.22/1.44 (s(s(z)) = elem!1),
% 1.22/1.44 inference(transitivity,[status(thm)],[254, 1057, 224])).
% 1.22/1.44 tff(1059,plain,
% 1.22/1.44 (r(s(s(s(z))), s(s(z))) <=> r(s(s(s(z))), elem!1)),
% 1.22/1.44 inference(monotonicity,[status(thm)],[1058])).
% 1.22/1.44 tff(1060,plain,
% 1.22/1.44 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(z)))),
% 1.22/1.44 inference(symmetry,[status(thm)],[1059])).
% 1.22/1.44 tff(1061,assumption,(r(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.22/1.44 tff(1062,plain,
% 1.22/1.44 (r(s(s(s(z))), s(s(z)))),
% 1.22/1.44 inference(modus_ponens,[status(thm)],[1061, 1060])).
% 1.22/1.44 tff(1063,plain,
% 1.22/1.44 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 1.22/1.44 inference(symmetry,[status(thm)],[1054])).
% 1.22/1.44 tff(1064,plain,
% 1.22/1.44 (s(s(s(z))) = s(elem!1)),
% 1.22/1.44 inference(transitivity,[status(thm)],[451, 1063, 228])).
% 1.22/1.44 tff(1065,plain,
% 1.22/1.44 (r(s(s(s(z))), z) <=> r(s(elem!1), z)),
% 1.22/1.44 inference(monotonicity,[status(thm)],[1064])).
% 1.22/1.44 tff(1066,plain,
% 1.22/1.44 (r(s(elem!1), z) <=> r(s(s(s(z))), z)),
% 1.22/1.44 inference(symmetry,[status(thm)],[1065])).
% 1.22/1.44 tff(1067,assumption,(r(s(s(s(z))), s(z))), introduced(assumption)).
% 1.22/1.44 tff(1068,plain,
% 1.22/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(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)))),
% 1.22/1.44 inference(rewrite,[status(thm)],[])).
% 1.22/1.44 tff(1069,plain,
% 1.22/1.44 (((~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)))),
% 1.22/1.44 inference(rewrite,[status(thm)],[])).
% 1.22/1.44 tff(1070,plain,
% 1.22/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(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))))),
% 1.22/1.44 inference(monotonicity,[status(thm)],[1069])).
% 1.22/1.44 tff(1071,plain,
% 1.22/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(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)))),
% 1.22/1.44 inference(transitivity,[status(thm)],[1070, 1068])).
% 1.22/1.44 tff(1072,plain,
% 1.22/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)))),
% 1.22/1.44 inference(quant_inst,[status(thm)],[])).
% 1.22/1.44 tff(1073,plain,
% 1.22/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1))),
% 1.22/1.44 inference(modus_ponens,[status(thm)],[1072, 1071])).
% 1.22/1.44 tff(1074,plain,
% 1.22/1.44 ($false),
% 1.22/1.44 inference(unit_resolution,[status(thm)],[1073, 37, 114, 1061, 1067])).
% 1.22/1.44 tff(1075,plain,((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.44 tff(1076,plain,
% 1.22/1.44 (~r(s(s(s(z))), s(z))),
% 1.22/1.44 inference(unit_resolution,[status(thm)],[1075, 1061, 114])).
% 1.22/1.44 tff(1077,plain,
% 1.22/1.44 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z)))),
% 1.22/1.44 inference(rewrite,[status(thm)],[])).
% 1.22/1.44 tff(1078,plain,
% 1.22/1.44 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z)))),
% 1.22/1.44 inference(quant_inst,[status(thm)],[])).
% 1.22/1.44 tff(1079,plain,
% 1.22/1.44 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 1.22/1.44 inference(modus_ponens,[status(thm)],[1078, 1077])).
% 1.22/1.44 tff(1080,plain,
% 1.22/1.44 ((s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 1.22/1.44 inference(unit_resolution,[status(thm)],[1079, 58])).
% 1.22/1.44 tff(1081,plain,
% 1.22/1.44 (b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 1.22/1.44 inference(unit_resolution,[status(thm)],[1080, 457])).
% 1.22/1.44 tff(1082,plain,
% 1.22/1.44 (b(s(s(s(z))), s(z))),
% 1.22/1.44 inference(unit_resolution,[status(thm)],[1081, 1076])).
% 1.22/1.44 tff(1083,assumption,(b(s(s(s(z))), z)), introduced(assumption)).
% 1.22/1.44 tff(1084,plain,
% 1.22/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.22/1.44 inference(rewrite,[status(thm)],[])).
% 1.22/1.44 tff(1085,plain,
% 1.22/1.44 (((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.22/1.44 inference(rewrite,[status(thm)],[])).
% 1.22/1.44 tff(1086,plain,
% 1.22/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))))),
% 1.22/1.45 inference(monotonicity,[status(thm)],[1085])).
% 1.22/1.45 tff(1087,plain,
% 1.22/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.22/1.45 inference(transitivity,[status(thm)],[1086, 1084])).
% 1.22/1.45 tff(1088,plain,
% 1.22/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 1.22/1.45 inference(quant_inst,[status(thm)],[])).
% 1.22/1.45 tff(1089,plain,
% 1.22/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))),
% 1.22/1.45 inference(modus_ponens,[status(thm)],[1088, 1087])).
% 1.22/1.45 tff(1090,plain,
% 1.22/1.45 ($false),
% 1.22/1.45 inference(unit_resolution,[status(thm)],[1089, 75, 372, 984, 1053, 1083])).
% 1.22/1.45 tff(1091,plain,((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.45 tff(1092,plain,
% 1.22/1.45 (~b(s(s(s(z))), z)),
% 1.22/1.45 inference(unit_resolution,[status(thm)],[1091, 1082, 1053, 372])).
% 1.22/1.45 tff(1093,plain,
% 1.22/1.45 (b(s(s(s(z))), z) <=> b(s(elem!1), z)),
% 1.22/1.45 inference(monotonicity,[status(thm)],[1064])).
% 1.22/1.45 tff(1094,plain,
% 1.22/1.45 ((~b(s(s(s(z))), z)) <=> (~b(s(elem!1), z))),
% 1.22/1.45 inference(monotonicity,[status(thm)],[1093])).
% 1.22/1.45 tff(1095,assumption,(~b(s(s(s(z))), z)), introduced(assumption)).
% 1.22/1.45 tff(1096,plain,
% 1.22/1.45 (~b(s(elem!1), z)),
% 1.22/1.45 inference(modus_ponens,[status(thm)],[1095, 1094])).
% 1.22/1.45 tff(1097,plain,
% 1.22/1.45 ($false),
% 1.22/1.45 inference(unit_resolution,[status(thm)],[798, 1096])).
% 1.22/1.45 tff(1098,plain,(b(s(s(s(z))), z) | (~b(s(elem!1), z)) | (~(s(s(elem!1)) = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.45 tff(1099,plain,
% 1.22/1.45 (~b(s(elem!1), z)),
% 1.22/1.45 inference(unit_resolution,[status(thm)],[1098, 1092, 1020])).
% 1.22/1.45 tff(1100,plain,
% 1.22/1.45 (r(s(elem!1), z)),
% 1.22/1.45 inference(unit_resolution,[status(thm)],[766, 1099])).
% 1.22/1.45 tff(1101,plain,
% 1.22/1.45 (r(s(s(s(z))), z)),
% 1.22/1.45 inference(modus_ponens,[status(thm)],[1100, 1066])).
% 1.22/1.45 tff(1102,plain,
% 1.22/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(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(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)))),
% 1.22/1.45 inference(rewrite,[status(thm)],[])).
% 1.22/1.45 tff(1103,plain,
% 1.22/1.45 (((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z))) <=> ((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)))),
% 1.22/1.45 inference(rewrite,[status(thm)],[])).
% 1.22/1.45 tff(1104,plain,
% 1.22/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z))))),
% 1.22/1.45 inference(monotonicity,[status(thm)],[1103])).
% 1.22/1.45 tff(1105,plain,
% 1.22/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)))),
% 1.22/1.45 inference(transitivity,[status(thm)],[1104, 1102])).
% 1.22/1.45 tff(1106,plain,
% 1.22/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)))),
% 1.22/1.45 inference(quant_inst,[status(thm)],[])).
% 1.22/1.45 tff(1107,plain,
% 1.22/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z))),
% 1.22/1.45 inference(modus_ponens,[status(thm)],[1106, 1105])).
% 1.22/1.45 tff(1108,plain,
% 1.22/1.45 ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z))),
% 1.22/1.45 inference(unit_resolution,[status(thm)],[1107, 37, 331])).
% 1.22/1.45 tff(1109,plain,
% 1.22/1.45 ($false),
% 1.22/1.45 inference(unit_resolution,[status(thm)],[1108, 1101, 1062])).
% 1.22/1.45 tff(1110,plain,((~r(s(s(s(z))), elem!1)) | (~r(z, s(s(z)))) | (~(s(s(elem!1)) = s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.45 tff(1111,plain,
% 1.22/1.45 (~r(s(s(s(z))), elem!1)),
% 1.22/1.45 inference(unit_resolution,[status(thm)],[1110, 1053, 1047, 1052, 1049, 114])).
% 1.22/1.45 tff(1112,plain,
% 1.22/1.45 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1))),
% 1.22/1.45 inference(rewrite,[status(thm)],[])).
% 1.22/1.45 tff(1113,plain,
% 1.22/1.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1))),
% 1.22/1.45 inference(quant_inst,[status(thm)],[])).
% 1.22/1.45 tff(1114,plain,
% 1.22/1.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1)),
% 1.22/1.45 inference(modus_ponens,[status(thm)],[1113, 1112])).
% 1.22/1.45 tff(1115,plain,
% 1.22/1.45 ((s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1)),
% 1.22/1.45 inference(unit_resolution,[status(thm)],[1114, 58])).
% 1.22/1.45 tff(1116,plain,
% 1.22/1.45 (b(s(s(s(z))), elem!1)),
% 1.22/1.45 inference(unit_resolution,[status(thm)],[1115, 1111, 1031])).
% 1.22/1.45 tff(1117,plain,
% 1.22/1.45 (b(s(elem!1), elem!1) <=> b(s(s(s(z))), elem!1)),
% 1.22/1.45 inference(monotonicity,[status(thm)],[1055])).
% 1.22/1.45 tff(1118,plain,
% 1.22/1.45 (b(s(s(s(z))), elem!1) <=> b(s(elem!1), elem!1)),
% 1.22/1.45 inference(symmetry,[status(thm)],[1117])).
% 1.22/1.45 tff(1119,assumption,(b(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.22/1.45 tff(1120,plain,
% 1.22/1.45 (b(s(elem!1), elem!1)),
% 1.22/1.45 inference(modus_ponens,[status(thm)],[1119, 1118])).
% 1.22/1.45 tff(1121,plain,
% 1.22/1.45 ($false),
% 1.22/1.45 inference(unit_resolution,[status(thm)],[966, 1120])).
% 1.22/1.45 tff(1122,plain,((~b(s(s(s(z))), elem!1)) | b(s(elem!1), elem!1) | (~(s(s(elem!1)) = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.45 tff(1123,plain,
% 1.22/1.45 (b(s(elem!1), elem!1)),
% 1.22/1.45 inference(unit_resolution,[status(thm)],[1122, 1116, 1047])).
% 1.22/1.45 tff(1124,assumption,(s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))), introduced(assumption)).
% 1.22/1.45 tff(1125,plain,
% 1.22/1.45 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(s(s(s(z)))))),
% 1.22/1.45 inference(monotonicity,[status(thm)],[1124])).
% 1.22/1.45 tff(1126,plain,
% 1.22/1.45 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 1.22/1.45 inference(symmetry,[status(thm)],[1125])).
% 1.22/1.45 tff(1127,plain,
% 1.22/1.45 (s(elem!1) = s(s(s(z)))),
% 1.22/1.45 inference(symmetry,[status(thm)],[1008])).
% 1.22/1.45 tff(1128,plain,
% 1.22/1.45 (s(elem!1) = s(s(s(s(s(s(z))))))),
% 1.22/1.45 inference(transitivity,[status(thm)],[1127, 451, 1126, 713])).
% 1.22/1.45 tff(1129,plain,
% 1.22/1.45 (inj_0(s(elem!1)) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.22/1.45 inference(monotonicity,[status(thm)],[1128])).
% 1.22/1.45 tff(1130,plain,
% 1.22/1.45 (s(s(z)) = s(s(s(s(s(z)))))),
% 1.22/1.45 inference(transitivity,[status(thm)],[310, 725, 1129, 730])).
% 1.22/1.45 tff(1131,plain,
% 1.22/1.45 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(z))))))),
% 1.22/1.45 inference(monotonicity,[status(thm)],[1130])).
% 1.22/1.45 tff(1132,plain,
% 1.22/1.45 (s(z) = s(s(s(s(z))))),
% 1.22/1.45 inference(transitivity,[status(thm)],[134, 1131, 832])).
% 1.22/1.45 tff(1133,plain,
% 1.22/1.45 ($false),
% 1.22/1.45 inference(unit_resolution,[status(thm)],[484, 1132])).
% 1.22/1.45 tff(1134,plain,((~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(z)))))) | (~(s(s(z)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.45 tff(1135,plain,
% 1.22/1.45 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(z)))))),
% 1.22/1.45 inference(unit_resolution,[status(thm)],[1134, 310])).
% 1.22/1.45 tff(1136,plain,
% 1.22/1.45 (s(s(z)) = s(s(s(s(s(s(z))))))),
% 1.22/1.45 inference(transitivity,[status(thm)],[310, 725, 724, 713])).
% 1.22/1.45 tff(1137,plain,
% 1.22/1.45 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.22/1.45 inference(monotonicity,[status(thm)],[1136])).
% 1.22/1.45 tff(1138,plain,
% 1.22/1.45 (s(z) = s(s(s(s(s(z)))))),
% 1.22/1.45 inference(transitivity,[status(thm)],[134, 1137, 730])).
% 1.22/1.45 tff(1139,plain,
% 1.22/1.45 (inj_0(s(z)) = inj_0(s(s(s(s(s(z))))))),
% 1.22/1.45 inference(monotonicity,[status(thm)],[1138])).
% 1.22/1.45 tff(1140,plain,
% 1.22/1.45 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(z))),
% 1.22/1.45 inference(symmetry,[status(thm)],[1139])).
% 1.22/1.45 tff(1141,plain,
% 1.22/1.45 (s(s(s(s(z)))) = z),
% 1.22/1.45 inference(transitivity,[status(thm)],[833, 1140, 128])).
% 1.22/1.45 tff(1142,plain,
% 1.22/1.45 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(z)))) = z))),
% 1.22/1.45 inference(quant_inst,[status(thm)],[])).
% 1.22/1.45 tff(1143,plain,
% 1.22/1.45 (~(s(s(s(s(z)))) = z)),
% 1.22/1.45 inference(unit_resolution,[status(thm)],[1142, 143])).
% 1.22/1.45 tff(1144,plain,
% 1.22/1.45 ($false),
% 1.22/1.45 inference(unit_resolution,[status(thm)],[1143, 1141])).
% 1.22/1.45 tff(1145,plain,((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) | (~(s(s(z)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.45 tff(1146,plain,
% 1.22/1.45 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.22/1.45 inference(unit_resolution,[status(thm)],[1145, 310])).
% 1.22/1.45 tff(1147,plain,
% 1.22/1.45 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 1.22/1.45 inference(monotonicity,[status(thm)],[1008])).
% 1.22/1.45 tff(1148,plain,
% 1.22/1.45 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(z)))), elem!1)),
% 1.22/1.45 inference(monotonicity,[status(thm)],[310])).
% 1.22/1.45 tff(1149,plain,
% 1.22/1.45 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(z)))),
% 1.22/1.45 inference(symmetry,[status(thm)],[1148])).
% 1.22/1.45 tff(1150,plain,
% 1.22/1.45 (b(s(s(s(s(z)))), s(s(z)))),
% 1.22/1.45 inference(modus_ponens,[status(thm)],[287, 1149])).
% 1.22/1.45 tff(1151,plain,
% 1.22/1.45 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(z))), elem!1)),
% 1.22/1.45 inference(monotonicity,[status(thm)],[310])).
% 1.22/1.45 tff(1152,plain,
% 1.22/1.45 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(z)))),
% 1.22/1.45 inference(symmetry,[status(thm)],[1151])).
% 1.22/1.45 tff(1153,plain,
% 1.22/1.45 (b(s(s(s(z))), s(s(z)))),
% 1.22/1.45 inference(modus_ponens,[status(thm)],[1116, 1152])).
% 1.22/1.45 tff(1154,assumption,(b(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 1.22/1.45 tff(1155,assumption,(b(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 1.22/1.45 tff(1156,plain,
% 1.22/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.22/1.45 inference(rewrite,[status(thm)],[])).
% 1.22/1.45 tff(1157,plain,
% 1.22/1.45 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.22/1.45 inference(rewrite,[status(thm)],[])).
% 1.22/1.45 tff(1158,plain,
% 1.22/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.22/1.45 inference(monotonicity,[status(thm)],[1157])).
% 1.22/1.45 tff(1159,plain,
% 1.22/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.22/1.45 inference(transitivity,[status(thm)],[1158, 1156])).
% 1.22/1.45 tff(1160,plain,
% 1.22/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.22/1.45 inference(quant_inst,[status(thm)],[])).
% 1.22/1.45 tff(1161,plain,
% 1.22/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.22/1.45 inference(modus_ponens,[status(thm)],[1160, 1159])).
% 1.22/1.45 tff(1162,plain,
% 1.22/1.45 ($false),
% 1.22/1.45 inference(unit_resolution,[status(thm)],[1161, 75, 983, 895, 1155, 1154])).
% 1.22/1.45 tff(1163,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.45 tff(1164,plain,
% 1.22/1.45 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.22/1.45 inference(unit_resolution,[status(thm)],[1163, 1153, 1150, 895])).
% 1.22/1.45 tff(1165,plain,
% 1.22/1.45 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.22/1.45 inference(unit_resolution,[status(thm)],[575, 1164])).
% 1.22/1.45 tff(1166,plain,
% 1.22/1.45 (r(s(elem!1), s(s(s(s(z)))))),
% 1.22/1.45 inference(modus_ponens,[status(thm)],[1165, 1147])).
% 1.22/1.45 tff(1167,assumption,(r(s(elem!1), s(s(s(s(z)))))), introduced(assumption)).
% 1.22/1.45 tff(1168,assumption,(b(s(s(s(s(s(s(s(z))))))), elem!1)), introduced(assumption)).
% 1.22/1.45 tff(1169,plain,
% 1.22/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.22/1.45 inference(rewrite,[status(thm)],[])).
% 1.22/1.45 tff(1170,plain,
% 1.22/1.45 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.22/1.45 inference(rewrite,[status(thm)],[])).
% 1.22/1.45 tff(1171,plain,
% 1.22/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 1.22/1.45 inference(monotonicity,[status(thm)],[1170])).
% 1.22/1.45 tff(1172,plain,
% 1.22/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.22/1.45 inference(transitivity,[status(thm)],[1171, 1169])).
% 1.22/1.45 tff(1173,plain,
% 1.22/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.22/1.45 inference(quant_inst,[status(thm)],[])).
% 1.22/1.45 tff(1174,plain,
% 1.22/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 1.22/1.45 inference(modus_ponens,[status(thm)],[1173, 1172])).
% 1.22/1.45 tff(1175,plain,
% 1.22/1.45 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 1.22/1.45 inference(unit_resolution,[status(thm)],[1174, 75, 286, 287, 1168])).
% 1.22/1.45 tff(1176,assumption,(~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(z)))))), introduced(assumption)).
% 1.22/1.45 tff(1177,plain,
% 1.22/1.45 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 1.22/1.45 inference(rewrite,[status(thm)],[])).
% 1.22/1.45 tff(1178,plain,
% 1.22/1.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 1.22/1.45 inference(quant_inst,[status(thm)],[])).
% 1.22/1.45 tff(1179,plain,
% 1.22/1.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 1.22/1.45 inference(modus_ponens,[status(thm)],[1178, 1177])).
% 1.22/1.45 tff(1180,plain,
% 1.22/1.45 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 1.22/1.45 inference(unit_resolution,[status(thm)],[1179, 58, 1176, 1175])).
% 1.22/1.45 tff(1181,plain,
% 1.22/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.22/1.45 inference(rewrite,[status(thm)],[])).
% 1.22/1.45 tff(1182,plain,
% 1.22/1.45 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.22/1.46 inference(rewrite,[status(thm)],[])).
% 1.22/1.46 tff(1183,plain,
% 1.22/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 1.22/1.46 inference(monotonicity,[status(thm)],[1182])).
% 1.22/1.46 tff(1184,plain,
% 1.22/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.22/1.46 inference(transitivity,[status(thm)],[1183, 1181])).
% 1.22/1.46 tff(1185,plain,
% 1.22/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.22/1.46 inference(quant_inst,[status(thm)],[])).
% 1.22/1.46 tff(1186,plain,
% 1.22/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 1.22/1.46 inference(modus_ponens,[status(thm)],[1185, 1184])).
% 1.22/1.46 tff(1187,plain,
% 1.22/1.46 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.22/1.46 inference(unit_resolution,[status(thm)],[1186, 75, 286, 287, 1168, 921])).
% 1.22/1.46 tff(1188,plain,
% 1.22/1.46 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.22/1.46 inference(unit_resolution,[status(thm)],[793, 58, 790, 1187])).
% 1.22/1.46 tff(1189,assumption,(r(s(elem!1), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.22/1.46 tff(1190,assumption,(r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))), introduced(assumption)).
% 1.22/1.46 tff(1191,plain,
% 1.22/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(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(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.22/1.46 inference(rewrite,[status(thm)],[])).
% 1.22/1.46 tff(1192,plain,
% 1.22/1.46 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.22/1.46 inference(rewrite,[status(thm)],[])).
% 1.22/1.46 tff(1193,plain,
% 1.22/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 1.22/1.46 inference(monotonicity,[status(thm)],[1192])).
% 1.22/1.46 tff(1194,plain,
% 1.22/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.22/1.46 inference(transitivity,[status(thm)],[1193, 1191])).
% 1.22/1.46 tff(1195,plain,
% 1.22/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.22/1.46 inference(quant_inst,[status(thm)],[])).
% 1.22/1.46 tff(1196,plain,
% 1.22/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 1.22/1.46 inference(modus_ponens,[status(thm)],[1195, 1194])).
% 1.22/1.46 tff(1197,plain,
% 1.22/1.46 ($false),
% 1.22/1.46 inference(unit_resolution,[status(thm)],[1196, 37, 1167, 1190, 1189])).
% 1.22/1.46 tff(1198,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.46 tff(1199,plain,
% 1.22/1.46 ($false),
% 1.22/1.46 inference(unit_resolution,[status(thm)],[1198, 1188, 1180, 1167])).
% 1.22/1.46 tff(1200,plain,((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.46 tff(1201,plain,
% 1.22/1.46 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.22/1.46 inference(unit_resolution,[status(thm)],[1200, 1166, 1146, 1135, 286, 287, 1123])).
% 1.22/1.46 tff(1202,plain,
% 1.22/1.46 (r(s(z), s(s(z))) <=> r(s(z), elem!1)),
% 1.22/1.46 inference(monotonicity,[status(thm)],[310])).
% 1.22/1.46 tff(1203,plain,
% 1.22/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.22/1.46 inference(rewrite,[status(thm)],[])).
% 1.22/1.46 tff(1204,plain,
% 1.22/1.46 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.22/1.46 inference(rewrite,[status(thm)],[])).
% 1.22/1.46 tff(1205,plain,
% 1.22/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z))))))),
% 1.22/1.46 inference(monotonicity,[status(thm)],[1204])).
% 1.22/1.46 tff(1206,plain,
% 1.22/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.22/1.46 inference(transitivity,[status(thm)],[1205, 1203])).
% 1.22/1.46 tff(1207,plain,
% 1.22/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))),
% 1.22/1.46 inference(quant_inst,[status(thm)],[])).
% 1.22/1.46 tff(1208,plain,
% 1.22/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z))))),
% 1.22/1.46 inference(modus_ponens,[status(thm)],[1207, 1206])).
% 1.22/1.46 tff(1209,plain,
% 1.22/1.46 ($false),
% 1.22/1.46 inference(unit_resolution,[status(thm)],[1208, 75, 402, 1053, 895, 1155, 1154])).
% 1.22/1.46 tff(1210,plain,((~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.46 tff(1211,plain,
% 1.22/1.46 (~b(s(z), s(s(z)))),
% 1.22/1.46 inference(unit_resolution,[status(thm)],[1210, 1153, 895, 1150, 1053])).
% 1.22/1.46 tff(1212,plain,
% 1.22/1.46 (r(s(z), s(s(z)))),
% 1.22/1.46 inference(unit_resolution,[status(thm)],[416, 1211])).
% 1.22/1.46 tff(1213,plain,
% 1.22/1.46 (r(s(z), elem!1)),
% 1.22/1.46 inference(modus_ponens,[status(thm)],[1212, 1202])).
% 1.22/1.46 tff(1214,plain,
% 1.22/1.46 (((~![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(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(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(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.22/1.46 inference(rewrite,[status(thm)],[])).
% 1.22/1.46 tff(1215,plain,
% 1.22/1.46 (((~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.22/1.46 inference(rewrite,[status(thm)],[])).
% 1.22/1.46 tff(1216,plain,
% 1.22/1.46 (((~![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(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(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(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 1.22/1.46 inference(monotonicity,[status(thm)],[1215])).
% 1.22/1.46 tff(1217,plain,
% 1.22/1.46 (((~![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(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(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(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.22/1.46 inference(transitivity,[status(thm)],[1216, 1214])).
% 1.22/1.46 tff(1218,plain,
% 1.22/1.46 ((~![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(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.22/1.46 inference(quant_inst,[status(thm)],[])).
% 1.22/1.46 tff(1219,plain,
% 1.22/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))),
% 1.22/1.46 inference(modus_ponens,[status(thm)],[1218, 1217])).
% 1.22/1.46 tff(1220,plain,
% 1.22/1.46 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.22/1.46 inference(unit_resolution,[status(thm)],[1219, 37, 588, 738])).
% 1.22/1.46 tff(1221,assumption,(s(s(s(s(s(s(s(z))))))) = s(z)), introduced(assumption)).
% 1.22/1.46 tff(1222,plain,
% 1.22/1.46 (s(z) = s(s(s(s(s(s(s(z)))))))),
% 1.22/1.46 inference(symmetry,[status(thm)],[1221])).
% 1.22/1.46 tff(1223,plain,
% 1.22/1.46 (inj_0(s(z)) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 1.22/1.46 inference(monotonicity,[status(thm)],[1222])).
% 1.22/1.46 tff(1224,plain,
% 1.22/1.46 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(z))),
% 1.22/1.46 inference(symmetry,[status(thm)],[1223])).
% 1.22/1.46 tff(1225,plain,
% 1.22/1.46 (s(s(s(s(s(s(z)))))) = z),
% 1.22/1.46 inference(transitivity,[status(thm)],[714, 1224, 128])).
% 1.22/1.46 tff(1226,plain,
% 1.22/1.46 ($false),
% 1.22/1.46 inference(unit_resolution,[status(thm)],[717, 1225])).
% 1.22/1.46 tff(1227,plain,(~(s(s(s(s(s(s(s(z))))))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.46 tff(1228,plain,
% 1.22/1.46 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(z)) | b(s(s(s(s(s(s(s(z))))))), s(z)) | r(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(z)) | b(s(s(s(s(s(s(s(z))))))), s(z)) | r(s(s(s(s(s(s(s(z))))))), s(z)))),
% 1.22/1.46 inference(rewrite,[status(thm)],[])).
% 1.22/1.46 tff(1229,plain,
% 1.22/1.46 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(z)) | b(s(s(s(s(s(s(s(z))))))), s(z)) | r(s(s(s(s(s(s(s(z))))))), s(z)))),
% 1.22/1.46 inference(quant_inst,[status(thm)],[])).
% 1.22/1.46 tff(1230,plain,
% 1.22/1.46 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(z)) | b(s(s(s(s(s(s(s(z))))))), s(z)) | r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.22/1.46 inference(modus_ponens,[status(thm)],[1229, 1228])).
% 1.22/1.46 tff(1231,plain,
% 1.22/1.46 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.22/1.46 inference(unit_resolution,[status(thm)],[1230, 58, 1227, 1220])).
% 1.22/1.46 tff(1232,plain,
% 1.22/1.46 (((~![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)))),
% 1.22/1.46 inference(rewrite,[status(thm)],[])).
% 1.22/1.46 tff(1233,plain,
% 1.22/1.46 (((~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)))),
% 1.22/1.46 inference(rewrite,[status(thm)],[])).
% 1.22/1.46 tff(1234,plain,
% 1.22/1.46 (((~![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))))),
% 1.22/1.46 inference(monotonicity,[status(thm)],[1233])).
% 1.22/1.46 tff(1235,plain,
% 1.22/1.46 (((~![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)))),
% 1.22/1.46 inference(transitivity,[status(thm)],[1234, 1232])).
% 1.22/1.46 tff(1236,plain,
% 1.22/1.46 ((~![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)))),
% 1.22/1.46 inference(quant_inst,[status(thm)],[])).
% 1.22/1.46 tff(1237,plain,
% 1.22/1.46 ((~![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))),
% 1.22/1.46 inference(modus_ponens,[status(thm)],[1236, 1235])).
% 1.22/1.46 tff(1238,plain,
% 1.22/1.46 (~r(s(z), z)),
% 1.22/1.46 inference(unit_resolution,[status(thm)],[1237, 37, 300, 588])).
% 1.22/1.46 tff(1239,plain,
% 1.22/1.46 (b(s(z), z)),
% 1.22/1.46 inference(unit_resolution,[status(thm)],[169, 1238])).
% 1.22/1.46 tff(1240,plain,
% 1.22/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 1.22/1.46 inference(rewrite,[status(thm)],[])).
% 1.22/1.46 tff(1241,plain,
% 1.22/1.46 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 1.22/1.46 inference(rewrite,[status(thm)],[])).
% 1.22/1.46 tff(1242,plain,
% 1.22/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 1.22/1.46 inference(monotonicity,[status(thm)],[1241])).
% 1.22/1.46 tff(1243,plain,
% 1.22/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 1.22/1.46 inference(transitivity,[status(thm)],[1242, 1240])).
% 1.22/1.46 tff(1244,plain,
% 1.22/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.22/1.46 inference(quant_inst,[status(thm)],[])).
% 1.22/1.46 tff(1245,plain,
% 1.22/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 1.22/1.46 inference(modus_ponens,[status(thm)],[1244, 1243])).
% 1.22/1.46 tff(1246,plain,
% 1.22/1.46 ($false),
% 1.22/1.46 inference(unit_resolution,[status(thm)],[1245, 75, 1239, 782, 751, 1231])).
% 1.22/1.46 tff(1247,plain,((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(z), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.46 tff(1248,plain,
% 1.22/1.46 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.22/1.46 inference(unit_resolution,[status(thm)],[1247, 1213, 300])).
% 1.22/1.46 tff(1249,plain,
% 1.22/1.46 ($false),
% 1.22/1.46 inference(unit_resolution,[status(thm)],[813, 1248, 1201, 1046])).
% 1.22/1.46 tff(1250,plain,((~b(s(z), s(s(s(z))))) | (~r(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~(s(s(z)) = elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (s(s(s(z))) = elem!1) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.47 tff(1251,plain,
% 1.22/1.47 (~b(s(z), s(s(s(z))))),
% 1.22/1.47 inference(unit_resolution,[status(thm)],[1250, 1003, 286, 287, 300, 888, 1027, 1036])).
% 1.22/1.47 tff(1252,plain,
% 1.22/1.47 ((s(z) = s(s(s(z)))) <=> (s(s(s(z))) = s(z))),
% 1.22/1.47 inference(commutativity,[status(thm)],[])).
% 1.22/1.47 tff(1253,assumption,(s(z) = s(s(s(z)))), introduced(assumption)).
% 1.22/1.47 tff(1254,plain,
% 1.22/1.47 (s(s(s(z))) = s(z)),
% 1.22/1.47 inference(modus_ponens,[status(thm)],[1253, 1252])).
% 1.22/1.47 tff(1255,assumption,(~(s(s(s(z))) = s(z))), introduced(assumption)).
% 1.22/1.47 tff(1256,plain,
% 1.22/1.47 ($false),
% 1.22/1.47 inference(unit_resolution,[status(thm)],[1255, 1254])).
% 1.22/1.47 tff(1257,plain,((~(s(z) = s(s(s(z))))) | (s(s(s(z))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.47 tff(1258,plain,
% 1.22/1.47 (~(s(z) = s(s(s(z))))),
% 1.22/1.47 inference(unit_resolution,[status(thm)],[1257, 457])).
% 1.22/1.47 tff(1259,plain,
% 1.22/1.47 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z)))))),
% 1.22/1.47 inference(rewrite,[status(thm)],[])).
% 1.22/1.47 tff(1260,plain,
% 1.22/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z)))))),
% 1.22/1.47 inference(quant_inst,[status(thm)],[])).
% 1.22/1.47 tff(1261,plain,
% 1.22/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 1.22/1.47 inference(modus_ponens,[status(thm)],[1260, 1259])).
% 1.22/1.47 tff(1262,plain,
% 1.22/1.47 ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 1.22/1.47 inference(unit_resolution,[status(thm)],[1261, 58])).
% 1.22/1.47 tff(1263,plain,
% 1.22/1.47 (b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 1.22/1.47 inference(unit_resolution,[status(thm)],[1262, 1258])).
% 1.22/1.47 tff(1264,plain,
% 1.22/1.47 (r(s(z), s(s(s(z))))),
% 1.22/1.47 inference(unit_resolution,[status(thm)],[1263, 1251])).
% 1.22/1.47 tff(1265,assumption,(r(s(z), s(s(s(z))))), introduced(assumption)).
% 1.22/1.47 tff(1266,assumption,(r(elem!1, s(s(s(z))))), introduced(assumption)).
% 1.22/1.47 tff(1267,plain,
% 1.22/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(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(elem!1, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.22/1.47 inference(rewrite,[status(thm)],[])).
% 1.22/1.47 tff(1268,plain,
% 1.22/1.47 (((~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.22/1.47 inference(rewrite,[status(thm)],[])).
% 1.22/1.47 tff(1269,plain,
% 1.22/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(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(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))))),
% 1.22/1.47 inference(monotonicity,[status(thm)],[1268])).
% 1.22/1.47 tff(1270,plain,
% 1.22/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(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(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.22/1.47 inference(transitivity,[status(thm)],[1269, 1267])).
% 1.22/1.47 tff(1271,plain,
% 1.22/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(z))))),
% 1.22/1.47 inference(quant_inst,[status(thm)],[])).
% 1.22/1.47 tff(1272,plain,
% 1.22/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))),
% 1.22/1.47 inference(modus_ponens,[status(thm)],[1271, 1270])).
% 1.22/1.47 tff(1273,plain,
% 1.22/1.47 ($false),
% 1.22/1.47 inference(unit_resolution,[status(thm)],[1272, 37, 114, 1266, 1265])).
% 1.22/1.47 tff(1274,plain,((~r(s(z), s(s(s(z))))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.47 tff(1275,plain,
% 1.22/1.47 (~r(elem!1, s(s(s(z))))),
% 1.22/1.47 inference(unit_resolution,[status(thm)],[1274, 1264, 1036])).
% 1.22/1.47 tff(1276,plain,
% 1.22/1.47 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z)))))),
% 1.22/1.47 inference(rewrite,[status(thm)],[])).
% 1.22/1.47 tff(1277,plain,
% 1.22/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z)))))),
% 1.22/1.47 inference(quant_inst,[status(thm)],[])).
% 1.22/1.47 tff(1278,plain,
% 1.22/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z))))),
% 1.22/1.47 inference(modus_ponens,[status(thm)],[1277, 1276])).
% 1.22/1.47 tff(1279,plain,
% 1.22/1.47 ((elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z))))),
% 1.22/1.47 inference(unit_resolution,[status(thm)],[1278, 58])).
% 1.22/1.47 tff(1280,plain,
% 1.22/1.47 (b(elem!1, s(s(s(z))))),
% 1.22/1.47 inference(unit_resolution,[status(thm)],[1279, 1275, 1034])).
% 1.22/1.47 tff(1281,plain,
% 1.22/1.47 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 1.22/1.47 inference(monotonicity,[status(thm)],[1021])).
% 1.22/1.47 tff(1282,plain,
% 1.22/1.47 (b(s(s(elem!1)), s(s(z))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 1.22/1.47 inference(symmetry,[status(thm)],[1281])).
% 1.22/1.47 tff(1283,assumption,(b(s(s(elem!1)), s(s(z)))), introduced(assumption)).
% 1.22/1.47 tff(1284,plain,
% 1.22/1.47 (b(s(s(s(s(z)))), s(s(z)))),
% 1.22/1.47 inference(modus_ponens,[status(thm)],[1283, 1282])).
% 1.22/1.47 tff(1285,plain,
% 1.22/1.47 (b(s(s(z)), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.22/1.47 inference(monotonicity,[status(thm)],[1058])).
% 1.22/1.47 tff(1286,plain,
% 1.22/1.47 (b(elem!1, s(s(s(z)))) <=> b(s(s(z)), s(s(s(z))))),
% 1.22/1.47 inference(symmetry,[status(thm)],[1285])).
% 1.22/1.47 tff(1287,assumption,(b(elem!1, s(s(s(z))))), introduced(assumption)).
% 1.22/1.47 tff(1288,plain,
% 1.22/1.47 (b(s(s(z)), s(s(s(z))))),
% 1.22/1.47 inference(modus_ponens,[status(thm)],[1287, 1286])).
% 1.22/1.47 tff(1289,plain,
% 1.22/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.22/1.47 inference(rewrite,[status(thm)],[])).
% 1.22/1.47 tff(1290,plain,
% 1.22/1.47 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.22/1.47 inference(rewrite,[status(thm)],[])).
% 1.22/1.47 tff(1291,plain,
% 1.22/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.22/1.47 inference(monotonicity,[status(thm)],[1290])).
% 1.22/1.47 tff(1292,plain,
% 1.22/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.22/1.47 inference(transitivity,[status(thm)],[1291, 1289])).
% 1.22/1.47 tff(1293,plain,
% 1.22/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.22/1.47 inference(quant_inst,[status(thm)],[])).
% 1.22/1.47 tff(1294,plain,
% 1.22/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.22/1.47 inference(modus_ponens,[status(thm)],[1293, 1292])).
% 1.22/1.47 tff(1295,plain,
% 1.22/1.47 ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))),
% 1.22/1.47 inference(unit_resolution,[status(thm)],[1294, 75, 983, 895])).
% 1.22/1.47 tff(1296,plain,
% 1.22/1.47 ($false),
% 1.22/1.47 inference(unit_resolution,[status(thm)],[1295, 1288, 1284])).
% 1.22/1.47 tff(1297,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~(s(s(elem!1)) = s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.47 tff(1298,plain,
% 1.22/1.47 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.22/1.47 inference(unit_resolution,[status(thm)],[1297, 1280, 1014, 888, 1018])).
% 1.22/1.47 tff(1299,plain,
% 1.22/1.47 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.22/1.47 inference(unit_resolution,[status(thm)],[575, 1298])).
% 1.22/1.47 tff(1300,plain,
% 1.22/1.47 (r(s(elem!1), s(s(s(s(z)))))),
% 1.22/1.47 inference(modus_ponens,[status(thm)],[1299, 1005])).
% 1.22/1.47 tff(1301,plain,
% 1.22/1.47 ((s(s(z)) = s(z)) <=> (elem!1 = s(z))),
% 1.22/1.47 inference(monotonicity,[status(thm)],[1003])).
% 1.22/1.47 tff(1302,plain,
% 1.22/1.47 ((s(s(z)) = s(z)) <=> (s(z) = elem!1)),
% 1.22/1.47 inference(transitivity,[status(thm)],[1301, 91])).
% 1.22/1.47 tff(1303,plain,
% 1.22/1.47 ((~(s(s(z)) = s(z))) <=> (~(s(z) = elem!1))),
% 1.22/1.47 inference(monotonicity,[status(thm)],[1302])).
% 1.22/1.47 tff(1304,plain,
% 1.22/1.47 (~(s(z) = elem!1)),
% 1.22/1.47 inference(modus_ponens,[status(thm)],[148, 1303])).
% 1.22/1.47 tff(1305,assumption,(~(elem!1 = s(s(s(z))))), introduced(assumption)).
% 1.22/1.47 tff(1306,plain,
% 1.22/1.47 (~r(elem!1, s(s(s(z))))),
% 1.22/1.47 inference(unit_resolution,[status(thm)],[1274, 1265, 114])).
% 1.22/1.47 tff(1307,plain,
% 1.22/1.47 (b(elem!1, s(s(s(z))))),
% 1.22/1.47 inference(unit_resolution,[status(thm)],[1279, 1306, 1305])).
% 1.22/1.47 tff(1308,assumption,(r(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 1.22/1.47 tff(1309,plain,
% 1.22/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.22/1.47 inference(rewrite,[status(thm)],[])).
% 1.22/1.47 tff(1310,plain,
% 1.22/1.47 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.22/1.47 inference(rewrite,[status(thm)],[])).
% 1.22/1.47 tff(1311,plain,
% 1.22/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, 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(z))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.22/1.47 inference(monotonicity,[status(thm)],[1310])).
% 1.22/1.47 tff(1312,plain,
% 1.22/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, 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(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.22/1.47 inference(transitivity,[status(thm)],[1311, 1309])).
% 1.22/1.47 tff(1313,plain,
% 1.22/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))))),
% 1.22/1.47 inference(quant_inst,[status(thm)],[])).
% 1.22/1.47 tff(1314,plain,
% 1.22/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.22/1.47 inference(modus_ponens,[status(thm)],[1313, 1312])).
% 1.22/1.47 tff(1315,plain,
% 1.22/1.47 ($false),
% 1.22/1.47 inference(unit_resolution,[status(thm)],[1314, 37, 468, 1265, 1308])).
% 1.22/1.47 tff(1316,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.47 tff(1317,plain,
% 1.22/1.47 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.22/1.47 inference(unit_resolution,[status(thm)],[1316, 1265, 468])).
% 1.22/1.47 tff(1318,plain,
% 1.22/1.47 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.22/1.47 inference(unit_resolution,[status(thm)],[575, 1317])).
% 1.22/1.47 tff(1319,plain,
% 1.22/1.47 ($false),
% 1.22/1.47 inference(unit_resolution,[status(thm)],[1297, 1318, 1307, 895, 1020, 1283])).
% 1.22/1.47 tff(1320,plain,((~r(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~(s(s(elem!1)) = s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(z)))) | (elem!1 = s(s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.47 tff(1321,plain,
% 1.22/1.47 (~r(s(z), s(s(s(s(z)))))),
% 1.22/1.47 inference(unit_resolution,[status(thm)],[1320, 1264, 1014, 888, 1034, 1018, 1036])).
% 1.22/1.47 tff(1322,plain,
% 1.22/1.47 (b(s(z), s(s(s(s(z)))))),
% 1.22/1.47 inference(unit_resolution,[status(thm)],[489, 1321])).
% 1.22/1.47 tff(1323,plain,
% 1.22/1.47 (~b(s(z), elem!1)),
% 1.22/1.47 inference(unit_resolution,[status(thm)],[586, 1322, 286, 287])).
% 1.22/1.47 tff(1324,plain,
% 1.22/1.47 (r(s(z), elem!1)),
% 1.22/1.47 inference(unit_resolution,[status(thm)],[601, 1323, 1304])).
% 1.22/1.47 tff(1325,plain,
% 1.22/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))),
% 1.22/1.47 inference(rewrite,[status(thm)],[])).
% 1.22/1.47 tff(1326,plain,
% 1.22/1.47 (((~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z))) <=> ((~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))),
% 1.22/1.47 inference(rewrite,[status(thm)],[])).
% 1.22/1.47 tff(1327,plain,
% 1.22/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z))))),
% 1.22/1.47 inference(monotonicity,[status(thm)],[1326])).
% 1.22/1.47 tff(1328,plain,
% 1.22/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))),
% 1.22/1.47 inference(transitivity,[status(thm)],[1327, 1325])).
% 1.22/1.47 tff(1329,plain,
% 1.22/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)))),
% 1.22/1.47 inference(quant_inst,[status(thm)],[])).
% 1.22/1.47 tff(1330,plain,
% 1.22/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z))),
% 1.22/1.47 inference(modus_ponens,[status(thm)],[1329, 1328])).
% 1.22/1.47 tff(1331,plain,
% 1.22/1.47 (~r(s(s(s(z))), z)),
% 1.22/1.47 inference(unit_resolution,[status(thm)],[1330, 37, 300, 1061])).
% 1.22/1.47 tff(1332,plain,
% 1.22/1.47 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z))),
% 1.22/1.47 inference(rewrite,[status(thm)],[])).
% 1.22/1.47 tff(1333,plain,
% 1.22/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z))),
% 1.22/1.47 inference(quant_inst,[status(thm)],[])).
% 1.22/1.47 tff(1334,plain,
% 1.22/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z)),
% 1.22/1.47 inference(modus_ponens,[status(thm)],[1333, 1332])).
% 1.22/1.47 tff(1335,plain,
% 1.22/1.47 (b(s(s(s(z))), z)),
% 1.22/1.47 inference(unit_resolution,[status(thm)],[1334, 58, 221, 1331])).
% 1.22/1.47 tff(1336,plain,
% 1.22/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))))),
% 1.22/1.47 inference(rewrite,[status(thm)],[])).
% 1.22/1.47 tff(1337,plain,
% 1.22/1.47 (((~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))))),
% 1.22/1.47 inference(rewrite,[status(thm)],[])).
% 1.22/1.47 tff(1338,plain,
% 1.22/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z)))))))),
% 1.22/1.47 inference(monotonicity,[status(thm)],[1337])).
% 1.22/1.47 tff(1339,plain,
% 1.22/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))))),
% 1.22/1.47 inference(transitivity,[status(thm)],[1338, 1336])).
% 1.22/1.47 tff(1340,plain,
% 1.22/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))))),
% 1.22/1.47 inference(quant_inst,[status(thm)],[])).
% 1.22/1.47 tff(1341,plain,
% 1.22/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z)))))),
% 1.22/1.47 inference(modus_ponens,[status(thm)],[1340, 1339])).
% 1.22/1.47 tff(1342,plain,
% 1.22/1.47 (~r(s(z), s(s(s(z))))),
% 1.22/1.47 inference(unit_resolution,[status(thm)],[1341, 37, 588, 1061])).
% 1.22/1.47 tff(1343,plain,
% 1.22/1.47 (b(s(z), s(s(s(z))))),
% 1.22/1.47 inference(unit_resolution,[status(thm)],[1263, 1342])).
% 1.22/1.47 tff(1344,plain,
% 1.22/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~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(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))),
% 1.22/1.48 inference(rewrite,[status(thm)],[])).
% 1.22/1.48 tff(1345,plain,
% 1.22/1.48 (((~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))),
% 1.22/1.48 inference(rewrite,[status(thm)],[])).
% 1.22/1.48 tff(1346,plain,
% 1.22/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1))))),
% 1.22/1.48 inference(monotonicity,[status(thm)],[1345])).
% 1.22/1.48 tff(1347,plain,
% 1.22/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))),
% 1.22/1.48 inference(transitivity,[status(thm)],[1346, 1344])).
% 1.22/1.48 tff(1348,plain,
% 1.22/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 1.22/1.48 inference(quant_inst,[status(thm)],[])).
% 1.22/1.48 tff(1349,plain,
% 1.22/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1))),
% 1.22/1.48 inference(modus_ponens,[status(thm)],[1348, 1347])).
% 1.22/1.48 tff(1350,plain,
% 1.22/1.48 (~r(s(s(s(z))), s(z))),
% 1.22/1.48 inference(unit_resolution,[status(thm)],[1349, 37, 588, 1061])).
% 1.22/1.48 tff(1351,plain,
% 1.22/1.48 (b(s(s(s(z))), s(z))),
% 1.22/1.48 inference(unit_resolution,[status(thm)],[1081, 1350])).
% 1.22/1.48 tff(1352,plain,
% 1.22/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z))))),
% 1.22/1.48 inference(rewrite,[status(thm)],[])).
% 1.22/1.48 tff(1353,plain,
% 1.22/1.48 (((~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z)))) <=> ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z))))),
% 1.22/1.48 inference(rewrite,[status(thm)],[])).
% 1.22/1.48 tff(1354,plain,
% 1.22/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z)))))),
% 1.22/1.48 inference(monotonicity,[status(thm)],[1353])).
% 1.22/1.48 tff(1355,plain,
% 1.22/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z))))),
% 1.22/1.48 inference(transitivity,[status(thm)],[1354, 1352])).
% 1.22/1.48 tff(1356,plain,
% 1.22/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z))))),
% 1.22/1.48 inference(quant_inst,[status(thm)],[])).
% 1.22/1.48 tff(1357,plain,
% 1.22/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z)))),
% 1.22/1.48 inference(modus_ponens,[status(thm)],[1356, 1355])).
% 1.22/1.48 tff(1358,plain,
% 1.22/1.48 ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z)))),
% 1.22/1.48 inference(unit_resolution,[status(thm)],[1357, 37])).
% 1.22/1.48 tff(1359,plain,
% 1.22/1.48 (~r(z, s(z))),
% 1.22/1.48 inference(unit_resolution,[status(thm)],[1358, 300, 588])).
% 1.22/1.48 tff(1360,plain,
% 1.22/1.48 (b(z, s(z))),
% 1.22/1.48 inference(unit_resolution,[status(thm)],[187, 1359])).
% 1.22/1.48 tff(1361,plain,
% 1.22/1.48 ($false),
% 1.22/1.48 inference(unit_resolution,[status(thm)],[1089, 75, 1360, 1351, 1343, 1335])).
% 1.22/1.48 tff(1362,plain,((~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.48 tff(1363,plain,
% 1.22/1.48 (~r(s(s(s(z))), elem!1)),
% 1.22/1.48 inference(unit_resolution,[status(thm)],[1362, 1324, 300])).
% 1.22/1.48 tff(1364,plain,
% 1.22/1.48 (b(s(s(s(z))), elem!1)),
% 1.22/1.48 inference(unit_resolution,[status(thm)],[1115, 1363, 1027])).
% 1.22/1.48 tff(1365,plain,
% 1.22/1.48 (b(s(elem!1), elem!1)),
% 1.22/1.48 inference(unit_resolution,[status(thm)],[1122, 1364, 1014])).
% 1.22/1.48 tff(1366,plain,
% 1.22/1.48 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(z)))))),
% 1.22/1.48 inference(unit_resolution,[status(thm)],[1134, 1003])).
% 1.22/1.48 tff(1367,plain,
% 1.22/1.48 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.22/1.48 inference(unit_resolution,[status(thm)],[1145, 1003])).
% 1.22/1.48 tff(1368,plain,
% 1.22/1.48 ((s(s(s(s(s(s(s(z))))))) = s(s(z))) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.22/1.48 inference(monotonicity,[status(thm)],[1003])).
% 1.22/1.48 tff(1369,plain,
% 1.22/1.48 ((~(s(s(s(s(s(s(s(z))))))) = s(s(z)))) <=> (~(s(s(s(s(s(s(s(z))))))) = elem!1))),
% 1.22/1.48 inference(monotonicity,[status(thm)],[1368])).
% 1.22/1.48 tff(1370,plain,
% 1.22/1.48 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.22/1.48 inference(modus_ponens,[status(thm)],[1045, 1369])).
% 1.22/1.48 tff(1371,plain,
% 1.22/1.48 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.22/1.48 inference(unit_resolution,[status(thm)],[1247, 1324, 300])).
% 1.22/1.48 tff(1372,plain,
% 1.22/1.48 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.22/1.48 inference(unit_resolution,[status(thm)],[813, 1371, 1370])).
% 1.22/1.48 tff(1373,plain,
% 1.22/1.48 (~r(s(elem!1), s(s(s(s(z)))))),
% 1.22/1.48 inference(unit_resolution,[status(thm)],[1200, 1372, 1367, 1366, 286, 287, 1365])).
% 1.22/1.48 tff(1374,plain,
% 1.22/1.48 ($false),
% 1.22/1.48 inference(unit_resolution,[status(thm)],[1373, 1300])).
% 1.22/1.48 tff(1375,plain,(b(elem!1, s(z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (elem!1 = s(s(s(s(z))))) | (s(s(elem!1)) = s(s(z))) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.22/1.48 tff(1376,plain,
% 1.22/1.48 (b(elem!1, s(z))),
% 1.22/1.48 inference(unit_resolution,[status(thm)],[1375, 299, 287, 286, 274, 266, 99])).
% 1.22/1.48 tff(1377,plain,
% 1.22/1.48 (b(elem!1, s(z))),
% 1.22/1.48 inference(unit_resolution,[status(thm)],[1375, 300, 287, 286, 274, 266, 99])).
% 1.22/1.48 tff(1378,plain,
% 1.22/1.48 (b(elem!1, s(z)) <=> b(elem!1, elem!1)),
% 1.22/1.48 inference(monotonicity,[status(thm)],[93])).
% 1.22/1.48 tff(1379,plain,
% 1.22/1.48 (b(elem!1, elem!1) <=> b(elem!1, s(z))),
% 1.22/1.48 inference(symmetry,[status(thm)],[1378])).
% 1.22/1.48 tff(1380,plain,
% 1.22/1.48 ((~b(elem!1, elem!1)) <=> (~b(elem!1, s(z)))),
% 1.22/1.48 inference(monotonicity,[status(thm)],[1379])).
% 1.22/1.48 tff(1381,plain,
% 1.22/1.48 (^[X: $i] : refl((~b(X, X)) <=> (~b(X, X)))),
% 1.22/1.48 inference(bind,[status(th)],[])).
% 1.22/1.48 tff(1382,plain,
% 1.22/1.48 (![X: $i] : (~b(X, X)) <=> ![X: $i] : (~b(X, X))),
% 1.22/1.48 inference(quant_intro,[status(thm)],[1381])).
% 1.22/1.48 tff(1383,plain,
% 1.22/1.48 (![X: $i] : (~b(X, X)) <=> ![X: $i] : (~b(X, X))),
% 1.22/1.48 inference(rewrite,[status(thm)],[])).
% 1.22/1.48 tff(1384,axiom,(![X: $i] : (~b(X, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bi')).
% 1.22/1.48 tff(1385,plain,
% 1.22/1.48 (![X: $i] : (~b(X, X))),
% 1.22/1.48 inference(modus_ponens,[status(thm)],[1384, 1383])).
% 1.22/1.48 tff(1386,plain,(
% 1.22/1.48 ![X: $i] : (~b(X, X))),
% 1.22/1.48 inference(skolemize,[status(sab)],[1385])).
% 1.22/1.48 tff(1387,plain,
% 1.22/1.48 (![X: $i] : (~b(X, X))),
% 1.22/1.48 inference(modus_ponens,[status(thm)],[1386, 1382])).
% 1.22/1.48 tff(1388,plain,
% 1.22/1.48 ((~![X: $i] : (~b(X, X))) | (~b(elem!1, elem!1))),
% 1.22/1.48 inference(quant_inst,[status(thm)],[])).
% 1.22/1.48 tff(1389,plain,
% 1.22/1.48 (~b(elem!1, elem!1)),
% 1.22/1.48 inference(unit_resolution,[status(thm)],[1388, 1387])).
% 1.22/1.48 tff(1390,plain,
% 1.22/1.48 (~b(elem!1, s(z))),
% 1.22/1.48 inference(modus_ponens,[status(thm)],[1389, 1380])).
% 1.22/1.48 tff(1391,assumption,(b(elem!1, s(z))), introduced(assumption)).
% 1.22/1.48 tff(1392,plain,
% 1.22/1.48 ($false),
% 1.22/1.48 inference(unit_resolution,[status(thm)],[1391, 1390])).
% 1.22/1.48 tff(1393,plain,((~(s(z) = elem!1)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.48 tff(1394,plain,
% 1.22/1.48 (~(s(z) = elem!1)),
% 1.22/1.48 inference(unit_resolution,[status(thm)],[1393, 1377])).
% 1.22/1.48 tff(1395,plain,
% 1.22/1.48 (~r(s(z), elem!1)),
% 1.22/1.48 inference(unit_resolution,[status(thm)],[1358, 506, 300])).
% 1.22/1.48 tff(1396,plain,
% 1.22/1.48 (b(s(z), elem!1)),
% 1.22/1.48 inference(unit_resolution,[status(thm)],[601, 1395, 1394])).
% 1.22/1.48 tff(1397,plain,
% 1.22/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.22/1.48 inference(rewrite,[status(thm)],[])).
% 1.22/1.48 tff(1398,plain,
% 1.22/1.48 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), 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(z), elem!1)))),
% 1.22/1.48 inference(rewrite,[status(thm)],[])).
% 1.22/1.48 tff(1399,plain,
% 1.22/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))))),
% 1.22/1.48 inference(monotonicity,[status(thm)],[1398])).
% 1.22/1.48 tff(1400,plain,
% 1.22/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.22/1.48 inference(transitivity,[status(thm)],[1399, 1397])).
% 1.22/1.48 tff(1401,plain,
% 1.22/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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))))),
% 1.22/1.48 inference(quant_inst,[status(thm)],[])).
% 1.22/1.48 tff(1402,plain,
% 1.22/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))),
% 1.22/1.48 inference(modus_ponens,[status(thm)],[1401, 1400])).
% 1.22/1.48 tff(1403,plain,
% 1.22/1.48 (~b(s(s(s(s(z)))), s(z))),
% 1.22/1.48 inference(unit_resolution,[status(thm)],[1402, 75, 1396, 1377, 287])).
% 1.22/1.48 tff(1404,plain,
% 1.22/1.48 (((~![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)))),
% 1.22/1.48 inference(rewrite,[status(thm)],[])).
% 1.22/1.48 tff(1405,plain,
% 1.22/1.48 ((~![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)))),
% 1.22/1.48 inference(quant_inst,[status(thm)],[])).
% 1.22/1.48 tff(1406,plain,
% 1.22/1.48 ((~![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))),
% 1.22/1.48 inference(modus_ponens,[status(thm)],[1405, 1404])).
% 1.22/1.48 tff(1407,plain,
% 1.22/1.48 (r(s(s(s(s(z)))), s(z))),
% 1.22/1.48 inference(unit_resolution,[status(thm)],[1406, 58, 1403, 483])).
% 1.22/1.48 tff(1408,assumption,(r(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.22/1.48 tff(1409,assumption,(r(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.22/1.48 tff(1410,plain,
% 1.22/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(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, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.22/1.48 inference(rewrite,[status(thm)],[])).
% 1.22/1.48 tff(1411,plain,
% 1.22/1.48 (((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.22/1.48 inference(rewrite,[status(thm)],[])).
% 1.22/1.48 tff(1412,plain,
% 1.22/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))))),
% 1.22/1.48 inference(monotonicity,[status(thm)],[1411])).
% 1.22/1.48 tff(1413,plain,
% 1.22/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.22/1.48 inference(transitivity,[status(thm)],[1412, 1410])).
% 1.22/1.48 tff(1414,plain,
% 1.22/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.22/1.48 inference(quant_inst,[status(thm)],[])).
% 1.22/1.48 tff(1415,plain,
% 1.22/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))),
% 1.22/1.48 inference(modus_ponens,[status(thm)],[1414, 1413])).
% 1.22/1.48 tff(1416,plain,
% 1.22/1.48 ($false),
% 1.22/1.48 inference(unit_resolution,[status(thm)],[1415, 37, 506, 1409, 1408])).
% 1.22/1.48 tff(1417,plain,((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.48 tff(1418,plain,
% 1.22/1.48 (~r(s(s(s(s(z)))), z)),
% 1.22/1.48 inference(unit_resolution,[status(thm)],[1417, 1407, 506])).
% 1.22/1.48 tff(1419,plain,
% 1.22/1.48 (((~![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))),
% 1.22/1.48 inference(rewrite,[status(thm)],[])).
% 1.22/1.48 tff(1420,plain,
% 1.22/1.48 ((~![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))),
% 1.22/1.48 inference(quant_inst,[status(thm)],[])).
% 1.22/1.48 tff(1421,plain,
% 1.22/1.48 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = z) | b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z)),
% 1.22/1.48 inference(modus_ponens,[status(thm)],[1420, 1419])).
% 1.22/1.48 tff(1422,plain,
% 1.22/1.48 (b(s(s(s(s(z)))), z)),
% 1.22/1.48 inference(unit_resolution,[status(thm)],[1421, 58, 1143, 1418])).
% 1.22/1.48 tff(1423,assumption,(b(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.22/1.48 tff(1424,plain,
% 1.22/1.48 ($false),
% 1.22/1.48 inference(unit_resolution,[status(thm)],[15, 1058])).
% 1.22/1.48 tff(1425,plain,((~(s(s(elem!1)) = s(s(s(s(z)))))) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.22/1.48 tff(1426,plain,
% 1.22/1.48 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 1.22/1.48 inference(unit_resolution,[status(thm)],[1425, 15])).
% 1.22/1.48 tff(1427,plain,
% 1.22/1.48 (~r(z, s(s(z)))),
% 1.22/1.48 inference(unit_resolution,[status(thm)],[339, 889, 300])).
% 1.22/1.48 tff(1428,plain,
% 1.22/1.48 (b(z, s(s(z)))),
% 1.22/1.48 inference(unit_resolution,[status(thm)],[351, 1427])).
% 1.22/1.48 tff(1429,plain,
% 1.22/1.48 (~r(s(s(z)), z)),
% 1.22/1.48 inference(unit_resolution,[status(thm)],[328, 889, 300])).
% 1.22/1.48 tff(1430,plain,
% 1.22/1.48 (b(s(s(z)), z)),
% 1.22/1.48 inference(unit_resolution,[status(thm)],[202, 1429])).
% 1.22/1.48 tff(1431,plain,
% 1.22/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.22/1.48 inference(rewrite,[status(thm)],[])).
% 1.22/1.48 tff(1432,plain,
% 1.22/1.48 (((~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.22/1.48 inference(rewrite,[status(thm)],[])).
% 1.22/1.48 tff(1433,plain,
% 1.22/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 1.22/1.48 inference(monotonicity,[status(thm)],[1432])).
% 1.22/1.48 tff(1434,plain,
% 1.22/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.22/1.48 inference(transitivity,[status(thm)],[1433, 1431])).
% 1.22/1.48 tff(1435,plain,
% 1.22/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(z))))),
% 1.22/1.48 inference(quant_inst,[status(thm)],[])).
% 1.22/1.48 tff(1436,plain,
% 1.22/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 1.22/1.48 inference(modus_ponens,[status(thm)],[1435, 1434])).
% 1.22/1.48 tff(1437,plain,
% 1.22/1.48 ($false),
% 1.22/1.48 inference(unit_resolution,[status(thm)],[1436, 75, 1391, 578, 286, 287])).
% 1.22/1.48 tff(1438,plain,((~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.48 tff(1439,plain,
% 1.22/1.48 (~b(s(z), s(s(s(s(z)))))),
% 1.22/1.48 inference(unit_resolution,[status(thm)],[1438, 1391, 286, 287])).
% 1.22/1.48 tff(1440,plain,
% 1.22/1.48 (r(s(z), s(s(s(s(z)))))),
% 1.22/1.48 inference(unit_resolution,[status(thm)],[489, 1439])).
% 1.22/1.48 tff(1441,plain,
% 1.22/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.22/1.48 inference(rewrite,[status(thm)],[])).
% 1.22/1.48 tff(1442,plain,
% 1.22/1.48 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.22/1.49 inference(rewrite,[status(thm)],[])).
% 1.22/1.49 tff(1443,plain,
% 1.22/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z))))))))),
% 1.22/1.49 inference(monotonicity,[status(thm)],[1442])).
% 1.22/1.49 tff(1444,plain,
% 1.22/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.22/1.49 inference(transitivity,[status(thm)],[1443, 1441])).
% 1.22/1.49 tff(1445,plain,
% 1.22/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), 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)))))),
% 1.22/1.49 inference(quant_inst,[status(thm)],[])).
% 1.22/1.49 tff(1446,plain,
% 1.22/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z))))))),
% 1.22/1.49 inference(modus_ponens,[status(thm)],[1445, 1444])).
% 1.22/1.49 tff(1447,plain,
% 1.22/1.49 (~r(s(z), s(s(z)))),
% 1.22/1.49 inference(unit_resolution,[status(thm)],[1446, 37, 1440, 467])).
% 1.22/1.49 tff(1448,plain,
% 1.22/1.49 (b(s(z), s(s(z)))),
% 1.22/1.49 inference(unit_resolution,[status(thm)],[416, 1447])).
% 1.22/1.49 tff(1449,plain,
% 1.22/1.49 (~b(z, s(z))),
% 1.22/1.49 inference(unit_resolution,[status(thm)],[410, 1448, 1428, 1430])).
% 1.22/1.49 tff(1450,plain,
% 1.22/1.49 (r(z, s(z))),
% 1.22/1.49 inference(unit_resolution,[status(thm)],[187, 1449])).
% 1.22/1.49 tff(1451,plain,
% 1.22/1.49 (~r(s(s(z)), s(z))),
% 1.22/1.49 inference(unit_resolution,[status(thm)],[476, 467, 1440])).
% 1.22/1.49 tff(1452,plain,
% 1.22/1.49 (b(s(s(z)), s(z))),
% 1.22/1.49 inference(unit_resolution,[status(thm)],[153, 1451])).
% 1.22/1.49 tff(1453,plain,
% 1.22/1.49 (~(elem!1 = s(z))),
% 1.22/1.49 inference(unit_resolution,[status(thm)],[358, 1452, 99])).
% 1.22/1.49 tff(1454,plain,
% 1.22/1.49 (~(s(z) = elem!1)),
% 1.22/1.49 inference(unit_resolution,[status(thm)],[97, 1453])).
% 1.22/1.49 tff(1455,plain,
% 1.22/1.49 (~r(s(z), elem!1)),
% 1.22/1.49 inference(unit_resolution,[status(thm)],[1358, 1450, 300])).
% 1.22/1.49 tff(1456,plain,
% 1.22/1.49 (b(s(z), elem!1)),
% 1.22/1.49 inference(unit_resolution,[status(thm)],[601, 1455, 1454])).
% 1.22/1.49 tff(1457,assumption,(b(s(s(elem!1)), s(z))), introduced(assumption)).
% 1.22/1.49 tff(1458,plain,
% 1.22/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.22/1.49 inference(rewrite,[status(thm)],[])).
% 1.22/1.49 tff(1459,plain,
% 1.22/1.49 (((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), 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(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.22/1.49 inference(rewrite,[status(thm)],[])).
% 1.22/1.49 tff(1460,plain,
% 1.22/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1)), s(z))) | (~b(s(z), 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(X1, 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(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))))),
% 1.22/1.49 inference(monotonicity,[status(thm)],[1459])).
% 1.22/1.49 tff(1461,plain,
% 1.22/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1)), s(z))) | (~b(s(z), 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(X1, 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(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.22/1.49 inference(transitivity,[status(thm)],[1460, 1458])).
% 1.22/1.49 tff(1462,plain,
% 1.22/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.22/1.49 inference(quant_inst,[status(thm)],[])).
% 1.22/1.49 tff(1463,plain,
% 1.22/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))),
% 1.22/1.49 inference(modus_ponens,[status(thm)],[1462, 1461])).
% 1.22/1.49 tff(1464,plain,
% 1.22/1.49 ($false),
% 1.22/1.49 inference(unit_resolution,[status(thm)],[1463, 75, 1457, 107, 1391, 309, 1283])).
% 1.22/1.49 tff(1465,plain,((~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.49 tff(1466,plain,
% 1.22/1.49 (~b(s(s(elem!1)), s(z))),
% 1.22/1.49 inference(unit_resolution,[status(thm)],[1465, 1283, 1391, 309, 107])).
% 1.22/1.49 tff(1467,plain,
% 1.22/1.49 (r(s(s(elem!1)), s(z))),
% 1.22/1.49 inference(unit_resolution,[status(thm)],[561, 1466])).
% 1.22/1.49 tff(1468,plain,
% 1.22/1.49 (~r(s(s(elem!1)), z)),
% 1.22/1.49 inference(unit_resolution,[status(thm)],[512, 37, 300, 1467, 506])).
% 1.22/1.49 tff(1469,plain,
% 1.22/1.49 (b(s(s(elem!1)), z)),
% 1.22/1.49 inference(unit_resolution,[status(thm)],[518, 58, 515, 1468])).
% 1.22/1.49 tff(1470,plain,
% 1.22/1.49 ($false),
% 1.22/1.49 inference(unit_resolution,[status(thm)],[546, 75, 370, 401, 1283, 1469])).
% 1.22/1.49 tff(1471,plain,((~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~r(z, elem!1)) | (~r(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.49 tff(1472,plain,
% 1.22/1.49 (~b(s(s(elem!1)), s(s(z)))),
% 1.22/1.49 inference(unit_resolution,[status(thm)],[1471, 1456, 300, 1452, 1450, 1391, 1430, 1428])).
% 1.22/1.49 tff(1473,assumption,(~r(s(s(elem!1)), s(s(z)))), introduced(assumption)).
% 1.22/1.49 tff(1474,assumption,(~b(s(s(elem!1)), s(s(z)))), introduced(assumption)).
% 1.22/1.49 tff(1475,plain,
% 1.22/1.49 ($false),
% 1.22/1.49 inference(unit_resolution,[status(thm)],[504, 58, 266, 1474, 1473])).
% 1.22/1.49 tff(1476,plain,(r(s(s(elem!1)), s(s(z))) | (s(s(elem!1)) = s(s(z))) | b(s(s(elem!1)), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.49 tff(1477,plain,
% 1.22/1.49 (r(s(s(elem!1)), s(s(z)))),
% 1.22/1.49 inference(unit_resolution,[status(thm)],[1476, 1472, 266])).
% 1.22/1.49 tff(1478,plain,
% 1.22/1.49 (~(elem!1 = s(s(z)))),
% 1.22/1.49 inference(modus_ponens,[status(thm)],[15, 308])).
% 1.22/1.49 tff(1479,plain,
% 1.22/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))),
% 1.22/1.49 inference(rewrite,[status(thm)],[])).
% 1.22/1.49 tff(1480,plain,
% 1.22/1.49 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))),
% 1.22/1.49 inference(rewrite,[status(thm)],[])).
% 1.22/1.49 tff(1481,plain,
% 1.22/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z))))))),
% 1.22/1.49 inference(monotonicity,[status(thm)],[1480])).
% 1.22/1.49 tff(1482,plain,
% 1.22/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))),
% 1.22/1.49 inference(transitivity,[status(thm)],[1481, 1479])).
% 1.22/1.49 tff(1483,plain,
% 1.22/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))),
% 1.22/1.49 inference(quant_inst,[status(thm)],[])).
% 1.22/1.49 tff(1484,plain,
% 1.22/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z))))),
% 1.22/1.49 inference(modus_ponens,[status(thm)],[1483, 1482])).
% 1.22/1.49 tff(1485,plain,
% 1.22/1.49 (~b(elem!1, s(s(z)))),
% 1.22/1.49 inference(unit_resolution,[status(thm)],[1484, 75, 1391, 1452, 1448])).
% 1.22/1.49 tff(1486,plain,
% 1.22/1.49 ((elem!1 = s(s(z))) | r(elem!1, s(s(z)))),
% 1.22/1.49 inference(unit_resolution,[status(thm)],[398, 58, 1485])).
% 1.22/1.49 tff(1487,plain,
% 1.22/1.49 (r(elem!1, s(s(z)))),
% 1.22/1.49 inference(unit_resolution,[status(thm)],[1486, 1478])).
% 1.22/1.49 tff(1488,assumption,(r(s(s(elem!1)), s(s(z)))), introduced(assumption)).
% 1.22/1.49 tff(1489,assumption,(r(elem!1, s(s(z)))), introduced(assumption)).
% 1.22/1.49 tff(1490,assumption,(r(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.22/1.49 tff(1491,plain,
% 1.22/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(z)))))),
% 1.22/1.49 inference(rewrite,[status(thm)],[])).
% 1.22/1.49 tff(1492,plain,
% 1.22/1.49 (((~r(s(s(elem!1)), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(s(z)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(z)))))),
% 1.22/1.49 inference(rewrite,[status(thm)],[])).
% 1.22/1.49 tff(1493,plain,
% 1.22/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(elem!1)), s(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(s(z)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(z))))))),
% 1.22/1.49 inference(monotonicity,[status(thm)],[1492])).
% 1.22/1.49 tff(1494,plain,
% 1.22/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(elem!1)), s(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(s(z)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(z)))))),
% 1.22/1.49 inference(transitivity,[status(thm)],[1493, 1491])).
% 1.22/1.49 tff(1495,plain,
% 1.22/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(elem!1, s(s(elem!1)))))),
% 1.22/1.49 inference(quant_inst,[status(thm)],[])).
% 1.22/1.49 tff(1496,plain,
% 1.22/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(z))))),
% 1.22/1.49 inference(modus_ponens,[status(thm)],[1495, 1494])).
% 1.22/1.49 tff(1497,plain,
% 1.22/1.49 ($false),
% 1.22/1.49 inference(unit_resolution,[status(thm)],[1496, 37, 1490, 1489, 1488])).
% 1.22/1.49 tff(1498,plain,((~r(s(s(elem!1)), s(s(z)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.49 tff(1499,plain,
% 1.22/1.49 (~r(elem!1, s(s(elem!1)))),
% 1.22/1.49 inference(unit_resolution,[status(thm)],[1498, 1487, 1477])).
% 1.22/1.49 tff(1500,plain,
% 1.22/1.49 ((z = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = z)),
% 1.22/1.49 inference(commutativity,[status(thm)],[])).
% 1.22/1.49 tff(1501,plain,
% 1.22/1.49 ((s(s(s(s(z)))) = z) <=> (z = s(s(s(s(z)))))),
% 1.22/1.49 inference(symmetry,[status(thm)],[1500])).
% 1.22/1.49 tff(1502,plain,
% 1.22/1.49 ((~(s(s(s(s(z)))) = z)) <=> (~(z = s(s(s(s(z))))))),
% 1.22/1.49 inference(monotonicity,[status(thm)],[1501])).
% 1.22/1.49 tff(1503,plain,
% 1.22/1.49 (~(z = s(s(s(s(z)))))),
% 1.22/1.49 inference(modus_ponens,[status(thm)],[1143, 1502])).
% 1.22/1.49 tff(1504,plain,
% 1.22/1.49 (~b(s(s(s(s(z)))), s(z))),
% 1.22/1.49 inference(unit_resolution,[status(thm)],[1402, 75, 1456, 1391, 287])).
% 1.22/1.49 tff(1505,plain,
% 1.22/1.49 (r(s(s(s(s(z)))), s(z))),
% 1.22/1.49 inference(unit_resolution,[status(thm)],[1406, 58, 1504, 483])).
% 1.22/1.49 tff(1506,plain,
% 1.22/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 1.22/1.49 inference(rewrite,[status(thm)],[])).
% 1.22/1.49 tff(1507,plain,
% 1.22/1.49 (((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 1.22/1.49 inference(rewrite,[status(thm)],[])).
% 1.22/1.49 tff(1508,plain,
% 1.22/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z))))))))),
% 1.22/1.49 inference(monotonicity,[status(thm)],[1507])).
% 1.22/1.49 tff(1509,plain,
% 1.22/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 1.22/1.49 inference(transitivity,[status(thm)],[1508, 1506])).
% 1.22/1.49 tff(1510,plain,
% 1.22/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 1.22/1.49 inference(quant_inst,[status(thm)],[])).
% 1.22/1.49 tff(1511,plain,
% 1.22/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z))))))),
% 1.22/1.49 inference(modus_ponens,[status(thm)],[1510, 1509])).
% 1.22/1.50 tff(1512,plain,
% 1.22/1.50 (~r(z, s(s(s(s(z)))))),
% 1.22/1.50 inference(unit_resolution,[status(thm)],[1511, 37, 1450, 1505])).
% 1.22/1.50 tff(1513,plain,
% 1.22/1.50 (((~![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))))))),
% 1.22/1.50 inference(rewrite,[status(thm)],[])).
% 1.22/1.50 tff(1514,plain,
% 1.22/1.50 ((~![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))))))),
% 1.22/1.50 inference(quant_inst,[status(thm)],[])).
% 1.22/1.50 tff(1515,plain,
% 1.22/1.50 ((~![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)))))),
% 1.22/1.50 inference(modus_ponens,[status(thm)],[1514, 1513])).
% 1.22/1.50 tff(1516,plain,
% 1.22/1.50 ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z)))))),
% 1.22/1.50 inference(unit_resolution,[status(thm)],[1515, 58, 1512])).
% 1.22/1.50 tff(1517,plain,
% 1.22/1.50 (b(z, s(s(s(s(z)))))),
% 1.22/1.50 inference(unit_resolution,[status(thm)],[1516, 1503])).
% 1.22/1.50 tff(1518,assumption,(b(z, elem!1)), introduced(assumption)).
% 1.22/1.50 tff(1519,plain,
% 1.22/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)))),
% 1.22/1.50 inference(rewrite,[status(thm)],[])).
% 1.22/1.50 tff(1520,plain,
% 1.22/1.50 (((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)))),
% 1.22/1.50 inference(rewrite,[status(thm)],[])).
% 1.22/1.50 tff(1521,plain,
% 1.22/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1))))),
% 1.22/1.50 inference(monotonicity,[status(thm)],[1520])).
% 1.22/1.50 tff(1522,plain,
% 1.22/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)))),
% 1.22/1.50 inference(transitivity,[status(thm)],[1521, 1519])).
% 1.22/1.50 tff(1523,plain,
% 1.22/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 1.22/1.50 inference(quant_inst,[status(thm)],[])).
% 1.22/1.50 tff(1524,plain,
% 1.22/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1))),
% 1.22/1.50 inference(modus_ponens,[status(thm)],[1523, 1522])).
% 1.22/1.50 tff(1525,plain,
% 1.22/1.50 ($false),
% 1.22/1.50 inference(unit_resolution,[status(thm)],[1524, 75, 1518, 107, 371, 1391])).
% 1.22/1.50 tff(1526,plain,((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.22/1.50 tff(1527,plain,
% 1.22/1.50 (~b(z, elem!1)),
% 1.22/1.50 inference(unit_resolution,[status(thm)],[1526, 371, 107, 1391])).
% 1.32/1.50 tff(1528,plain,
% 1.32/1.50 (r(z, elem!1)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[298, 1527, 235])).
% 1.32/1.50 tff(1529,plain,
% 1.32/1.50 (~r(s(s(z)), z)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[328, 1528, 106])).
% 1.32/1.50 tff(1530,plain,
% 1.32/1.50 (b(s(s(z)), z)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[202, 1529])).
% 1.32/1.50 tff(1531,plain,
% 1.32/1.50 (~r(z, s(s(z)))),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[339, 1528, 106])).
% 1.32/1.50 tff(1532,plain,
% 1.32/1.50 (b(z, s(s(z)))),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[351, 1531])).
% 1.32/1.50 tff(1533,plain,
% 1.32/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(1534,plain,
% 1.32/1.50 (((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(1535,plain,
% 1.32/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))))),
% 1.32/1.50 inference(monotonicity,[status(thm)],[1534])).
% 1.32/1.50 tff(1536,plain,
% 1.32/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.32/1.50 inference(transitivity,[status(thm)],[1535, 1533])).
% 1.32/1.50 tff(1537,plain,
% 1.32/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.32/1.50 inference(quant_inst,[status(thm)],[])).
% 1.32/1.50 tff(1538,plain,
% 1.32/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[1537, 1536])).
% 1.32/1.50 tff(1539,plain,
% 1.32/1.50 ($false),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[1538, 75, 371, 309, 1532, 1530])).
% 1.32/1.50 tff(1540,plain,((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)) | (z = elem!1) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.50 tff(1541,plain,
% 1.32/1.50 (~b(s(z), z)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[1540, 1456, 294, 1452, 889, 1391])).
% 1.32/1.50 tff(1542,plain,
% 1.32/1.50 (r(s(z), z)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[169, 1541])).
% 1.32/1.50 tff(1543,plain,
% 1.32/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(1544,plain,
% 1.32/1.50 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(1545,plain,
% 1.32/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.32/1.50 inference(monotonicity,[status(thm)],[1544])).
% 1.32/1.50 tff(1546,plain,
% 1.32/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.32/1.50 inference(transitivity,[status(thm)],[1545, 1543])).
% 1.32/1.50 tff(1547,plain,
% 1.32/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.32/1.50 inference(quant_inst,[status(thm)],[])).
% 1.32/1.50 tff(1548,plain,
% 1.32/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[1547, 1546])).
% 1.32/1.50 tff(1549,plain,
% 1.32/1.50 (~r(s(s(z)), s(s(s(z))))),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[1548, 37, 1308, 467])).
% 1.32/1.50 tff(1550,assumption,(s(s(z)) = s(s(s(z)))), introduced(assumption)).
% 1.32/1.50 tff(1551,plain,
% 1.32/1.50 (inj_0(s(s(z))) = inj_0(s(s(s(z))))),
% 1.32/1.50 inference(monotonicity,[status(thm)],[1550])).
% 1.32/1.50 tff(1552,plain,
% 1.32/1.50 (inj_0(s(s(s(z)))) = inj_0(s(s(z)))),
% 1.32/1.50 inference(symmetry,[status(thm)],[1551])).
% 1.32/1.50 tff(1553,plain,
% 1.32/1.50 (s(s(s(z))) = s(s(z))),
% 1.32/1.50 inference(symmetry,[status(thm)],[1550])).
% 1.32/1.50 tff(1554,plain,
% 1.32/1.50 (s(s(s(z))) = s(z)),
% 1.32/1.50 inference(transitivity,[status(thm)],[1553, 254, 1552, 133])).
% 1.32/1.50 tff(1555,plain,
% 1.32/1.50 ($false),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[457, 1554])).
% 1.32/1.50 tff(1556,plain,(~(s(s(z)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.50 tff(1557,plain,
% 1.32/1.50 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z)))))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(1558,plain,
% 1.32/1.50 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z)))))),
% 1.32/1.50 inference(quant_inst,[status(thm)],[])).
% 1.32/1.50 tff(1559,plain,
% 1.32/1.50 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[1558, 1557])).
% 1.32/1.50 tff(1560,plain,
% 1.32/1.50 (b(s(s(z)), s(s(s(z))))),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[1559, 58, 1556, 1549])).
% 1.32/1.50 tff(1561,assumption,(r(s(z), z)), introduced(assumption)).
% 1.32/1.50 tff(1562,plain,
% 1.32/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(1563,plain,
% 1.32/1.50 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(1564,plain,
% 1.32/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.32/1.50 inference(monotonicity,[status(thm)],[1563])).
% 1.32/1.50 tff(1565,plain,
% 1.32/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.32/1.50 inference(transitivity,[status(thm)],[1564, 1562])).
% 1.32/1.50 tff(1566,plain,
% 1.32/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))),
% 1.32/1.50 inference(quant_inst,[status(thm)],[])).
% 1.32/1.50 tff(1567,plain,
% 1.32/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[1566, 1565])).
% 1.32/1.50 tff(1568,plain,
% 1.32/1.50 (~r(s(s(s(z))), s(z))),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[1567, 37, 1561, 468, 1308])).
% 1.32/1.50 tff(1569,plain,
% 1.32/1.50 (b(s(s(s(z))), s(z))),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[1081, 1568])).
% 1.32/1.50 tff(1570,plain,
% 1.32/1.50 (~r(s(s(z)), s(z))),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[476, 467, 468])).
% 1.32/1.50 tff(1571,plain,
% 1.32/1.50 (b(s(s(z)), s(z))),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[153, 1570])).
% 1.32/1.50 tff(1572,plain,
% 1.32/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(1573,plain,
% 1.32/1.50 (((~b(elem!1, s(z))) | (~b(s(s(s(z))), 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(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(1574,plain,
% 1.32/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z)))))))),
% 1.32/1.50 inference(monotonicity,[status(thm)],[1573])).
% 1.32/1.50 tff(1575,plain,
% 1.32/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.32/1.50 inference(transitivity,[status(thm)],[1574, 1572])).
% 1.32/1.50 tff(1576,plain,
% 1.32/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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))))))),
% 1.32/1.50 inference(quant_inst,[status(thm)],[])).
% 1.32/1.50 tff(1577,plain,
% 1.32/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z)))))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[1576, 1575])).
% 1.32/1.50 tff(1578,plain,
% 1.32/1.50 ($false),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[1577, 75, 107, 1391, 1571, 1569, 1560])).
% 1.32/1.50 tff(1579,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.50 tff(1580,plain,
% 1.32/1.50 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[1579, 1456, 1391, 1542, 1440, 467])).
% 1.32/1.50 tff(1581,plain,
% 1.32/1.50 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[575, 1580])).
% 1.32/1.50 tff(1582,assumption,(b(z, s(s(s(s(z)))))), introduced(assumption)).
% 1.32/1.50 tff(1583,plain,
% 1.32/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(1584,plain,
% 1.32/1.50 (((~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(1585,plain,
% 1.32/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 1.32/1.50 inference(monotonicity,[status(thm)],[1584])).
% 1.32/1.50 tff(1586,plain,
% 1.32/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.32/1.51 inference(transitivity,[status(thm)],[1585, 1583])).
% 1.32/1.51 tff(1587,plain,
% 1.32/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 1.32/1.51 inference(quant_inst,[status(thm)],[])).
% 1.32/1.51 tff(1588,plain,
% 1.32/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[1587, 1586])).
% 1.32/1.51 tff(1589,plain,
% 1.32/1.51 (~b(s(s(s(z))), z)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1588, 75, 286, 983, 287, 1582])).
% 1.32/1.51 tff(1590,plain,
% 1.32/1.51 (r(s(s(s(z))), z)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1334, 58, 221, 1589])).
% 1.32/1.51 tff(1591,plain,
% 1.32/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(1592,plain,
% 1.32/1.51 (((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(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(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(1593,plain,
% 1.32/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.32/1.51 inference(monotonicity,[status(thm)],[1592])).
% 1.32/1.51 tff(1594,plain,
% 1.32/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.32/1.51 inference(transitivity,[status(thm)],[1593, 1591])).
% 1.32/1.51 tff(1595,plain,
% 1.32/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))),
% 1.32/1.51 inference(quant_inst,[status(thm)],[])).
% 1.32/1.51 tff(1596,plain,
% 1.32/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[1595, 1594])).
% 1.32/1.51 tff(1597,plain,
% 1.32/1.51 (~b(s(s(s(z))), elem!1)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1596, 75, 286, 983, 287])).
% 1.32/1.51 tff(1598,plain,
% 1.32/1.51 (r(s(s(s(z))), elem!1)),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1115, 1597, 1031])).
% 1.32/1.51 tff(1599,plain,
% 1.32/1.51 ($false),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1330, 37, 300, 1598, 1590])).
% 1.32/1.51 tff(1600,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, elem!1)) | (s(s(s(z))) = elem!1) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.51 tff(1601,plain,
% 1.32/1.51 (s(s(s(z))) = elem!1),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1600, 1581, 300, 286, 287, 1517])).
% 1.32/1.51 tff(1602,assumption,(elem!1 = s(s(elem!1))), introduced(assumption)).
% 1.32/1.51 tff(1603,plain,
% 1.32/1.51 (s(elem!1) = s(s(s(elem!1)))),
% 1.32/1.51 inference(monotonicity,[status(thm)],[1602])).
% 1.32/1.51 tff(1604,plain,
% 1.32/1.51 (s(s(s(z))) = s(s(elem!1))),
% 1.32/1.51 inference(transitivity,[status(thm)],[213, 1602])).
% 1.32/1.51 tff(1605,plain,
% 1.32/1.51 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 1.32/1.51 inference(monotonicity,[status(thm)],[1604])).
% 1.32/1.51 tff(1606,plain,
% 1.32/1.51 (s(s(z)) = s(s(s(elem!1)))),
% 1.32/1.51 inference(transitivity,[status(thm)],[254, 1605, 228, 1603])).
% 1.32/1.51 tff(1607,plain,
% 1.32/1.51 (inj_0(s(s(z))) = inj_0(s(s(s(elem!1))))),
% 1.32/1.51 inference(monotonicity,[status(thm)],[1606])).
% 1.32/1.51 tff(1608,plain,
% 1.32/1.51 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(z)))),
% 1.32/1.51 inference(symmetry,[status(thm)],[1607])).
% 1.32/1.51 tff(1609,plain,
% 1.32/1.51 (s(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 1.32/1.51 inference(symmetry,[status(thm)],[11])).
% 1.32/1.51 tff(1610,plain,
% 1.32/1.51 (s(s(elem!1)) = s(z)),
% 1.32/1.51 inference(transitivity,[status(thm)],[1609, 1608, 133])).
% 1.32/1.51 tff(1611,plain,
% 1.32/1.51 ($false),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[556, 1610])).
% 1.32/1.51 tff(1612,plain,((~(elem!1 = s(s(elem!1)))) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.51 tff(1613,plain,
% 1.32/1.51 (~(elem!1 = s(s(elem!1)))),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1612, 1601])).
% 1.32/1.51 tff(1614,plain,
% 1.32/1.51 (((~![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))))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(1615,plain,
% 1.32/1.51 ((~![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))))),
% 1.32/1.51 inference(quant_inst,[status(thm)],[])).
% 1.32/1.51 tff(1616,plain,
% 1.32/1.51 ((~![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)))),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[1615, 1614])).
% 1.32/1.51 tff(1617,plain,
% 1.32/1.51 ((elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1)))),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1616, 58])).
% 1.32/1.51 tff(1618,plain,
% 1.32/1.51 (b(elem!1, s(s(elem!1)))),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1617, 1613, 1499])).
% 1.32/1.51 tff(1619,assumption,(b(s(s(elem!1)), s(s(s(s(z)))))), introduced(assumption)).
% 1.32/1.51 tff(1620,assumption,(b(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.32/1.51 tff(1621,plain,
% 1.32/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(1622,plain,
% 1.32/1.51 (((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(1623,plain,
% 1.32/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.32/1.51 inference(monotonicity,[status(thm)],[1622])).
% 1.32/1.51 tff(1624,plain,
% 1.32/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.32/1.51 inference(transitivity,[status(thm)],[1623, 1621])).
% 1.32/1.51 tff(1625,plain,
% 1.32/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(elem!1)))))),
% 1.32/1.51 inference(quant_inst,[status(thm)],[])).
% 1.32/1.51 tff(1626,plain,
% 1.32/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[1625, 1624])).
% 1.32/1.51 tff(1627,plain,
% 1.32/1.51 ($false),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1626, 75, 1620, 286, 1619, 287])).
% 1.32/1.51 tff(1628,plain,((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.51 tff(1629,plain,
% 1.32/1.51 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1628, 1618, 286, 287])).
% 1.32/1.51 tff(1630,assumption,(~(elem!1 = s(s(elem!1)))), introduced(assumption)).
% 1.32/1.51 tff(1631,plain,
% 1.32/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(1632,plain,
% 1.32/1.51 (((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~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(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(1633,plain,
% 1.32/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))) | (~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(X1, 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(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))))),
% 1.32/1.51 inference(monotonicity,[status(thm)],[1632])).
% 1.32/1.51 tff(1634,plain,
% 1.32/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))) | (~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(X1, 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(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.32/1.51 inference(transitivity,[status(thm)],[1633, 1631])).
% 1.32/1.51 tff(1635,plain,
% 1.32/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))))),
% 1.32/1.51 inference(quant_inst,[status(thm)],[])).
% 1.32/1.51 tff(1636,plain,
% 1.32/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[1635, 1634])).
% 1.32/1.51 tff(1637,plain,
% 1.32/1.51 ($false),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1636, 75, 1457, 107, 1620, 1391])).
% 1.32/1.51 tff(1638,plain,((~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.51 tff(1639,plain,
% 1.32/1.51 (~b(elem!1, s(s(elem!1)))),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1638, 1457, 107, 1391])).
% 1.32/1.51 tff(1640,plain,
% 1.32/1.51 (r(elem!1, s(s(elem!1)))),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1617, 1639, 1630])).
% 1.32/1.51 tff(1641,plain,
% 1.32/1.51 (~b(s(s(elem!1)), s(s(z)))),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1465, 1457, 1391, 309, 107])).
% 1.32/1.51 tff(1642,plain,
% 1.32/1.51 (r(s(s(elem!1)), s(s(z)))),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1476, 1641, 266])).
% 1.32/1.51 tff(1643,plain,
% 1.32/1.51 ($false),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1498, 1642, 1640, 1489])).
% 1.32/1.51 tff(1644,plain,((~b(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(z)))) | (s(s(elem!1)) = s(s(z))) | (elem!1 = s(s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.51 tff(1645,plain,
% 1.32/1.51 (~b(s(s(elem!1)), s(z))),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1644, 1613, 1391, 1452, 266, 1487, 1456])).
% 1.32/1.51 tff(1646,plain,
% 1.32/1.51 (r(s(s(elem!1)), s(z))),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[561, 1645])).
% 1.32/1.51 tff(1647,assumption,(r(s(s(elem!1)), s(s(s(s(z)))))), introduced(assumption)).
% 1.32/1.51 tff(1648,plain,
% 1.32/1.51 (((~![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(elem!1)), 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(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(1649,plain,
% 1.32/1.51 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(1650,plain,
% 1.32/1.51 (((~![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(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))))),
% 1.32/1.51 inference(monotonicity,[status(thm)],[1649])).
% 1.32/1.51 tff(1651,plain,
% 1.32/1.51 (((~![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(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.32/1.51 inference(transitivity,[status(thm)],[1650, 1648])).
% 1.32/1.51 tff(1652,plain,
% 1.32/1.51 ((~![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(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(z))))),
% 1.32/1.51 inference(quant_inst,[status(thm)],[])).
% 1.32/1.51 tff(1653,plain,
% 1.32/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[1652, 1651])).
% 1.32/1.51 tff(1654,plain,
% 1.32/1.51 ($false),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1653, 37, 494, 468, 1647])).
% 1.32/1.51 tff(1655,plain,((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.51 tff(1656,plain,
% 1.32/1.51 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1655, 1646, 1440])).
% 1.32/1.51 tff(1657,plain,
% 1.32/1.51 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(z))))) | b(s(s(elem!1)), s(s(s(s(z))))) | r(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(z))))) | b(s(s(elem!1)), s(s(s(s(z))))) | r(s(s(elem!1)), s(s(s(s(z))))))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(1658,plain,
% 1.32/1.51 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(z))))) | b(s(s(elem!1)), s(s(s(s(z))))) | r(s(s(elem!1)), s(s(s(s(z))))))),
% 1.32/1.51 inference(quant_inst,[status(thm)],[])).
% 1.32/1.51 tff(1659,plain,
% 1.32/1.51 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(z))))) | b(s(s(elem!1)), s(s(s(s(z))))) | r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[1658, 1657])).
% 1.32/1.51 tff(1660,plain,
% 1.32/1.51 ((s(s(elem!1)) = s(s(s(s(z))))) | b(s(s(elem!1)), s(s(s(s(z))))) | r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[1659, 58])).
% 1.32/1.51 tff(1661,plain,
% 1.32/1.51 ($false),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[1660, 1656, 1629, 1426])).
% 1.32/1.52 tff(1662,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (s(s(elem!1)) = s(s(z))) | (~r(z, elem!1)) | (s(s(z)) = elem!1) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.32/1.52 tff(1663,plain,
% 1.32/1.52 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[1662, 15, 287, 1391, 266, 300, 286, 99])).
% 1.32/1.52 tff(1664,plain,
% 1.32/1.52 (b(s(s(z)), s(s(s(s(z)))))),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[465, 1663])).
% 1.32/1.52 tff(1665,plain,
% 1.32/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.32/1.52 inference(rewrite,[status(thm)],[])).
% 1.32/1.52 tff(1666,plain,
% 1.32/1.52 (((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.32/1.52 inference(rewrite,[status(thm)],[])).
% 1.32/1.52 tff(1667,plain,
% 1.32/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))))),
% 1.32/1.52 inference(monotonicity,[status(thm)],[1666])).
% 1.32/1.52 tff(1668,plain,
% 1.32/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.32/1.52 inference(transitivity,[status(thm)],[1667, 1665])).
% 1.32/1.52 tff(1669,plain,
% 1.32/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))))))),
% 1.32/1.52 inference(quant_inst,[status(thm)],[])).
% 1.32/1.52 tff(1670,plain,
% 1.32/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 1.32/1.52 inference(modus_ponens,[status(thm)],[1669, 1668])).
% 1.32/1.52 tff(1671,plain,
% 1.32/1.52 ($false),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[1670, 75, 1428, 1430, 1664, 1423])).
% 1.32/1.52 tff(1672,plain,((s(s(z)) = elem!1) | (~b(s(s(s(s(z)))), z)) | (~r(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (s(s(elem!1)) = s(s(z))) | (~b(elem!1, s(s(s(s(z)))))) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.32/1.52 tff(1673,plain,
% 1.32/1.52 (s(s(z)) = elem!1),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[1672, 1422, 300, 287, 1377, 266, 286, 99])).
% 1.32/1.52 tff(1674,plain,
% 1.32/1.52 ((s(s(s(s(s(s(s(z))))))) = s(s(z))) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.32/1.52 inference(monotonicity,[status(thm)],[1673])).
% 1.32/1.52 tff(1675,plain,
% 1.32/1.52 ((~(s(s(s(s(s(s(s(z))))))) = s(s(z)))) <=> (~(s(s(s(s(s(s(s(z))))))) = elem!1))),
% 1.32/1.52 inference(monotonicity,[status(thm)],[1674])).
% 1.32/1.52 tff(1676,plain,
% 1.32/1.52 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.32/1.52 inference(modus_ponens,[status(thm)],[1045, 1675])).
% 1.32/1.52 tff(1677,plain,
% 1.32/1.52 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[1145, 1673])).
% 1.32/1.52 tff(1678,plain,
% 1.32/1.52 (s(s(s(z))) = s(elem!1)),
% 1.32/1.52 inference(monotonicity,[status(thm)],[1673])).
% 1.32/1.52 tff(1679,plain,
% 1.32/1.52 (s(elem!1) = s(s(s(z)))),
% 1.32/1.52 inference(symmetry,[status(thm)],[1678])).
% 1.32/1.52 tff(1680,plain,
% 1.32/1.52 (r(s(elem!1), elem!1) <=> r(s(s(s(z))), elem!1)),
% 1.32/1.52 inference(monotonicity,[status(thm)],[1679])).
% 1.32/1.52 tff(1681,plain,
% 1.32/1.52 (r(s(s(s(z))), elem!1) <=> r(s(elem!1), elem!1)),
% 1.32/1.52 inference(symmetry,[status(thm)],[1680])).
% 1.32/1.52 tff(1682,plain,
% 1.32/1.52 (b(s(s(z)), s(z)) <=> b(elem!1, s(z))),
% 1.32/1.52 inference(monotonicity,[status(thm)],[1673])).
% 1.32/1.52 tff(1683,plain,
% 1.32/1.52 (b(elem!1, s(z)) <=> b(s(s(z)), s(z))),
% 1.32/1.52 inference(symmetry,[status(thm)],[1682])).
% 1.32/1.52 tff(1684,plain,
% 1.32/1.52 (b(s(s(z)), s(z))),
% 1.32/1.52 inference(modus_ponens,[status(thm)],[1377, 1683])).
% 1.32/1.52 tff(1685,plain,
% 1.32/1.52 (~b(s(z), s(s(s(s(z)))))),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[1438, 1377, 286, 287])).
% 1.32/1.52 tff(1686,plain,
% 1.32/1.52 (r(s(z), s(s(s(s(z)))))),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[489, 1685])).
% 1.32/1.52 tff(1687,plain,
% 1.32/1.52 (~r(z, s(s(s(s(z)))))),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[1511, 37, 506, 1407])).
% 1.32/1.52 tff(1688,plain,
% 1.32/1.52 ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z)))))),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[1515, 58, 1687])).
% 1.32/1.52 tff(1689,plain,
% 1.32/1.52 (b(z, s(s(s(s(z)))))),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[1688, 1503])).
% 1.32/1.52 tff(1690,plain,
% 1.32/1.52 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[1013, 1673])).
% 1.32/1.52 tff(1691,plain,
% 1.32/1.52 (~(s(s(s(z))) = elem!1)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[1026, 1690, 274])).
% 1.32/1.52 tff(1692,plain,
% 1.32/1.52 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[1600, 1691, 300, 286, 287, 1689])).
% 1.32/1.52 tff(1693,plain,
% 1.32/1.52 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[575, 1692])).
% 1.32/1.52 tff(1694,plain,
% 1.32/1.52 (~r(s(z), s(s(s(z))))),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[1316, 1693, 1686])).
% 1.32/1.52 tff(1695,plain,
% 1.32/1.52 (b(s(z), s(s(s(z))))),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[1263, 1694])).
% 1.32/1.52 tff(1696,plain,
% 1.32/1.52 (~r(elem!1, s(z))),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[367, 506, 300])).
% 1.32/1.52 tff(1697,plain,
% 1.32/1.52 (r(s(elem!1), s(z)) <=> r(s(s(s(z))), s(z))),
% 1.32/1.52 inference(monotonicity,[status(thm)],[1679])).
% 1.32/1.52 tff(1698,plain,
% 1.32/1.52 ((~r(s(elem!1), s(z))) <=> (~r(s(s(s(z))), s(z)))),
% 1.32/1.52 inference(monotonicity,[status(thm)],[1697])).
% 1.32/1.52 tff(1699,plain,
% 1.32/1.52 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 1.32/1.52 inference(monotonicity,[status(thm)],[1678])).
% 1.32/1.52 tff(1700,plain,
% 1.32/1.52 (r(s(elem!1), s(s(s(s(z)))))),
% 1.32/1.52 inference(modus_ponens,[status(thm)],[1693, 1699])).
% 1.32/1.52 tff(1701,plain,
% 1.32/1.52 (((~![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(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)))))))),
% 1.32/1.52 inference(rewrite,[status(thm)],[])).
% 1.32/1.52 tff(1702,plain,
% 1.32/1.52 (((~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)))))))),
% 1.32/1.52 inference(rewrite,[status(thm)],[])).
% 1.32/1.52 tff(1703,plain,
% 1.32/1.52 (((~![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(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))))))))),
% 1.32/1.52 inference(monotonicity,[status(thm)],[1702])).
% 1.32/1.52 tff(1704,plain,
% 1.32/1.52 (((~![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(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)))))))),
% 1.32/1.52 inference(transitivity,[status(thm)],[1703, 1701])).
% 1.32/1.52 tff(1705,plain,
% 1.32/1.52 ((~![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(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))))),
% 1.32/1.52 inference(quant_inst,[status(thm)],[])).
% 1.32/1.52 tff(1706,plain,
% 1.32/1.52 ((~![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(s(z)))))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(s(z))))))),
% 1.32/1.52 inference(modus_ponens,[status(thm)],[1705, 1704])).
% 1.32/1.52 tff(1707,plain,
% 1.32/1.52 (~r(s(elem!1), s(z))),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[1706, 37, 1686, 1700])).
% 1.32/1.52 tff(1708,plain,
% 1.32/1.52 (~r(s(s(s(z))), s(z))),
% 1.32/1.52 inference(modus_ponens,[status(thm)],[1707, 1698])).
% 1.32/1.52 tff(1709,plain,
% 1.32/1.52 (b(s(s(s(z))), s(z))),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[1081, 1708])).
% 1.32/1.52 tff(1710,assumption,(~r(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.32/1.52 tff(1711,assumption,(~r(elem!1, s(z))), introduced(assumption)).
% 1.32/1.52 tff(1712,plain,
% 1.32/1.52 (b(elem!1, s(z))),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[89, 359, 1711])).
% 1.32/1.52 tff(1713,plain,
% 1.32/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))))),
% 1.32/1.52 inference(rewrite,[status(thm)],[])).
% 1.32/1.52 tff(1714,plain,
% 1.32/1.52 (((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))))),
% 1.32/1.52 inference(rewrite,[status(thm)],[])).
% 1.32/1.52 tff(1715,plain,
% 1.32/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z)))))),
% 1.32/1.52 inference(monotonicity,[status(thm)],[1714])).
% 1.32/1.52 tff(1716,plain,
% 1.32/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))))),
% 1.32/1.52 inference(transitivity,[status(thm)],[1715, 1713])).
% 1.32/1.52 tff(1717,plain,
% 1.32/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.32/1.52 inference(quant_inst,[status(thm)],[])).
% 1.32/1.52 tff(1718,plain,
% 1.32/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z)))),
% 1.32/1.52 inference(modus_ponens,[status(thm)],[1717, 1716])).
% 1.32/1.52 tff(1719,plain,
% 1.32/1.52 (~b(s(s(s(z))), elem!1)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[1718, 75, 1712, 984, 1053])).
% 1.32/1.52 tff(1720,plain,
% 1.32/1.52 (s(s(s(z))) = elem!1),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[1115, 1719, 1710])).
% 1.32/1.52 tff(1721,plain,
% 1.32/1.52 (r(s(z), s(elem!1)) <=> r(s(z), s(s(s(s(z)))))),
% 1.32/1.52 inference(monotonicity,[status(thm)],[1019])).
% 1.32/1.52 tff(1722,plain,
% 1.32/1.52 (r(s(z), s(s(s(s(z))))) <=> r(s(z), s(elem!1))),
% 1.32/1.52 inference(symmetry,[status(thm)],[1721])).
% 1.32/1.52 tff(1723,plain,
% 1.32/1.52 (r(s(z), s(elem!1))),
% 1.32/1.52 inference(modus_ponens,[status(thm)],[468, 1722])).
% 1.32/1.52 tff(1724,assumption,(~r(s(z), s(elem!1))), introduced(assumption)).
% 1.32/1.52 tff(1725,plain,
% 1.32/1.52 ($false),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[1724, 1723])).
% 1.32/1.52 tff(1726,plain,(r(s(z), s(elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.52 tff(1727,plain,
% 1.32/1.52 (r(s(z), s(elem!1))),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[1726, 1720, 468])).
% 1.32/1.52 tff(1728,plain,
% 1.32/1.52 (b(s(z), s(s(s(z)))) <=> b(s(z), elem!1)),
% 1.32/1.52 inference(monotonicity,[status(thm)],[1720])).
% 1.32/1.52 tff(1729,plain,
% 1.32/1.52 (b(s(z), elem!1)),
% 1.32/1.52 inference(modus_ponens,[status(thm)],[1053, 1728])).
% 1.32/1.52 tff(1730,plain,
% 1.32/1.52 ((s(s(s(z))) = z) <=> (elem!1 = z)),
% 1.32/1.52 inference(monotonicity,[status(thm)],[1720])).
% 1.32/1.52 tff(1731,plain,
% 1.32/1.52 ((s(s(s(z))) = z) <=> (z = elem!1)),
% 1.32/1.52 inference(transitivity,[status(thm)],[1730, 216])).
% 1.32/1.52 tff(1732,plain,
% 1.32/1.52 ((~(s(s(s(z))) = z)) <=> (~(z = elem!1))),
% 1.32/1.52 inference(monotonicity,[status(thm)],[1731])).
% 1.32/1.52 tff(1733,plain,
% 1.32/1.52 (~(z = elem!1)),
% 1.32/1.52 inference(modus_ponens,[status(thm)],[221, 1732])).
% 1.32/1.52 tff(1734,plain,
% 1.32/1.52 (r(s(s(z)), s(s(s(z)))) <=> r(s(s(z)), elem!1)),
% 1.32/1.52 inference(monotonicity,[status(thm)],[1720])).
% 1.32/1.52 tff(1735,plain,
% 1.32/1.52 (~(s(z) = elem!1)),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[97, 359])).
% 1.32/1.52 tff(1736,plain,
% 1.32/1.52 (s(z) = elem!1),
% 1.32/1.52 inference(transitivity,[status(thm)],[134, 1551, 253, 1550, 213])).
% 1.32/1.52 tff(1737,plain,
% 1.32/1.52 ($false),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[108, 1736])).
% 1.32/1.52 tff(1738,plain,((~(s(s(z)) = s(s(s(z))))) | (s(z) = elem!1) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.52 tff(1739,plain,
% 1.32/1.52 (~(s(s(z)) = s(s(s(z))))),
% 1.32/1.52 inference(unit_resolution,[status(thm)],[1738, 1735, 1720])).
% 1.32/1.52 tff(1740,plain,
% 1.32/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.32/1.52 inference(rewrite,[status(thm)],[])).
% 1.32/1.52 tff(1741,plain,
% 1.32/1.52 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.32/1.52 inference(rewrite,[status(thm)],[])).
% 1.32/1.52 tff(1742,plain,
% 1.32/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z)))))))),
% 1.32/1.52 inference(monotonicity,[status(thm)],[1741])).
% 1.32/1.52 tff(1743,plain,
% 1.32/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.32/1.52 inference(transitivity,[status(thm)],[1742, 1740])).
% 1.32/1.52 tff(1744,plain,
% 1.32/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.32/1.53 inference(quant_inst,[status(thm)],[])).
% 1.32/1.53 tff(1745,plain,
% 1.32/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z)))))),
% 1.32/1.53 inference(modus_ponens,[status(thm)],[1744, 1743])).
% 1.32/1.53 tff(1746,plain,
% 1.32/1.53 (~b(s(s(z)), s(s(s(z))))),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[1745, 75, 309, 984, 1053])).
% 1.32/1.53 tff(1747,plain,
% 1.32/1.53 ((s(s(z)) = s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[1559, 58, 1746])).
% 1.32/1.53 tff(1748,plain,
% 1.32/1.53 (r(s(s(z)), s(s(s(z))))),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[1747, 1739])).
% 1.32/1.53 tff(1749,plain,
% 1.32/1.53 (r(s(s(z)), elem!1)),
% 1.32/1.53 inference(modus_ponens,[status(thm)],[1748, 1734])).
% 1.32/1.53 tff(1750,plain,
% 1.32/1.53 (~b(s(z), z)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[1540, 309, 1749, 1733, 1729, 1712])).
% 1.32/1.53 tff(1751,plain,
% 1.32/1.53 (r(s(z), z)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[169, 1750])).
% 1.32/1.53 tff(1752,assumption,(r(s(elem!1), z)), introduced(assumption)).
% 1.32/1.53 tff(1753,assumption,(r(s(z), s(elem!1))), introduced(assumption)).
% 1.32/1.53 tff(1754,plain,
% 1.32/1.53 (((~![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(elem!1), z)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))))),
% 1.32/1.53 inference(rewrite,[status(thm)],[])).
% 1.32/1.53 tff(1755,plain,
% 1.32/1.53 (((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1)))) <=> ((~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))))),
% 1.32/1.53 inference(rewrite,[status(thm)],[])).
% 1.32/1.53 tff(1756,plain,
% 1.32/1.53 (((~![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(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1)))))),
% 1.32/1.53 inference(monotonicity,[status(thm)],[1755])).
% 1.32/1.53 tff(1757,plain,
% 1.32/1.53 (((~![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(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))))),
% 1.32/1.53 inference(transitivity,[status(thm)],[1756, 1754])).
% 1.32/1.53 tff(1758,plain,
% 1.32/1.53 ((~![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(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))))),
% 1.32/1.53 inference(quant_inst,[status(thm)],[])).
% 1.32/1.53 tff(1759,plain,
% 1.32/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1)))),
% 1.32/1.53 inference(modus_ponens,[status(thm)],[1758, 1757])).
% 1.32/1.53 tff(1760,plain,
% 1.32/1.53 ($false),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[1759, 37, 1561, 1753, 1752])).
% 1.32/1.53 tff(1761,plain,((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.53 tff(1762,plain,
% 1.32/1.53 (~r(s(elem!1), z)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[1761, 1751, 1727])).
% 1.32/1.53 tff(1763,plain,
% 1.32/1.53 (b(s(elem!1), z)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[766, 1762])).
% 1.32/1.53 tff(1764,plain,
% 1.32/1.53 ((~(s(s(s(s(z)))) = elem!1)) <=> (~(elem!1 = s(s(s(s(z))))))),
% 1.32/1.53 inference(monotonicity,[status(thm)],[239])).
% 1.32/1.53 tff(1765,plain,
% 1.32/1.53 (~(elem!1 = s(s(s(s(z)))))),
% 1.32/1.53 inference(modus_ponens,[status(thm)],[267, 1764])).
% 1.32/1.53 tff(1766,plain,
% 1.32/1.53 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[1026, 1720, 1765])).
% 1.32/1.53 tff(1767,assumption,(s(elem!1) = s(s(elem!1))), introduced(assumption)).
% 1.32/1.53 tff(1768,plain,
% 1.32/1.53 (s(s(elem!1)) = s(elem!1)),
% 1.32/1.53 inference(symmetry,[status(thm)],[1767])).
% 1.32/1.53 tff(1769,plain,
% 1.32/1.53 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.32/1.53 inference(transitivity,[status(thm)],[1768, 1019])).
% 1.32/1.53 tff(1770,plain,
% 1.32/1.53 ($false),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[1011, 1769])).
% 1.32/1.53 tff(1771,plain,((~(s(elem!1) = s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(s(z))))) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.53 tff(1772,plain,
% 1.32/1.53 (~(s(elem!1) = s(s(elem!1)))),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[1771, 1766, 1720])).
% 1.32/1.53 tff(1773,plain,
% 1.32/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.32/1.53 inference(rewrite,[status(thm)],[])).
% 1.32/1.53 tff(1774,plain,
% 1.32/1.53 (((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z))))) <=> ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.32/1.53 inference(rewrite,[status(thm)],[])).
% 1.32/1.53 tff(1775,plain,
% 1.32/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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, s(z))) | (~b(s(z), 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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))))),
% 1.32/1.53 inference(monotonicity,[status(thm)],[1774])).
% 1.32/1.53 tff(1776,plain,
% 1.32/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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, s(z))) | (~b(s(z), 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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.32/1.53 inference(transitivity,[status(thm)],[1775, 1773])).
% 1.32/1.53 tff(1777,plain,
% 1.32/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))),
% 1.32/1.53 inference(quant_inst,[status(thm)],[])).
% 1.32/1.53 tff(1778,plain,
% 1.32/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))),
% 1.32/1.53 inference(modus_ponens,[status(thm)],[1777, 1776])).
% 1.32/1.53 tff(1779,plain,
% 1.32/1.53 ($false),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[1778, 75, 372, 107, 1391, 309, 370])).
% 1.32/1.53 tff(1780,plain,((~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.53 tff(1781,plain,
% 1.32/1.53 (~b(z, s(s(z)))),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[1780, 372, 1391, 309, 107])).
% 1.32/1.53 tff(1782,plain,
% 1.32/1.53 (r(z, s(s(z)))),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[351, 1781])).
% 1.32/1.53 tff(1783,plain,
% 1.32/1.53 (~r(z, elem!1)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[339, 1782, 106])).
% 1.32/1.53 tff(1784,plain,
% 1.32/1.53 (b(z, elem!1)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[298, 1783, 235])).
% 1.32/1.53 tff(1785,plain,
% 1.32/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, elem!1)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, elem!1)) | (~b(s(z), elem!1)))),
% 1.32/1.53 inference(rewrite,[status(thm)],[])).
% 1.32/1.53 tff(1786,plain,
% 1.32/1.53 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1))) <=> ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)))),
% 1.32/1.53 inference(rewrite,[status(thm)],[])).
% 1.32/1.53 tff(1787,plain,
% 1.32/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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, s(z))) | (~b(s(z), 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(X1, 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(z, elem!1)) | (~b(s(z), elem!1))))),
% 1.32/1.53 inference(monotonicity,[status(thm)],[1786])).
% 1.32/1.53 tff(1788,plain,
% 1.32/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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, s(z))) | (~b(s(z), 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(X1, 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(z, elem!1)) | (~b(s(z), elem!1)))),
% 1.32/1.53 inference(transitivity,[status(thm)],[1787, 1785])).
% 1.32/1.53 tff(1789,plain,
% 1.32/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))),
% 1.32/1.53 inference(quant_inst,[status(thm)],[])).
% 1.32/1.53 tff(1790,plain,
% 1.32/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1))),
% 1.32/1.53 inference(modus_ponens,[status(thm)],[1789, 1788])).
% 1.32/1.53 tff(1791,plain,
% 1.32/1.53 ($false),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[1790, 75, 1784, 372, 107, 1391])).
% 1.32/1.53 tff(1792,plain,((~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (z = elem!1) | (~r(s(s(z)), elem!1)) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.53 tff(1793,plain,
% 1.32/1.53 (~b(z, s(z))),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[1792, 1729, 1712, 1733, 1749, 309])).
% 1.32/1.53 tff(1794,plain,
% 1.32/1.53 (r(z, s(z))),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[187, 1793])).
% 1.32/1.53 tff(1795,plain,
% 1.32/1.53 (~(elem!1 = s(s(elem!1)))),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[1612, 1720])).
% 1.32/1.53 tff(1796,plain,
% 1.32/1.53 (elem!1 = s(s(s(z)))),
% 1.32/1.53 inference(symmetry,[status(thm)],[1720])).
% 1.32/1.53 tff(1797,plain,
% 1.32/1.53 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(s(z))))),
% 1.32/1.53 inference(monotonicity,[status(thm)],[1796])).
% 1.32/1.53 tff(1798,plain,
% 1.32/1.53 ((s(s(z)) = s(s(s(z)))) <=> (s(s(z)) = elem!1)),
% 1.32/1.53 inference(symmetry,[status(thm)],[1797])).
% 1.32/1.53 tff(1799,plain,
% 1.32/1.53 ((s(s(z)) = s(s(s(z)))) <=> (elem!1 = s(s(z)))),
% 1.32/1.53 inference(transitivity,[status(thm)],[1798, 307])).
% 1.32/1.53 tff(1800,plain,
% 1.32/1.53 ((~(s(s(z)) = s(s(s(z))))) <=> (~(elem!1 = s(s(z))))),
% 1.32/1.53 inference(monotonicity,[status(thm)],[1799])).
% 1.32/1.53 tff(1801,plain,
% 1.32/1.53 (~(elem!1 = s(s(z)))),
% 1.32/1.53 inference(modus_ponens,[status(thm)],[1739, 1800])).
% 1.32/1.53 tff(1802,plain,
% 1.32/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 1.32/1.53 inference(rewrite,[status(thm)],[])).
% 1.32/1.53 tff(1803,plain,
% 1.32/1.53 (((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 1.32/1.53 inference(rewrite,[status(thm)],[])).
% 1.32/1.53 tff(1804,plain,
% 1.32/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(z)))))),
% 1.32/1.53 inference(monotonicity,[status(thm)],[1803])).
% 1.32/1.53 tff(1805,plain,
% 1.32/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 1.32/1.53 inference(transitivity,[status(thm)],[1804, 1802])).
% 1.32/1.53 tff(1806,plain,
% 1.32/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))),
% 1.32/1.53 inference(quant_inst,[status(thm)],[])).
% 1.32/1.53 tff(1807,plain,
% 1.32/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(z)))),
% 1.32/1.53 inference(modus_ponens,[status(thm)],[1806, 1805])).
% 1.32/1.53 tff(1808,plain,
% 1.32/1.53 (~b(elem!1, s(s(z)))),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[1807, 75, 1712, 309, 984, 1053])).
% 1.32/1.53 tff(1809,plain,
% 1.32/1.53 ((elem!1 = s(s(z))) | r(elem!1, s(s(z)))),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[398, 58, 1808])).
% 1.32/1.53 tff(1810,plain,
% 1.32/1.53 (r(elem!1, s(s(z)))),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[1809, 1801])).
% 1.32/1.53 tff(1811,plain,
% 1.32/1.53 (~b(s(s(elem!1)), s(z))),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[1644, 1810, 266, 1795, 1712, 309, 1729])).
% 1.32/1.53 tff(1812,plain,
% 1.32/1.53 (r(s(s(elem!1)), s(z))),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[561, 1811])).
% 1.32/1.53 tff(1813,plain,
% 1.32/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)))),
% 1.32/1.53 inference(rewrite,[status(thm)],[])).
% 1.32/1.53 tff(1814,plain,
% 1.32/1.53 (((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)))),
% 1.32/1.53 inference(rewrite,[status(thm)],[])).
% 1.32/1.53 tff(1815,plain,
% 1.32/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z))))),
% 1.32/1.53 inference(monotonicity,[status(thm)],[1814])).
% 1.32/1.53 tff(1816,plain,
% 1.32/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)))),
% 1.32/1.53 inference(transitivity,[status(thm)],[1815, 1813])).
% 1.32/1.53 tff(1817,plain,
% 1.32/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)))),
% 1.32/1.53 inference(quant_inst,[status(thm)],[])).
% 1.32/1.53 tff(1818,plain,
% 1.32/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z))),
% 1.32/1.53 inference(modus_ponens,[status(thm)],[1817, 1816])).
% 1.32/1.53 tff(1819,plain,
% 1.32/1.53 (~r(s(s(elem!1)), z)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[1818, 37, 1812, 1794])).
% 1.32/1.53 tff(1820,plain,
% 1.32/1.53 (b(s(s(elem!1)), z)),
% 1.32/1.53 inference(unit_resolution,[status(thm)],[518, 58, 515, 1819])).
% 1.32/1.53 tff(1821,plain,
% 1.32/1.53 ((z = s(s(elem!1))) <=> (s(s(elem!1)) = z)),
% 1.32/1.53 inference(commutativity,[status(thm)],[])).
% 1.32/1.53 tff(1822,plain,
% 1.32/1.53 ((s(s(elem!1)) = z) <=> (z = s(s(elem!1)))),
% 1.32/1.53 inference(symmetry,[status(thm)],[1821])).
% 1.32/1.53 tff(1823,plain,
% 1.32/1.53 ((~(s(s(elem!1)) = z)) <=> (~(z = s(s(elem!1))))),
% 1.32/1.53 inference(monotonicity,[status(thm)],[1822])).
% 1.32/1.53 tff(1824,plain,
% 1.32/1.53 (~(z = s(s(elem!1)))),
% 1.32/1.53 inference(modus_ponens,[status(thm)],[515, 1823])).
% 1.32/1.53 tff(1825,plain,
% 1.32/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))))),
% 1.32/1.53 inference(rewrite,[status(thm)],[])).
% 1.32/1.53 tff(1826,plain,
% 1.32/1.53 (((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))))),
% 1.32/1.53 inference(rewrite,[status(thm)],[])).
% 1.32/1.53 tff(1827,plain,
% 1.32/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1))))))),
% 1.32/1.53 inference(monotonicity,[status(thm)],[1826])).
% 1.32/1.53 tff(1828,plain,
% 1.32/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))))),
% 1.32/1.53 inference(transitivity,[status(thm)],[1827, 1825])).
% 1.32/1.53 tff(1829,plain,
% 1.32/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))))),
% 1.32/1.53 inference(quant_inst,[status(thm)],[])).
% 1.32/1.53 tff(1830,plain,
% 1.32/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1))))),
% 1.32/1.54 inference(modus_ponens,[status(thm)],[1829, 1828])).
% 1.32/1.54 tff(1831,plain,
% 1.32/1.54 (~r(z, s(s(elem!1)))),
% 1.32/1.54 inference(unit_resolution,[status(thm)],[1830, 37, 1812, 1794])).
% 1.32/1.54 tff(1832,plain,
% 1.32/1.54 (((~![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))))),
% 1.32/1.54 inference(rewrite,[status(thm)],[])).
% 1.32/1.54 tff(1833,plain,
% 1.32/1.54 ((~![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))))),
% 1.32/1.54 inference(quant_inst,[status(thm)],[])).
% 1.32/1.54 tff(1834,plain,
% 1.32/1.54 ((~![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)))),
% 1.32/1.54 inference(modus_ponens,[status(thm)],[1833, 1832])).
% 1.32/1.54 tff(1835,plain,
% 1.32/1.54 ((z = s(s(elem!1))) | b(z, s(s(elem!1)))),
% 1.32/1.54 inference(unit_resolution,[status(thm)],[1834, 58, 1831])).
% 1.32/1.54 tff(1836,plain,
% 1.32/1.54 (b(z, s(s(elem!1)))),
% 1.32/1.54 inference(unit_resolution,[status(thm)],[1835, 1824])).
% 1.32/1.54 tff(1837,plain,
% 1.32/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1), s(s(elem!1)))))),
% 1.32/1.54 inference(rewrite,[status(thm)],[])).
% 1.32/1.54 tff(1838,plain,
% 1.32/1.54 (((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.32/1.54 inference(rewrite,[status(thm)],[])).
% 1.32/1.54 tff(1839,plain,
% 1.32/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1), s(s(elem!1))))))),
% 1.32/1.54 inference(monotonicity,[status(thm)],[1838])).
% 1.32/1.54 tff(1840,plain,
% 1.32/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1), s(s(elem!1)))))),
% 1.32/1.54 inference(transitivity,[status(thm)],[1839, 1837])).
% 1.32/1.54 tff(1841,plain,
% 1.32/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.32/1.54 inference(quant_inst,[status(thm)],[])).
% 1.32/1.54 tff(1842,plain,
% 1.32/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1), s(s(elem!1))))),
% 1.32/1.54 inference(modus_ponens,[status(thm)],[1841, 1840])).
% 1.32/1.54 tff(1843,plain,
% 1.32/1.54 (~b(s(elem!1), s(s(elem!1)))),
% 1.32/1.54 inference(unit_resolution,[status(thm)],[1842, 75, 1763, 1836, 1820])).
% 1.32/1.54 tff(1844,assumption,(~r(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 1.32/1.54 tff(1845,assumption,(~(s(elem!1) = s(s(elem!1)))), introduced(assumption)).
% 1.32/1.54 tff(1846,assumption,(~b(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 1.32/1.54 tff(1847,plain,
% 1.32/1.54 (((~![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))))),
% 1.32/1.54 inference(rewrite,[status(thm)],[])).
% 1.32/1.54 tff(1848,plain,
% 1.32/1.54 ((~![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))))),
% 1.32/1.54 inference(quant_inst,[status(thm)],[])).
% 1.32/1.54 tff(1849,plain,
% 1.32/1.54 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1)))),
% 1.32/1.54 inference(modus_ponens,[status(thm)],[1848, 1847])).
% 1.32/1.54 tff(1850,plain,
% 1.32/1.54 ($false),
% 1.32/1.54 inference(unit_resolution,[status(thm)],[1849, 58, 1846, 1845, 1844])).
% 1.32/1.54 tff(1851,plain,(r(s(elem!1), s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.54 tff(1852,plain,
% 1.32/1.54 (r(s(elem!1), s(s(elem!1)))),
% 1.32/1.54 inference(unit_resolution,[status(thm)],[1851, 1843, 1772])).
% 1.32/1.54 tff(1853,plain,
% 1.32/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))) | (~b(s(elem!1), z)))),
% 1.32/1.54 inference(rewrite,[status(thm)],[])).
% 1.32/1.54 tff(1854,plain,
% 1.32/1.54 (((~b(s(s(elem!1)), z)) | (~b(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(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)))),
% 1.32/1.54 inference(rewrite,[status(thm)],[])).
% 1.32/1.54 tff(1855,plain,
% 1.32/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(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(X1, 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(elem!1))) | (~b(s(elem!1), z))))),
% 1.32/1.54 inference(monotonicity,[status(thm)],[1854])).
% 1.32/1.54 tff(1856,plain,
% 1.32/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(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(X1, 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(elem!1))) | (~b(s(elem!1), z)))),
% 1.32/1.54 inference(transitivity,[status(thm)],[1855, 1853])).
% 1.32/1.54 tff(1857,plain,
% 1.32/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(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))))),
% 1.32/1.54 inference(quant_inst,[status(thm)],[])).
% 1.32/1.54 tff(1858,plain,
% 1.32/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z))),
% 1.32/1.54 inference(modus_ponens,[status(thm)],[1857, 1856])).
% 1.32/1.54 tff(1859,plain,
% 1.32/1.54 (~b(s(s(elem!1)), s(elem!1))),
% 1.32/1.54 inference(unit_resolution,[status(thm)],[1858, 75, 1763, 1836, 1820])).
% 1.32/1.54 tff(1860,plain,
% 1.32/1.54 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.32/1.54 inference(monotonicity,[status(thm)],[1019])).
% 1.32/1.54 tff(1861,plain,
% 1.32/1.54 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(elem!1))),
% 1.32/1.54 inference(symmetry,[status(thm)],[1860])).
% 1.32/1.54 tff(1862,plain,
% 1.32/1.54 (b(s(s(elem!1)), s(elem!1))),
% 1.32/1.54 inference(modus_ponens,[status(thm)],[1619, 1861])).
% 1.32/1.54 tff(1863,assumption,(~b(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 1.32/1.54 tff(1864,plain,
% 1.32/1.54 ($false),
% 1.32/1.54 inference(unit_resolution,[status(thm)],[1863, 1862])).
% 1.32/1.54 tff(1865,plain,((~b(s(s(elem!1)), s(s(s(s(z)))))) | b(s(s(elem!1)), s(elem!1)) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.54 tff(1866,plain,
% 1.32/1.54 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.32/1.54 inference(unit_resolution,[status(thm)],[1865, 1859, 1720])).
% 1.32/1.54 tff(1867,plain,
% 1.32/1.54 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.32/1.54 inference(unit_resolution,[status(thm)],[1660, 1866, 1766])).
% 1.32/1.54 tff(1868,plain,
% 1.32/1.54 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.32/1.54 inference(monotonicity,[status(thm)],[1019])).
% 1.32/1.54 tff(1869,plain,
% 1.32/1.54 (r(s(s(elem!1)), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(elem!1))),
% 1.32/1.54 inference(symmetry,[status(thm)],[1868])).
% 1.32/1.54 tff(1870,plain,
% 1.32/1.54 (r(s(s(elem!1)), s(elem!1))),
% 1.32/1.54 inference(modus_ponens,[status(thm)],[1647, 1869])).
% 1.32/1.54 tff(1871,assumption,(r(s(z), s(s(elem!1)))), introduced(assumption)).
% 1.32/1.54 tff(1872,plain,
% 1.32/1.54 (((~![X0: $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(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(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.32/1.54 inference(rewrite,[status(thm)],[])).
% 1.32/1.54 tff(1873,plain,
% 1.32/1.54 (((~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.32/1.54 inference(rewrite,[status(thm)],[])).
% 1.32/1.54 tff(1874,plain,
% 1.32/1.54 (((~![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)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))))),
% 1.32/1.54 inference(monotonicity,[status(thm)],[1873])).
% 1.32/1.54 tff(1875,plain,
% 1.32/1.54 (((~![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)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.32/1.54 inference(transitivity,[status(thm)],[1874, 1872])).
% 1.32/1.54 tff(1876,plain,
% 1.32/1.54 ((~![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)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))))),
% 1.32/1.54 inference(quant_inst,[status(thm)],[])).
% 1.32/1.54 tff(1877,plain,
% 1.32/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.32/1.54 inference(modus_ponens,[status(thm)],[1876, 1875])).
% 1.32/1.54 tff(1878,plain,
% 1.32/1.54 ((~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.32/1.54 inference(unit_resolution,[status(thm)],[1877, 37, 1871])).
% 1.32/1.54 tff(1879,plain,
% 1.32/1.54 ($false),
% 1.32/1.54 inference(unit_resolution,[status(thm)],[1878, 1870, 1723])).
% 1.32/1.54 tff(1880,plain,((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(z), s(s(elem!1)))) | (~(s(s(s(z))) = elem!1)) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.54 tff(1881,plain,
% 1.32/1.54 (~r(s(z), s(s(elem!1)))),
% 1.32/1.54 inference(unit_resolution,[status(thm)],[1880, 1867, 1720, 468])).
% 1.32/1.54 tff(1882,plain,
% 1.32/1.54 ((s(z) = s(s(elem!1))) <=> (s(s(elem!1)) = s(z))),
% 1.32/1.54 inference(commutativity,[status(thm)],[])).
% 1.32/1.54 tff(1883,plain,
% 1.32/1.54 ((s(s(elem!1)) = s(z)) <=> (s(z) = s(s(elem!1)))),
% 1.32/1.54 inference(symmetry,[status(thm)],[1882])).
% 1.32/1.54 tff(1884,plain,
% 1.32/1.54 ((~(s(s(elem!1)) = s(z))) <=> (~(s(z) = s(s(elem!1))))),
% 1.32/1.54 inference(monotonicity,[status(thm)],[1883])).
% 1.32/1.54 tff(1885,plain,
% 1.32/1.54 (~(s(z) = s(s(elem!1)))),
% 1.32/1.54 inference(modus_ponens,[status(thm)],[556, 1884])).
% 1.32/1.54 tff(1886,plain,
% 1.32/1.54 (((~![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))))),
% 1.32/1.54 inference(rewrite,[status(thm)],[])).
% 1.32/1.54 tff(1887,plain,
% 1.32/1.54 ((~![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))))),
% 1.32/1.54 inference(quant_inst,[status(thm)],[])).
% 1.32/1.54 tff(1888,plain,
% 1.32/1.54 ((~![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)))),
% 1.32/1.54 inference(modus_ponens,[status(thm)],[1887, 1886])).
% 1.32/1.54 tff(1889,plain,
% 1.32/1.54 ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 1.32/1.54 inference(unit_resolution,[status(thm)],[1888, 58])).
% 1.32/1.54 tff(1890,plain,
% 1.32/1.54 (b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 1.32/1.54 inference(unit_resolution,[status(thm)],[1889, 1885])).
% 1.32/1.54 tff(1891,plain,
% 1.32/1.54 (b(s(z), s(s(elem!1)))),
% 1.32/1.54 inference(unit_resolution,[status(thm)],[1890, 1881])).
% 1.32/1.54 tff(1892,assumption,(b(s(s(elem!1)), z)), introduced(assumption)).
% 1.32/1.54 tff(1893,assumption,(b(z, s(s(elem!1)))), introduced(assumption)).
% 1.32/1.54 tff(1894,assumption,(b(s(z), s(s(elem!1)))), introduced(assumption)).
% 1.32/1.54 tff(1895,plain,
% 1.32/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), elem!1)))),
% 1.32/1.54 inference(rewrite,[status(thm)],[])).
% 1.32/1.54 tff(1896,plain,
% 1.32/1.54 (((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), elem!1)))),
% 1.32/1.54 inference(rewrite,[status(thm)],[])).
% 1.32/1.54 tff(1897,plain,
% 1.32/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), 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(X1, 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)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), elem!1))))),
% 1.32/1.54 inference(monotonicity,[status(thm)],[1896])).
% 1.32/1.54 tff(1898,plain,
% 1.32/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), 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(X1, 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)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), elem!1)))),
% 1.32/1.54 inference(transitivity,[status(thm)],[1897, 1895])).
% 1.32/1.54 tff(1899,plain,
% 1.32/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)))),
% 1.32/1.54 inference(quant_inst,[status(thm)],[])).
% 1.32/1.54 tff(1900,plain,
% 1.32/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), elem!1))),
% 1.32/1.54 inference(modus_ponens,[status(thm)],[1899, 1898])).
% 1.32/1.54 tff(1901,plain,
% 1.32/1.54 ($false),
% 1.32/1.54 inference(unit_resolution,[status(thm)],[1900, 75, 107, 1620, 1894, 1893, 1892])).
% 1.32/1.54 tff(1902,plain,((~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.54 tff(1903,plain,
% 1.32/1.54 (~b(elem!1, s(s(elem!1)))),
% 1.32/1.54 inference(unit_resolution,[status(thm)],[1902, 1891, 1836, 1820, 1729])).
% 1.32/1.54 tff(1904,plain,
% 1.32/1.54 (r(elem!1, s(s(elem!1)))),
% 1.32/1.54 inference(unit_resolution,[status(thm)],[1617, 1903, 1795])).
% 1.32/1.54 tff(1905,plain,
% 1.32/1.54 (elem!1 = s(s(s(z)))),
% 1.32/1.54 inference(symmetry,[status(thm)],[213])).
% 1.32/1.54 tff(1906,plain,
% 1.32/1.54 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.32/1.54 inference(monotonicity,[status(thm)],[1905])).
% 1.32/1.54 tff(1907,plain,
% 1.32/1.54 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(elem!1)), elem!1)),
% 1.32/1.54 inference(symmetry,[status(thm)],[1906])).
% 1.32/1.54 tff(1908,plain,
% 1.32/1.54 (~(elem!1 = s(s(elem!1)))),
% 1.32/1.54 inference(unit_resolution,[status(thm)],[1612, 213])).
% 1.32/1.54 tff(1909,plain,
% 1.32/1.54 ((s(s(s(z))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 1.32/1.54 inference(commutativity,[status(thm)],[])).
% 1.32/1.54 tff(1910,plain,
% 1.32/1.54 ((elem!1 = s(s(elem!1))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 1.32/1.54 inference(monotonicity,[status(thm)],[1905])).
% 1.32/1.54 tff(1911,plain,
% 1.32/1.54 ((elem!1 = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 1.32/1.54 inference(transitivity,[status(thm)],[1910, 1909])).
% 1.32/1.54 tff(1912,plain,
% 1.32/1.54 ((s(s(elem!1)) = s(s(s(z)))) <=> (elem!1 = s(s(elem!1)))),
% 1.32/1.54 inference(symmetry,[status(thm)],[1911])).
% 1.32/1.54 tff(1913,assumption,(s(s(elem!1)) = s(s(s(z)))), introduced(assumption)).
% 1.32/1.54 tff(1914,plain,
% 1.32/1.54 (elem!1 = s(s(elem!1))),
% 1.32/1.54 inference(modus_ponens,[status(thm)],[1913, 1912])).
% 1.32/1.54 tff(1915,plain,
% 1.32/1.54 ($false),
% 1.32/1.54 inference(unit_resolution,[status(thm)],[1630, 1914])).
% 1.32/1.54 tff(1916,plain,((~(s(s(elem!1)) = s(s(s(z))))) | (elem!1 = s(s(elem!1))) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.54 tff(1917,plain,
% 1.32/1.54 (~(s(s(elem!1)) = s(s(s(z))))),
% 1.32/1.54 inference(unit_resolution,[status(thm)],[1916, 1908, 213])).
% 1.32/1.54 tff(1918,assumption,(r(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 1.32/1.54 tff(1919,plain,
% 1.32/1.54 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(s(s(z))))),
% 1.32/1.54 inference(monotonicity,[status(thm)],[1905])).
% 1.32/1.54 tff(1920,plain,
% 1.32/1.54 (r(s(s(elem!1)), s(s(s(z)))) <=> r(s(s(elem!1)), elem!1)),
% 1.32/1.54 inference(symmetry,[status(thm)],[1919])).
% 1.32/1.54 tff(1921,assumption,(r(s(s(elem!1)), s(s(s(z))))), introduced(assumption)).
% 1.32/1.54 tff(1922,plain,
% 1.32/1.54 (r(s(s(elem!1)), elem!1)),
% 1.32/1.54 inference(modus_ponens,[status(thm)],[1921, 1920])).
% 1.32/1.54 tff(1923,plain,
% 1.32/1.54 (((~![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), s(s(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(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.32/1.55 inference(rewrite,[status(thm)],[])).
% 1.32/1.55 tff(1924,plain,
% 1.32/1.55 (((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.32/1.55 inference(rewrite,[status(thm)],[])).
% 1.32/1.55 tff(1925,plain,
% 1.32/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1))))))),
% 1.32/1.55 inference(monotonicity,[status(thm)],[1924])).
% 1.32/1.55 tff(1926,plain,
% 1.32/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.32/1.55 inference(transitivity,[status(thm)],[1925, 1923])).
% 1.32/1.55 tff(1927,plain,
% 1.32/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.32/1.55 inference(quant_inst,[status(thm)],[])).
% 1.32/1.55 tff(1928,plain,
% 1.32/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1))))),
% 1.32/1.55 inference(modus_ponens,[status(thm)],[1927, 1926])).
% 1.32/1.55 tff(1929,plain,
% 1.32/1.55 (~r(s(s(elem!1)), elem!1)),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[1928, 37, 752, 1918])).
% 1.32/1.55 tff(1930,plain,
% 1.32/1.55 ($false),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[1929, 1922])).
% 1.32/1.55 tff(1931,plain,((~r(s(s(elem!1)), s(s(s(z))))) | (~(s(s(s(z))) = elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.55 tff(1932,plain,
% 1.32/1.55 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[1931, 752, 1918, 213])).
% 1.32/1.55 tff(1933,plain,
% 1.32/1.55 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z)))))),
% 1.32/1.55 inference(rewrite,[status(thm)],[])).
% 1.32/1.55 tff(1934,plain,
% 1.32/1.55 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z)))))),
% 1.32/1.55 inference(quant_inst,[status(thm)],[])).
% 1.32/1.55 tff(1935,plain,
% 1.32/1.55 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z))))),
% 1.32/1.55 inference(modus_ponens,[status(thm)],[1934, 1933])).
% 1.32/1.55 tff(1936,plain,
% 1.32/1.55 ((s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z))))),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[1935, 58])).
% 1.32/1.55 tff(1937,plain,
% 1.32/1.55 (b(s(s(elem!1)), s(s(s(z))))),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[1936, 1932, 1917])).
% 1.32/1.55 tff(1938,plain,
% 1.32/1.55 (b(s(s(elem!1)), elem!1)),
% 1.32/1.55 inference(modus_ponens,[status(thm)],[1937, 1907])).
% 1.32/1.55 tff(1939,plain,
% 1.32/1.55 ((z = elem!1) <=> (elem!1 = z)),
% 1.32/1.55 inference(symmetry,[status(thm)],[216])).
% 1.32/1.55 tff(1940,plain,
% 1.32/1.55 ((s(s(s(z))) = z) <=> (elem!1 = z)),
% 1.32/1.55 inference(transitivity,[status(thm)],[218, 1939])).
% 1.32/1.55 tff(1941,plain,
% 1.32/1.55 ((~(s(s(s(z))) = z)) <=> (~(elem!1 = z))),
% 1.32/1.55 inference(monotonicity,[status(thm)],[1940])).
% 1.32/1.55 tff(1942,plain,
% 1.32/1.55 (~(elem!1 = z)),
% 1.32/1.55 inference(modus_ponens,[status(thm)],[221, 1941])).
% 1.32/1.55 tff(1943,plain,
% 1.32/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, 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(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.32/1.55 inference(rewrite,[status(thm)],[])).
% 1.32/1.55 tff(1944,plain,
% 1.32/1.55 (((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.32/1.55 inference(rewrite,[status(thm)],[])).
% 1.32/1.55 tff(1945,plain,
% 1.32/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1))))))),
% 1.32/1.55 inference(monotonicity,[status(thm)],[1944])).
% 1.32/1.55 tff(1946,plain,
% 1.32/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.32/1.55 inference(transitivity,[status(thm)],[1945, 1943])).
% 1.32/1.55 tff(1947,plain,
% 1.32/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)))),
% 1.32/1.55 inference(quant_inst,[status(thm)],[])).
% 1.32/1.55 tff(1948,plain,
% 1.32/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1))))),
% 1.32/1.55 inference(modus_ponens,[status(thm)],[1947, 1946])).
% 1.32/1.55 tff(1949,plain,
% 1.32/1.55 ($false),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[1948, 37, 155, 1490, 752, 1918])).
% 1.32/1.55 tff(1950,plain,((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.55 tff(1951,plain,
% 1.32/1.55 (~r(elem!1, z)),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[1950, 752, 1490, 1918])).
% 1.32/1.55 tff(1952,plain,
% 1.32/1.55 (b(elem!1, z)),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[387, 1951, 1942])).
% 1.32/1.55 tff(1953,plain,
% 1.32/1.55 (~r(s(s(elem!1)), z)),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[1818, 37, 494, 506])).
% 1.32/1.55 tff(1954,plain,
% 1.32/1.55 (b(s(s(elem!1)), z)),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[518, 58, 515, 1953])).
% 1.32/1.55 tff(1955,plain,
% 1.32/1.55 (~r(z, s(s(elem!1)))),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[1830, 37, 494, 506])).
% 1.32/1.55 tff(1956,plain,
% 1.32/1.55 ((z = s(s(elem!1))) | b(z, s(s(elem!1)))),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[1834, 58, 1955])).
% 1.32/1.55 tff(1957,plain,
% 1.32/1.55 (b(z, s(s(elem!1)))),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[1956, 1824])).
% 1.32/1.55 tff(1958,assumption,(b(elem!1, z)), introduced(assumption)).
% 1.32/1.55 tff(1959,plain,
% 1.32/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)))),
% 1.32/1.55 inference(rewrite,[status(thm)],[])).
% 1.32/1.55 tff(1960,plain,
% 1.32/1.55 (((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)))),
% 1.32/1.55 inference(rewrite,[status(thm)],[])).
% 1.32/1.55 tff(1961,plain,
% 1.32/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z))))),
% 1.32/1.55 inference(monotonicity,[status(thm)],[1960])).
% 1.32/1.55 tff(1962,plain,
% 1.32/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)))),
% 1.32/1.55 inference(transitivity,[status(thm)],[1961, 1959])).
% 1.32/1.55 tff(1963,plain,
% 1.32/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 1.32/1.55 inference(quant_inst,[status(thm)],[])).
% 1.32/1.55 tff(1964,plain,
% 1.32/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z))),
% 1.32/1.55 inference(modus_ponens,[status(thm)],[1963, 1962])).
% 1.32/1.55 tff(1965,plain,
% 1.32/1.55 ($false),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[1964, 75, 1958, 1957, 707, 1954])).
% 1.32/1.55 tff(1966,plain,((~r(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.55 tff(1967,plain,
% 1.32/1.55 (~b(s(s(elem!1)), elem!1)),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[1966, 1952, 506, 494])).
% 1.32/1.55 tff(1968,plain,
% 1.32/1.55 ($false),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[1967, 1938])).
% 1.32/1.55 tff(1969,plain,((~r(s(elem!1), elem!1)) | (~(s(s(s(z))) = elem!1)) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.55 tff(1970,plain,
% 1.32/1.55 (~r(s(elem!1), elem!1)),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[1969, 1904, 1794, 1812, 1720, 1852])).
% 1.32/1.55 tff(1971,plain,
% 1.32/1.55 (r(s(elem!1), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 1.32/1.55 inference(monotonicity,[status(thm)],[1019])).
% 1.32/1.55 tff(1972,plain,
% 1.32/1.55 (r(s(s(s(s(z)))), elem!1) <=> r(s(elem!1), elem!1)),
% 1.32/1.55 inference(symmetry,[status(thm)],[1971])).
% 1.32/1.55 tff(1973,plain,
% 1.32/1.55 (r(s(elem!1), elem!1)),
% 1.32/1.55 inference(modus_ponens,[status(thm)],[698, 1972])).
% 1.32/1.55 tff(1974,assumption,(~r(s(elem!1), elem!1)), introduced(assumption)).
% 1.32/1.55 tff(1975,plain,
% 1.32/1.55 ($false),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[1974, 1973])).
% 1.32/1.55 tff(1976,plain,((~r(s(s(s(s(z)))), elem!1)) | r(s(elem!1), elem!1) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.55 tff(1977,plain,
% 1.32/1.55 (~r(s(s(s(s(z)))), elem!1)),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[1976, 1970, 1720])).
% 1.32/1.55 tff(1978,plain,
% 1.32/1.55 (b(s(s(s(s(z)))), elem!1)),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[283, 1977, 267])).
% 1.32/1.55 tff(1979,plain,
% 1.32/1.55 (b(s(elem!1), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 1.32/1.55 inference(monotonicity,[status(thm)],[1019])).
% 1.32/1.55 tff(1980,plain,
% 1.32/1.55 (b(s(s(s(s(z)))), elem!1) <=> b(s(elem!1), elem!1)),
% 1.32/1.55 inference(symmetry,[status(thm)],[1979])).
% 1.32/1.55 tff(1981,plain,
% 1.32/1.55 (b(s(elem!1), elem!1)),
% 1.32/1.55 inference(modus_ponens,[status(thm)],[287, 1980])).
% 1.32/1.55 tff(1982,plain,
% 1.32/1.55 ($false),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[966, 1981])).
% 1.32/1.55 tff(1983,plain,((~b(s(s(s(s(z)))), elem!1)) | b(s(elem!1), elem!1) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.55 tff(1984,plain,
% 1.32/1.55 (b(s(elem!1), elem!1)),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[1983, 1978, 1720])).
% 1.32/1.55 tff(1985,plain,
% 1.32/1.55 (~r(s(s(elem!1)), s(s(z)))),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[1498, 1904, 1810])).
% 1.32/1.55 tff(1986,plain,
% 1.32/1.55 (b(s(s(elem!1)), s(s(z)))),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[1476, 1985, 266])).
% 1.32/1.55 tff(1987,plain,
% 1.32/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(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(X1, 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(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.32/1.55 inference(rewrite,[status(thm)],[])).
% 1.32/1.55 tff(1988,plain,
% 1.32/1.55 (((~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.32/1.55 inference(rewrite,[status(thm)],[])).
% 1.32/1.55 tff(1989,plain,
% 1.32/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 1.32/1.55 inference(monotonicity,[status(thm)],[1988])).
% 1.32/1.55 tff(1990,plain,
% 1.32/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.32/1.55 inference(transitivity,[status(thm)],[1989, 1987])).
% 1.32/1.55 tff(1991,plain,
% 1.32/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(elem!1)))))),
% 1.32/1.55 inference(quant_inst,[status(thm)],[])).
% 1.32/1.55 tff(1992,plain,
% 1.32/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 1.32/1.55 inference(modus_ponens,[status(thm)],[1991, 1990])).
% 1.32/1.55 tff(1993,plain,
% 1.32/1.55 ($false),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[1992, 75, 1894, 309, 402, 1283])).
% 1.32/1.55 tff(1994,plain,((~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.55 tff(1995,plain,
% 1.32/1.55 (~b(s(z), s(s(z)))),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[1994, 1986, 309, 1891])).
% 1.32/1.55 tff(1996,plain,
% 1.32/1.55 (r(s(z), s(s(z)))),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[416, 1995])).
% 1.32/1.55 tff(1997,assumption,(r(s(z), s(s(z)))), introduced(assumption)).
% 1.32/1.55 tff(1998,plain,
% 1.32/1.55 (((~![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(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(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.32/1.55 inference(rewrite,[status(thm)],[])).
% 1.32/1.55 tff(1999,plain,
% 1.32/1.55 (((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.32/1.55 inference(rewrite,[status(thm)],[])).
% 1.32/1.55 tff(2000,plain,
% 1.32/1.55 (((~![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(z)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z))))))),
% 1.32/1.55 inference(monotonicity,[status(thm)],[1999])).
% 1.32/1.55 tff(2001,plain,
% 1.32/1.55 (((~![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(z)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.32/1.55 inference(transitivity,[status(thm)],[2000, 1998])).
% 1.32/1.55 tff(2002,plain,
% 1.32/1.55 ((~![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(z)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(z, s(z))))),
% 1.32/1.55 inference(quant_inst,[status(thm)],[])).
% 1.32/1.55 tff(2003,plain,
% 1.32/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z))))),
% 1.32/1.55 inference(modus_ponens,[status(thm)],[2002, 2001])).
% 1.32/1.55 tff(2004,plain,
% 1.32/1.55 ($false),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[2003, 37, 506, 1997, 331])).
% 1.32/1.55 tff(2005,plain,((~r(z, s(s(z)))) | (~r(z, s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.55 tff(2006,plain,
% 1.32/1.55 (~r(z, s(s(z)))),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[2005, 1996, 1794])).
% 1.32/1.55 tff(2007,plain,
% 1.32/1.55 (b(z, s(s(z)))),
% 1.32/1.55 inference(unit_resolution,[status(thm)],[351, 2006])).
% 1.32/1.55 tff(2008,plain,
% 1.32/1.55 (((~![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(z), s(s(z)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 1.32/1.55 inference(rewrite,[status(thm)],[])).
% 1.32/1.55 tff(2009,plain,
% 1.32/1.55 (((~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(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 1.32/1.55 inference(rewrite,[status(thm)],[])).
% 1.32/1.55 tff(2010,plain,
% 1.32/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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(z), s(s(z)))) | (~r(s(s(z)), z))))),
% 1.32/1.55 inference(monotonicity,[status(thm)],[2009])).
% 1.32/1.55 tff(2011,plain,
% 1.32/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 1.32/1.55 inference(transitivity,[status(thm)],[2010, 2008])).
% 1.32/1.55 tff(2012,plain,
% 1.32/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))),
% 1.32/1.56 inference(quant_inst,[status(thm)],[])).
% 1.32/1.56 tff(2013,plain,
% 1.32/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z))),
% 1.32/1.56 inference(modus_ponens,[status(thm)],[2012, 2011])).
% 1.32/1.56 tff(2014,plain,
% 1.32/1.56 ($false),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[2013, 37, 1561, 1997, 320])).
% 1.32/1.56 tff(2015,plain,((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.56 tff(2016,plain,
% 1.32/1.56 (~r(s(s(z)), z)),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[2015, 1996, 1751])).
% 1.32/1.56 tff(2017,plain,
% 1.32/1.56 (b(s(s(z)), z)),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[202, 2016])).
% 1.32/1.56 tff(2018,plain,
% 1.32/1.56 (~r(z, elem!1)),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[1471, 2017, 1986, 2007, 1794, 1712, 309, 1729])).
% 1.32/1.56 tff(2019,plain,
% 1.32/1.56 (b(z, elem!1)),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[298, 2018, 1733])).
% 1.32/1.56 tff(2020,plain,
% 1.32/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), 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(X1, 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), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 1.32/1.56 inference(rewrite,[status(thm)],[])).
% 1.32/1.56 tff(2021,plain,
% 1.32/1.56 (((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))) <=> ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 1.32/1.56 inference(rewrite,[status(thm)],[])).
% 1.32/1.56 tff(2022,plain,
% 1.32/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1), elem!1)) | (~b(elem!1, 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(X1, 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), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))))),
% 1.32/1.56 inference(monotonicity,[status(thm)],[2021])).
% 1.32/1.56 tff(2023,plain,
% 1.32/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1), elem!1)) | (~b(elem!1, 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(X1, 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), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 1.32/1.56 inference(transitivity,[status(thm)],[2022, 2020])).
% 1.32/1.56 tff(2024,plain,
% 1.32/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 1.32/1.56 inference(quant_inst,[status(thm)],[])).
% 1.32/1.56 tff(2025,plain,
% 1.32/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))),
% 1.32/1.56 inference(modus_ponens,[status(thm)],[2024, 2023])).
% 1.32/1.56 tff(2026,plain,
% 1.32/1.56 ($false),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[2025, 75, 2019, 1729, 1712, 1984, 1763])).
% 1.32/1.56 tff(2027,plain,((~b(s(s(z)), s(z))) | (s(s(s(s(z)))) = elem!1) | (s(s(elem!1)) = s(s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | r(s(s(s(z))), elem!1) | (~b(s(s(s(z))), s(z))) | r(elem!1, s(z)) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.32/1.56 tff(2028,plain,
% 1.32/1.56 (r(s(s(s(z))), elem!1)),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[2027, 1709, 99, 266, 1686, 1696, 1695, 1684, 267])).
% 1.32/1.56 tff(2029,plain,
% 1.32/1.56 (r(s(elem!1), elem!1)),
% 1.32/1.56 inference(modus_ponens,[status(thm)],[2028, 1681])).
% 1.32/1.56 tff(2030,plain,
% 1.32/1.56 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[808, 2029, 300, 1677])).
% 1.32/1.56 tff(2031,plain,
% 1.32/1.56 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[813, 2030, 1676])).
% 1.32/1.56 tff(2032,plain,
% 1.32/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.32/1.56 inference(rewrite,[status(thm)],[])).
% 1.32/1.56 tff(2033,plain,
% 1.32/1.56 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.32/1.56 inference(rewrite,[status(thm)],[])).
% 1.32/1.56 tff(2034,plain,
% 1.32/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 1.32/1.56 inference(monotonicity,[status(thm)],[2033])).
% 1.32/1.56 tff(2035,plain,
% 1.32/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.32/1.56 inference(transitivity,[status(thm)],[2034, 2032])).
% 1.32/1.56 tff(2036,plain,
% 1.32/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.32/1.56 inference(quant_inst,[status(thm)],[])).
% 1.32/1.56 tff(2037,plain,
% 1.32/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 1.32/1.56 inference(modus_ponens,[status(thm)],[2036, 2035])).
% 1.32/1.56 tff(2038,plain,
% 1.32/1.56 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[2037, 75, 1396, 1377, 2031])).
% 1.32/1.56 tff(2039,plain,
% 1.32/1.56 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[1230, 58, 1227, 2038])).
% 1.32/1.56 tff(2040,plain,
% 1.32/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.32/1.56 inference(rewrite,[status(thm)],[])).
% 1.32/1.56 tff(2041,plain,
% 1.32/1.56 (((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.32/1.56 inference(rewrite,[status(thm)],[])).
% 1.32/1.56 tff(2042,plain,
% 1.32/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(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(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 1.32/1.56 inference(monotonicity,[status(thm)],[2041])).
% 1.32/1.56 tff(2043,plain,
% 1.32/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(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(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.32/1.56 inference(transitivity,[status(thm)],[2042, 2040])).
% 1.32/1.56 tff(2044,plain,
% 1.32/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(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(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.32/1.56 inference(quant_inst,[status(thm)],[])).
% 1.32/1.56 tff(2045,plain,
% 1.32/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 1.32/1.56 inference(modus_ponens,[status(thm)],[2044, 2043])).
% 1.32/1.56 tff(2046,plain,
% 1.32/1.56 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[2045, 75, 1396, 1377, 287, 2031])).
% 1.32/1.56 tff(2047,plain,
% 1.32/1.56 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(z)))))),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[1134, 1673])).
% 1.32/1.56 tff(2048,plain,
% 1.32/1.56 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[1179, 58, 2047, 2046])).
% 1.32/1.56 tff(2049,plain,
% 1.32/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $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(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.32/1.56 inference(rewrite,[status(thm)],[])).
% 1.32/1.56 tff(2050,plain,
% 1.32/1.56 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(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(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.32/1.56 inference(rewrite,[status(thm)],[])).
% 1.32/1.56 tff(2051,plain,
% 1.32/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(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(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 1.32/1.56 inference(monotonicity,[status(thm)],[2050])).
% 1.32/1.56 tff(2052,plain,
% 1.32/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(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(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.32/1.56 inference(transitivity,[status(thm)],[2051, 2049])).
% 1.32/1.56 tff(2053,plain,
% 1.32/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.32/1.56 inference(quant_inst,[status(thm)],[])).
% 1.32/1.56 tff(2054,plain,
% 1.32/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 1.32/1.56 inference(modus_ponens,[status(thm)],[2053, 2052])).
% 1.32/1.56 tff(2055,plain,
% 1.32/1.56 ($false),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[2054, 37, 1407, 2048, 2039])).
% 1.32/1.56 tff(2056,plain,((~r(z, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | b(s(s(z)), elem!1) | (s(s(elem!1)) = s(s(z))) | (s(s(s(s(z)))) = elem!1) | (~b(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.56 tff(2057,plain,
% 1.32/1.56 (~r(z, s(z))),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[2056, 299, 287, 99, 266, 267, 286])).
% 1.32/1.56 tff(2058,plain,
% 1.32/1.56 (b(z, s(z))),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[187, 2057])).
% 1.32/1.56 tff(2059,plain,
% 1.32/1.56 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[1662, 15, 287, 1391, 266, 299, 286, 99])).
% 1.32/1.56 tff(2060,plain,
% 1.32/1.56 (b(s(s(z)), s(s(s(s(z)))))),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[465, 2059])).
% 1.32/1.56 tff(2061,plain,
% 1.32/1.56 ((z = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = z)),
% 1.32/1.56 inference(commutativity,[status(thm)],[])).
% 1.32/1.56 tff(2062,plain,
% 1.32/1.56 ((s(s(s(s(s(z))))) = z) <=> (z = s(s(s(s(s(z))))))),
% 1.32/1.56 inference(symmetry,[status(thm)],[2061])).
% 1.32/1.56 tff(2063,plain,
% 1.32/1.56 ((~(s(s(s(s(s(z))))) = z)) <=> (~(z = s(s(s(s(s(z)))))))),
% 1.32/1.56 inference(monotonicity,[status(thm)],[2062])).
% 1.32/1.56 tff(2064,plain,
% 1.32/1.56 (~(z = s(s(s(s(s(z))))))),
% 1.32/1.56 inference(modus_ponens,[status(thm)],[734, 2063])).
% 1.32/1.56 tff(2065,plain,
% 1.32/1.56 (~r(s(s(z)), z)),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[328, 106, 299])).
% 1.32/1.56 tff(2066,plain,
% 1.32/1.56 (b(s(s(z)), z)),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[202, 2065])).
% 1.32/1.56 tff(2067,plain,
% 1.32/1.56 (~r(z, s(s(z)))),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[339, 106, 299])).
% 1.32/1.56 tff(2068,plain,
% 1.32/1.56 (b(z, s(s(z)))),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[351, 2067])).
% 1.32/1.56 tff(2069,plain,
% 1.32/1.56 (~b(s(z), s(s(z)))),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[410, 372, 2068, 2066])).
% 1.32/1.56 tff(2070,plain,
% 1.32/1.56 (r(s(z), s(s(z)))),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[416, 2069])).
% 1.32/1.56 tff(2071,plain,
% 1.32/1.56 (~r(z, s(z))),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[1358, 588, 300])).
% 1.32/1.56 tff(2072,plain,
% 1.32/1.56 (~r(s(s(z)), z)),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[328, 106, 300])).
% 1.32/1.56 tff(2073,plain,
% 1.32/1.56 (b(s(s(z)), z)),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[202, 2072])).
% 1.32/1.56 tff(2074,plain,
% 1.32/1.56 (~b(s(z), s(s(z)))),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[410, 678, 372, 2073])).
% 1.32/1.56 tff(2075,plain,
% 1.32/1.56 (r(s(z), s(s(z)))),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[416, 2074])).
% 1.32/1.56 tff(2076,plain,
% 1.32/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(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(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), elem!1)))),
% 1.32/1.56 inference(rewrite,[status(thm)],[])).
% 1.32/1.56 tff(2077,plain,
% 1.32/1.56 (((~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), elem!1)))),
% 1.32/1.56 inference(rewrite,[status(thm)],[])).
% 1.32/1.56 tff(2078,plain,
% 1.32/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), elem!1))))),
% 1.32/1.56 inference(monotonicity,[status(thm)],[2077])).
% 1.32/1.56 tff(2079,plain,
% 1.32/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), elem!1)))),
% 1.32/1.56 inference(transitivity,[status(thm)],[2078, 2076])).
% 1.32/1.56 tff(2080,plain,
% 1.32/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))))),
% 1.32/1.56 inference(quant_inst,[status(thm)],[])).
% 1.32/1.56 tff(2081,plain,
% 1.32/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), elem!1))),
% 1.32/1.56 inference(modus_ponens,[status(thm)],[2080, 2079])).
% 1.32/1.56 tff(2082,plain,
% 1.32/1.56 ($false),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[2081, 37, 588, 106, 2075])).
% 1.32/1.56 tff(2083,plain,((~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~b(z, s(z))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.56 tff(2084,plain,
% 1.32/1.56 (~b(z, s(z))),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[2083, 588, 300, 106])).
% 1.32/1.56 tff(2085,plain,
% 1.32/1.56 ($false),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[187, 2084, 2071])).
% 1.32/1.56 tff(2086,plain,((~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.56 tff(2087,plain,
% 1.32/1.56 (~r(s(z), elem!1)),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[2086, 106, 299])).
% 1.32/1.56 tff(2088,plain,
% 1.32/1.56 (b(z, s(z)) <=> b(z, elem!1)),
% 1.32/1.56 inference(monotonicity,[status(thm)],[93])).
% 1.32/1.56 tff(2089,plain,
% 1.32/1.56 (b(z, elem!1) <=> b(z, s(z))),
% 1.32/1.56 inference(symmetry,[status(thm)],[2088])).
% 1.32/1.56 tff(2090,plain,
% 1.32/1.56 ((~b(z, elem!1)) <=> (~b(z, s(z)))),
% 1.32/1.56 inference(monotonicity,[status(thm)],[2089])).
% 1.32/1.56 tff(2091,plain,
% 1.32/1.56 (~b(z, s(z))),
% 1.32/1.56 inference(modus_ponens,[status(thm)],[285, 2090])).
% 1.32/1.56 tff(2092,plain,
% 1.32/1.56 ($false),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[372, 2091])).
% 1.32/1.56 tff(2093,plain,((~(s(z) = elem!1)) | (~b(z, s(z))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.32/1.56 tff(2094,plain,
% 1.32/1.56 (~(s(z) = elem!1)),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[2093, 372, 285])).
% 1.32/1.56 tff(2095,plain,
% 1.32/1.56 (b(s(z), elem!1)),
% 1.32/1.56 inference(unit_resolution,[status(thm)],[601, 2094, 2087])).
% 1.32/1.57 tff(2096,plain,
% 1.32/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), elem!1)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), elem!1)) | (~b(elem!1, z)))),
% 1.32/1.57 inference(rewrite,[status(thm)],[])).
% 1.32/1.57 tff(2097,plain,
% 1.32/1.57 (((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z))) <=> ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, z)))),
% 1.32/1.57 inference(rewrite,[status(thm)],[])).
% 1.32/1.57 tff(2098,plain,
% 1.32/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z), elem!1)) | (~b(elem!1, z))))),
% 1.32/1.57 inference(monotonicity,[status(thm)],[2097])).
% 1.32/1.57 tff(2099,plain,
% 1.32/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z), elem!1)) | (~b(elem!1, z)))),
% 1.32/1.57 inference(transitivity,[status(thm)],[2098, 2096])).
% 1.32/1.57 tff(2100,plain,
% 1.32/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))),
% 1.32/1.57 inference(quant_inst,[status(thm)],[])).
% 1.32/1.57 tff(2101,plain,
% 1.32/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), elem!1)) | (~b(elem!1, z))),
% 1.32/1.57 inference(modus_ponens,[status(thm)],[2100, 2099])).
% 1.32/1.57 tff(2102,plain,
% 1.32/1.57 (~b(elem!1, z)),
% 1.32/1.57 inference(unit_resolution,[status(thm)],[2101, 75, 372, 2095, 1391])).
% 1.32/1.57 tff(2103,plain,
% 1.32/1.57 (r(elem!1, z)),
% 1.32/1.57 inference(unit_resolution,[status(thm)],[387, 2102, 305])).
% 1.32/1.57 tff(2104,assumption,(~b(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 1.32/1.57 tff(2105,plain,
% 1.32/1.57 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.32/1.57 inference(unit_resolution,[status(thm)],[575, 2104])).
% 1.32/1.57 tff(2106,plain,
% 1.32/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.32/1.57 inference(rewrite,[status(thm)],[])).
% 1.32/1.57 tff(2107,plain,
% 1.32/1.57 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.32/1.57 inference(rewrite,[status(thm)],[])).
% 1.32/1.57 tff(2108,plain,
% 1.32/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.32/1.57 inference(monotonicity,[status(thm)],[2107])).
% 1.32/1.57 tff(2109,plain,
% 1.32/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.32/1.57 inference(transitivity,[status(thm)],[2108, 2106])).
% 1.32/1.57 tff(2110,plain,
% 1.32/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))))),
% 1.32/1.57 inference(quant_inst,[status(thm)],[])).
% 1.32/1.57 tff(2111,plain,
% 1.32/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.32/1.57 inference(modus_ponens,[status(thm)],[2110, 2109])).
% 1.32/1.57 tff(2112,plain,
% 1.32/1.57 (~r(s(s(s(z))), s(z))),
% 1.32/1.57 inference(unit_resolution,[status(thm)],[2111, 37, 1997, 468, 2105])).
% 1.32/1.57 tff(2113,plain,
% 1.32/1.57 (b(s(s(s(z))), s(z))),
% 1.32/1.57 inference(unit_resolution,[status(thm)],[1081, 2112])).
% 1.32/1.57 tff(2114,plain,
% 1.32/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.32/1.57 inference(rewrite,[status(thm)],[])).
% 1.32/1.57 tff(2115,plain,
% 1.32/1.57 (((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.32/1.57 inference(rewrite,[status(thm)],[])).
% 1.32/1.57 tff(2116,plain,
% 1.32/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 1.32/1.57 inference(monotonicity,[status(thm)],[2115])).
% 1.32/1.57 tff(2117,plain,
% 1.32/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.32/1.57 inference(transitivity,[status(thm)],[2116, 2114])).
% 1.32/1.57 tff(2118,plain,
% 1.32/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))))),
% 1.32/1.57 inference(quant_inst,[status(thm)],[])).
% 1.32/1.57 tff(2119,plain,
% 1.32/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 1.32/1.57 inference(modus_ponens,[status(thm)],[2118, 2117])).
% 1.32/1.57 tff(2120,plain,
% 1.32/1.57 (~b(elem!1, s(s(s(z))))),
% 1.32/1.57 inference(unit_resolution,[status(thm)],[2119, 75, 107, 1391, 2113])).
% 1.32/1.57 tff(2121,plain,
% 1.32/1.57 (~r(s(z), s(s(s(z))))),
% 1.32/1.57 inference(unit_resolution,[status(thm)],[1316, 2105, 468])).
% 1.32/1.57 tff(2122,plain,
% 1.32/1.57 (b(s(z), s(s(s(z))))),
% 1.32/1.57 inference(unit_resolution,[status(thm)],[1263, 2121])).
% 1.32/1.57 tff(2123,plain,
% 1.32/1.57 (~b(s(s(s(z))), z)),
% 1.32/1.57 inference(unit_resolution,[status(thm)],[1091, 2113, 372, 2122])).
% 1.32/1.57 tff(2124,plain,
% 1.32/1.57 (r(s(s(s(z))), z)),
% 1.32/1.57 inference(unit_resolution,[status(thm)],[1334, 58, 221, 2123])).
% 1.32/1.57 tff(2125,plain,
% 1.32/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 1.32/1.57 inference(rewrite,[status(thm)],[])).
% 1.32/1.57 tff(2126,plain,
% 1.32/1.57 (((~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 1.32/1.57 inference(rewrite,[status(thm)],[])).
% 1.32/1.57 tff(2127,plain,
% 1.32/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), z))))),
% 1.32/1.57 inference(monotonicity,[status(thm)],[2126])).
% 1.32/1.57 tff(2128,plain,
% 1.32/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 1.32/1.57 inference(transitivity,[status(thm)],[2127, 2125])).
% 1.32/1.57 tff(2129,plain,
% 1.32/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, s(s(s(z))))))),
% 1.32/1.57 inference(quant_inst,[status(thm)],[])).
% 1.32/1.57 tff(2130,plain,
% 1.32/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), z))),
% 1.32/1.57 inference(modus_ponens,[status(thm)],[2129, 2128])).
% 1.32/1.57 tff(2131,plain,
% 1.32/1.57 (~r(elem!1, s(s(s(z))))),
% 1.32/1.57 inference(unit_resolution,[status(thm)],[2130, 37, 155, 2124])).
% 1.32/1.57 tff(2132,plain,
% 1.32/1.57 (elem!1 = s(s(s(z)))),
% 1.32/1.57 inference(unit_resolution,[status(thm)],[1279, 2131, 2120])).
% 1.32/1.57 tff(2133,plain,
% 1.32/1.57 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 1.32/1.57 inference(monotonicity,[status(thm)],[2132])).
% 1.32/1.57 tff(2134,plain,
% 1.32/1.57 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.32/1.57 inference(symmetry,[status(thm)],[2133])).
% 1.32/1.57 tff(2135,plain,
% 1.32/1.57 ((~b(s(s(s(z))), s(s(s(s(z)))))) <=> (~b(elem!1, s(s(s(s(z))))))),
% 1.32/1.57 inference(monotonicity,[status(thm)],[2134])).
% 1.32/1.57 tff(2136,plain,
% 1.32/1.57 (~b(elem!1, s(s(s(s(z)))))),
% 1.32/1.57 inference(modus_ponens,[status(thm)],[2104, 2135])).
% 1.32/1.57 tff(2137,plain,
% 1.32/1.57 ($false),
% 1.32/1.57 inference(unit_resolution,[status(thm)],[286, 2136])).
% 1.32/1.57 tff(2138,plain,(b(s(s(s(z))), s(s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~r(elem!1, z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.57 tff(2139,plain,
% 1.32/1.57 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.32/1.57 inference(unit_resolution,[status(thm)],[2138, 2103, 286, 2095, 1391, 372, 2070, 1440])).
% 1.32/1.57 tff(2140,plain,
% 1.32/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.32/1.57 inference(rewrite,[status(thm)],[])).
% 1.32/1.57 tff(2141,plain,
% 1.32/1.57 (((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.32/1.57 inference(rewrite,[status(thm)],[])).
% 1.32/1.57 tff(2142,plain,
% 1.32/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.32/1.57 inference(monotonicity,[status(thm)],[2141])).
% 1.32/1.57 tff(2143,plain,
% 1.32/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.32/1.57 inference(transitivity,[status(thm)],[2142, 2140])).
% 1.32/1.57 tff(2144,plain,
% 1.32/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))))),
% 1.32/1.57 inference(quant_inst,[status(thm)],[])).
% 1.32/1.57 tff(2145,plain,
% 1.32/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.32/1.57 inference(modus_ponens,[status(thm)],[2144, 2143])).
% 1.32/1.57 tff(2146,plain,
% 1.32/1.57 (~b(elem!1, s(s(s(z))))),
% 1.32/1.57 inference(unit_resolution,[status(thm)],[2145, 75, 286, 2139, 287])).
% 1.32/1.57 tff(2147,plain,
% 1.32/1.57 ((s(s(s(z))) = s(s(z))) <=> (s(s(z)) = s(s(s(z))))),
% 1.32/1.57 inference(commutativity,[status(thm)],[])).
% 1.32/1.57 tff(2148,plain,
% 1.32/1.57 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(z)))),
% 1.32/1.57 inference(symmetry,[status(thm)],[2147])).
% 1.32/1.57 tff(2149,plain,
% 1.32/1.57 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(z))))),
% 1.32/1.57 inference(monotonicity,[status(thm)],[2148])).
% 1.32/1.57 tff(2150,plain,
% 1.32/1.57 (~(s(s(s(z))) = s(s(z)))),
% 1.32/1.57 inference(modus_ponens,[status(thm)],[1556, 2149])).
% 1.32/1.57 tff(2151,plain,
% 1.32/1.57 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 1.32/1.57 inference(symmetry,[status(thm)],[640])).
% 1.32/1.57 tff(2152,plain,
% 1.32/1.58 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(z))))),
% 1.32/1.58 inference(monotonicity,[status(thm)],[2151])).
% 1.32/1.58 tff(2153,plain,
% 1.32/1.58 (~(s(s(s(s(z)))) = s(s(z)))),
% 1.32/1.58 inference(modus_ponens,[status(thm)],[459, 2152])).
% 1.32/1.58 tff(2154,plain,
% 1.32/1.58 (~b(s(s(s(s(z)))), s(z))),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[1402, 75, 2095, 1391, 287])).
% 1.32/1.58 tff(2155,plain,
% 1.32/1.58 (r(s(s(s(s(z)))), s(z))),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[1406, 58, 2154, 483])).
% 1.32/1.58 tff(2156,plain,
% 1.32/1.58 (~b(s(s(z)), s(z))),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[1780, 2095, 1391, 2068, 372])).
% 1.32/1.58 tff(2157,plain,
% 1.32/1.58 (r(s(s(z)), s(z))),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[153, 2156])).
% 1.32/1.58 tff(2158,plain,
% 1.32/1.58 (((~![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(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), elem!1)))),
% 1.32/1.58 inference(rewrite,[status(thm)],[])).
% 1.32/1.58 tff(2159,plain,
% 1.32/1.58 (((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), elem!1)))),
% 1.32/1.58 inference(rewrite,[status(thm)],[])).
% 1.32/1.58 tff(2160,plain,
% 1.32/1.58 (((~![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(s(s(z)))), s(z))) | (~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)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), elem!1))))),
% 1.32/1.58 inference(monotonicity,[status(thm)],[2159])).
% 1.32/1.58 tff(2161,plain,
% 1.32/1.58 (((~![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(s(s(z)))), s(z))) | (~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)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), elem!1)))),
% 1.32/1.58 inference(transitivity,[status(thm)],[2160, 2158])).
% 1.32/1.58 tff(2162,plain,
% 1.32/1.58 ((~![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(s(s(z)))), s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.32/1.58 inference(quant_inst,[status(thm)],[])).
% 1.32/1.58 tff(2163,plain,
% 1.32/1.58 ((~![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(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), elem!1))),
% 1.32/1.58 inference(modus_ponens,[status(thm)],[2162, 2161])).
% 1.32/1.58 tff(2164,plain,
% 1.32/1.58 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[2163, 37, 106, 2157, 2155])).
% 1.32/1.58 tff(2165,plain,
% 1.32/1.58 (((~![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))))),
% 1.32/1.58 inference(rewrite,[status(thm)],[])).
% 1.32/1.58 tff(2166,plain,
% 1.32/1.58 ((~![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))))),
% 1.32/1.58 inference(quant_inst,[status(thm)],[])).
% 1.32/1.58 tff(2167,plain,
% 1.32/1.58 ((~![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)))),
% 1.32/1.58 inference(modus_ponens,[status(thm)],[2166, 2165])).
% 1.32/1.58 tff(2168,plain,
% 1.32/1.58 ((s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z)))),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[2167, 58, 2164])).
% 1.32/1.58 tff(2169,plain,
% 1.32/1.58 (b(s(s(s(s(z)))), s(s(z)))),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[2168, 2153])).
% 1.32/1.58 tff(2170,plain,
% 1.32/1.58 (~b(s(s(s(z))), s(s(z)))),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[1163, 2139, 2169, 895])).
% 1.32/1.58 tff(2171,plain,
% 1.32/1.58 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z))))),
% 1.32/1.58 inference(rewrite,[status(thm)],[])).
% 1.32/1.58 tff(2172,plain,
% 1.32/1.58 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z))))),
% 1.32/1.58 inference(quant_inst,[status(thm)],[])).
% 1.32/1.58 tff(2173,plain,
% 1.32/1.58 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z)))),
% 1.32/1.58 inference(modus_ponens,[status(thm)],[2172, 2171])).
% 1.32/1.58 tff(2174,plain,
% 1.32/1.58 ((s(s(s(z))) = s(s(z))) | r(s(s(s(z))), s(s(z)))),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[2173, 58, 2170])).
% 1.32/1.58 tff(2175,plain,
% 1.32/1.58 (r(s(s(s(z))), s(s(z)))),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[2174, 2150])).
% 1.32/1.58 tff(2176,plain,
% 1.32/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(z)))))),
% 1.32/1.58 inference(rewrite,[status(thm)],[])).
% 1.32/1.58 tff(2177,plain,
% 1.32/1.58 (((~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(z)))))),
% 1.32/1.58 inference(rewrite,[status(thm)],[])).
% 1.32/1.58 tff(2178,plain,
% 1.32/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(z))))))),
% 1.32/1.58 inference(monotonicity,[status(thm)],[2177])).
% 1.32/1.58 tff(2179,plain,
% 1.32/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(z)))))),
% 1.32/1.58 inference(transitivity,[status(thm)],[2178, 2176])).
% 1.32/1.58 tff(2180,plain,
% 1.32/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(s(z))))))),
% 1.32/1.58 inference(quant_inst,[status(thm)],[])).
% 1.32/1.58 tff(2181,plain,
% 1.32/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(z))))),
% 1.32/1.58 inference(modus_ponens,[status(thm)],[2180, 2179])).
% 1.32/1.58 tff(2182,plain,
% 1.32/1.58 (~r(elem!1, s(s(s(z))))),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[2181, 37, 1489, 2175])).
% 1.32/1.58 tff(2183,plain,
% 1.32/1.58 (elem!1 = s(s(s(z)))),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[1279, 2182, 2146])).
% 1.32/1.58 tff(2184,plain,
% 1.32/1.58 (s(elem!1) = s(s(s(s(z))))),
% 1.32/1.58 inference(monotonicity,[status(thm)],[2183])).
% 1.32/1.58 tff(2185,plain,
% 1.32/1.58 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 1.32/1.58 inference(monotonicity,[status(thm)],[2184])).
% 1.32/1.58 tff(2186,plain,
% 1.32/1.58 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 1.32/1.58 inference(symmetry,[status(thm)],[2185])).
% 1.32/1.58 tff(2187,plain,
% 1.32/1.58 (r(z, s(s(s(s(s(z)))))) <=> r(z, s(s(elem!1)))),
% 1.32/1.58 inference(monotonicity,[status(thm)],[2186])).
% 1.32/1.58 tff(2188,plain,
% 1.32/1.58 (r(z, s(s(elem!1))) <=> r(z, s(s(s(s(s(z))))))),
% 1.32/1.58 inference(symmetry,[status(thm)],[2187])).
% 1.32/1.58 tff(2189,plain,
% 1.32/1.58 ((~r(z, s(s(elem!1)))) <=> (~r(z, s(s(s(s(s(z)))))))),
% 1.32/1.58 inference(monotonicity,[status(thm)],[2188])).
% 1.32/1.58 tff(2190,plain,
% 1.32/1.58 (~b(s(s(s(z))), elem!1)),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[1596, 75, 286, 2139, 287])).
% 1.32/1.58 tff(2191,plain,
% 1.32/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(z)))))),
% 1.32/1.58 inference(rewrite,[status(thm)],[])).
% 1.32/1.58 tff(2192,plain,
% 1.32/1.58 (((~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(z)))))),
% 1.32/1.58 inference(rewrite,[status(thm)],[])).
% 1.32/1.58 tff(2193,plain,
% 1.32/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(z))))))),
% 1.32/1.58 inference(monotonicity,[status(thm)],[2192])).
% 1.32/1.58 tff(2194,plain,
% 1.32/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(z)))))),
% 1.32/1.58 inference(transitivity,[status(thm)],[2193, 2191])).
% 1.32/1.58 tff(2195,plain,
% 1.32/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)))),
% 1.32/1.58 inference(quant_inst,[status(thm)],[])).
% 1.32/1.58 tff(2196,plain,
% 1.32/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(z))))),
% 1.32/1.58 inference(modus_ponens,[status(thm)],[2195, 2194])).
% 1.32/1.58 tff(2197,plain,
% 1.32/1.58 (~r(s(s(s(z))), elem!1)),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[2196, 37, 2103, 1489, 2175])).
% 1.32/1.58 tff(2198,plain,
% 1.32/1.58 (s(s(s(z))) = elem!1),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[1115, 2197, 2190])).
% 1.32/1.58 tff(2199,plain,
% 1.32/1.58 (r(s(z), s(elem!1))),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[1726, 2198, 1440])).
% 1.32/1.58 tff(2200,plain,
% 1.32/1.58 (b(s(elem!1), z) <=> b(s(s(s(s(z)))), z)),
% 1.32/1.58 inference(monotonicity,[status(thm)],[2184])).
% 1.32/1.58 tff(2201,plain,
% 1.32/1.58 (b(s(s(s(s(z)))), z) <=> b(s(elem!1), z)),
% 1.32/1.58 inference(symmetry,[status(thm)],[2200])).
% 1.32/1.58 tff(2202,plain,
% 1.32/1.58 ((~b(s(s(s(s(z)))), z)) <=> (~b(s(elem!1), z))),
% 1.32/1.58 inference(monotonicity,[status(thm)],[2201])).
% 1.32/1.58 tff(2203,plain,
% 1.32/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 1.32/1.58 inference(rewrite,[status(thm)],[])).
% 1.32/1.58 tff(2204,plain,
% 1.32/1.58 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 1.32/1.58 inference(rewrite,[status(thm)],[])).
% 1.32/1.58 tff(2205,plain,
% 1.32/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z))))),
% 1.32/1.58 inference(monotonicity,[status(thm)],[2204])).
% 1.32/1.58 tff(2206,plain,
% 1.32/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 1.32/1.58 inference(transitivity,[status(thm)],[2205, 2203])).
% 1.32/1.58 tff(2207,plain,
% 1.32/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))))),
% 1.32/1.58 inference(quant_inst,[status(thm)],[])).
% 1.32/1.58 tff(2208,plain,
% 1.32/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z))),
% 1.32/1.58 inference(modus_ponens,[status(thm)],[2207, 2206])).
% 1.32/1.58 tff(2209,plain,
% 1.32/1.58 ($false),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[2208, 75, 370, 401, 1423, 1154])).
% 1.32/1.58 tff(2210,plain,((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.58 tff(2211,plain,
% 1.32/1.58 (~b(s(s(s(s(z)))), z)),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[2210, 2169, 2066, 2068])).
% 1.32/1.58 tff(2212,plain,
% 1.32/1.58 (~b(s(elem!1), z)),
% 1.32/1.58 inference(modus_ponens,[status(thm)],[2211, 2202])).
% 1.32/1.58 tff(2213,plain,
% 1.32/1.58 (r(s(elem!1), z)),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[766, 2212])).
% 1.32/1.58 tff(2214,plain,
% 1.32/1.58 (~r(s(z), z)),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[1761, 2213, 2199])).
% 1.32/1.58 tff(2215,plain,
% 1.32/1.58 (b(s(z), z)),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[169, 2214])).
% 1.32/1.58 tff(2216,plain,
% 1.32/1.58 (~(elem!1 = s(s(elem!1)))),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[1612, 2198])).
% 1.32/1.58 tff(2217,assumption,(~r(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.32/1.58 tff(2218,plain,
% 1.32/1.58 (b(elem!1, s(s(elem!1)))),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[1617, 2217, 1630])).
% 1.32/1.58 tff(2219,plain,
% 1.32/1.58 (~(s(s(z)) = elem!1)),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[1013, 1011])).
% 1.32/1.58 tff(2220,plain,
% 1.32/1.58 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.32/1.58 inference(monotonicity,[status(thm)],[1602])).
% 1.32/1.58 tff(2221,plain,
% 1.32/1.58 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.32/1.58 inference(modus_ponens,[status(thm)],[287, 2220])).
% 1.32/1.58 tff(2222,plain,
% 1.32/1.58 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(elem!1)))),
% 1.32/1.58 inference(monotonicity,[status(thm)],[1602])).
% 1.32/1.58 tff(2223,plain,
% 1.32/1.58 (b(elem!1, s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 1.32/1.58 inference(monotonicity,[status(thm)],[1602])).
% 1.32/1.58 tff(2224,plain,
% 1.32/1.58 (b(s(s(elem!1)), s(s(z))) <=> b(elem!1, s(s(z)))),
% 1.32/1.58 inference(symmetry,[status(thm)],[2223])).
% 1.32/1.58 tff(2225,plain,
% 1.32/1.58 (b(s(s(elem!1)), s(s(z)))),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[1476, 501, 266])).
% 1.32/1.58 tff(2226,plain,
% 1.32/1.58 (b(elem!1, s(s(z)))),
% 1.32/1.58 inference(modus_ponens,[status(thm)],[2225, 2224])).
% 1.32/1.58 tff(2227,plain,
% 1.32/1.58 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[476, 115, 468])).
% 1.32/1.58 tff(2228,plain,
% 1.32/1.58 (b(s(s(z)), s(s(s(s(z)))))),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[463, 58, 2227, 459])).
% 1.32/1.58 tff(2229,plain,
% 1.32/1.58 ((s(s(z)) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(z)))),
% 1.32/1.58 inference(commutativity,[status(thm)],[])).
% 1.32/1.58 tff(2230,plain,
% 1.32/1.58 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(elem!1)))),
% 1.32/1.58 inference(monotonicity,[status(thm)],[1602])).
% 1.32/1.58 tff(2231,plain,
% 1.32/1.58 ((s(s(z)) = elem!1) <=> (s(s(elem!1)) = s(s(z)))),
% 1.32/1.58 inference(transitivity,[status(thm)],[2230, 2229])).
% 1.32/1.58 tff(2232,plain,
% 1.32/1.58 ((s(s(elem!1)) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 1.32/1.58 inference(symmetry,[status(thm)],[2231])).
% 1.32/1.58 tff(2233,plain,
% 1.32/1.58 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 1.32/1.58 inference(monotonicity,[status(thm)],[2232])).
% 1.32/1.58 tff(2234,plain,
% 1.32/1.58 (~(s(s(z)) = elem!1)),
% 1.32/1.58 inference(modus_ponens,[status(thm)],[266, 2233])).
% 1.32/1.58 tff(2235,plain,
% 1.32/1.58 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(s(elem!1)))),
% 1.32/1.58 inference(monotonicity,[status(thm)],[1602])).
% 1.32/1.58 tff(2236,plain,
% 1.32/1.58 (r(s(s(z)), s(s(elem!1))) <=> r(s(s(z)), elem!1)),
% 1.32/1.58 inference(symmetry,[status(thm)],[2235])).
% 1.32/1.58 tff(2237,plain,
% 1.32/1.58 ((~r(s(s(z)), s(s(elem!1)))) <=> (~r(s(s(z)), elem!1))),
% 1.32/1.58 inference(monotonicity,[status(thm)],[2236])).
% 1.32/1.58 tff(2238,plain,
% 1.32/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))))),
% 1.32/1.58 inference(rewrite,[status(thm)],[])).
% 1.32/1.58 tff(2239,plain,
% 1.32/1.58 (((~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(s(elem!1)))) | (~r(s(s(z)), s(z))))),
% 1.32/1.58 inference(rewrite,[status(thm)],[])).
% 1.32/1.58 tff(2240,plain,
% 1.32/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(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(s(elem!1)))) | (~r(s(s(z)), s(z)))))),
% 1.32/1.58 inference(monotonicity,[status(thm)],[2239])).
% 1.32/1.58 tff(2241,plain,
% 1.32/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(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(s(elem!1)))) | (~r(s(s(z)), s(z))))),
% 1.32/1.58 inference(transitivity,[status(thm)],[2240, 2238])).
% 1.32/1.58 tff(2242,plain,
% 1.32/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.32/1.58 inference(quant_inst,[status(thm)],[])).
% 1.32/1.58 tff(2243,plain,
% 1.32/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z)))),
% 1.32/1.58 inference(modus_ponens,[status(thm)],[2242, 2241])).
% 1.32/1.58 tff(2244,plain,
% 1.32/1.58 (~r(s(s(z)), s(s(elem!1)))),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[2243, 37, 494, 115])).
% 1.32/1.58 tff(2245,plain,
% 1.32/1.58 (~r(s(s(z)), elem!1)),
% 1.32/1.58 inference(modus_ponens,[status(thm)],[2244, 2237])).
% 1.32/1.58 tff(2246,plain,
% 1.32/1.58 (b(s(s(z)), elem!1)),
% 1.32/1.58 inference(unit_resolution,[status(thm)],[104, 2245, 2234])).
% 1.32/1.58 tff(2247,assumption,(b(elem!1, s(s(z)))), introduced(assumption)).
% 1.32/1.58 tff(2248,plain,
% 1.32/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(z)))))),
% 1.32/1.59 inference(rewrite,[status(thm)],[])).
% 1.32/1.59 tff(2249,plain,
% 1.32/1.59 (((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(z)))))),
% 1.32/1.59 inference(rewrite,[status(thm)],[])).
% 1.32/1.59 tff(2250,plain,
% 1.32/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(z))))))),
% 1.32/1.59 inference(monotonicity,[status(thm)],[2249])).
% 1.32/1.59 tff(2251,plain,
% 1.32/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(z)))))),
% 1.32/1.59 inference(transitivity,[status(thm)],[2250, 2248])).
% 1.32/1.59 tff(2252,plain,
% 1.32/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.32/1.59 inference(quant_inst,[status(thm)],[])).
% 1.32/1.59 tff(2253,plain,
% 1.32/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(z))))),
% 1.32/1.59 inference(modus_ponens,[status(thm)],[2252, 2251])).
% 1.32/1.59 tff(2254,plain,
% 1.32/1.59 ($false),
% 1.32/1.59 inference(unit_resolution,[status(thm)],[2253, 75, 964, 287, 2247, 895])).
% 1.32/1.59 tff(2255,plain,((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.59 tff(2256,plain,
% 1.32/1.59 (~b(elem!1, s(s(z)))),
% 1.32/1.59 inference(unit_resolution,[status(thm)],[2255, 2246, 287, 2228])).
% 1.32/1.59 tff(2257,plain,
% 1.32/1.59 ($false),
% 1.32/1.59 inference(unit_resolution,[status(thm)],[2256, 2226])).
% 1.32/1.59 tff(2258,plain,((~r(s(s(z)), s(z))) | (~(elem!1 = s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (s(s(elem!1)) = s(s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.32/1.59 tff(2259,plain,
% 1.32/1.59 (~r(s(s(z)), s(z))),
% 1.32/1.59 inference(unit_resolution,[status(thm)],[2258, 1602, 287, 266, 494, 468])).
% 1.32/1.59 tff(2260,plain,
% 1.32/1.59 (b(s(s(z)), s(z))),
% 1.32/1.59 inference(unit_resolution,[status(thm)],[153, 2259])).
% 1.32/1.59 tff(2261,plain,
% 1.32/1.59 (~b(z, s(s(z)))),
% 1.32/1.59 inference(unit_resolution,[status(thm)],[380, 2260, 371, 372])).
% 1.32/1.59 tff(2262,plain,
% 1.32/1.59 (r(z, s(s(z)))),
% 1.32/1.59 inference(unit_resolution,[status(thm)],[351, 2261])).
% 1.32/1.59 tff(2263,plain,
% 1.32/1.59 (~r(s(s(z)), elem!1)),
% 1.32/1.59 inference(unit_resolution,[status(thm)],[339, 2262, 300])).
% 1.32/1.59 tff(2264,plain,
% 1.32/1.59 (b(s(s(z)), elem!1)),
% 1.32/1.59 inference(unit_resolution,[status(thm)],[104, 2263, 15])).
% 1.32/1.59 tff(2265,plain,
% 1.32/1.59 (b(s(s(z)), s(s(elem!1)))),
% 1.32/1.59 inference(modus_ponens,[status(thm)],[2264, 2222])).
% 1.32/1.59 tff(2266,plain,
% 1.32/1.59 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.32/1.59 inference(monotonicity,[status(thm)],[1602])).
% 1.32/1.59 tff(2267,plain,
% 1.32/1.59 (~(s(s(s(z))) = elem!1)),
% 1.32/1.59 inference(unit_resolution,[status(thm)],[1612, 1602])).
% 1.32/1.59 tff(2268,plain,
% 1.32/1.59 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.32/1.59 inference(monotonicity,[status(thm)],[1602])).
% 1.32/1.59 tff(2269,plain,
% 1.32/1.59 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.32/1.59 inference(modus_ponens,[status(thm)],[286, 2268])).
% 1.32/1.59 tff(2270,plain,
% 1.32/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.32/1.59 inference(rewrite,[status(thm)],[])).
% 1.32/1.59 tff(2271,plain,
% 1.32/1.59 (((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.32/1.59 inference(rewrite,[status(thm)],[])).
% 1.32/1.59 tff(2272,plain,
% 1.32/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))))),
% 1.32/1.59 inference(monotonicity,[status(thm)],[2271])).
% 1.32/1.59 tff(2273,plain,
% 1.32/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.32/1.59 inference(transitivity,[status(thm)],[2272, 2270])).
% 1.32/1.59 tff(2274,plain,
% 1.32/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.32/1.59 inference(quant_inst,[status(thm)],[])).
% 1.32/1.59 tff(2275,plain,
% 1.32/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 1.32/1.59 inference(modus_ponens,[status(thm)],[2274, 2273])).
% 1.32/1.59 tff(2276,plain,
% 1.32/1.59 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.32/1.59 inference(unit_resolution,[status(thm)],[2275, 75, 2269, 2265, 2221])).
% 1.32/1.59 tff(2277,plain,
% 1.32/1.59 (r(s(s(z)), s(s(s(s(z)))))),
% 1.32/1.59 inference(unit_resolution,[status(thm)],[465, 2276])).
% 1.32/1.59 tff(2278,plain,
% 1.32/1.59 (~b(s(s(z)), z)),
% 1.32/1.59 inference(unit_resolution,[status(thm)],[194, 75, 372, 371, 2260])).
% 1.32/1.59 tff(2279,plain,
% 1.32/1.59 (r(s(s(z)), z)),
% 1.32/1.59 inference(unit_resolution,[status(thm)],[202, 2278])).
% 1.32/1.59 tff(2280,plain,
% 1.32/1.59 (((~![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(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(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(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 1.32/1.59 inference(rewrite,[status(thm)],[])).
% 1.32/1.59 tff(2281,plain,
% 1.32/1.59 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 1.32/1.59 inference(rewrite,[status(thm)],[])).
% 1.32/1.59 tff(2282,plain,
% 1.32/1.59 (((~![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(s(s(s(z)))))) | (~r(s(z), s(s(s(s(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(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(z))))))))),
% 1.32/1.59 inference(monotonicity,[status(thm)],[2281])).
% 1.32/1.59 tff(2283,plain,
% 1.32/1.59 (((~![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(s(s(s(z)))))) | (~r(s(z), s(s(s(s(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(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 1.32/1.59 inference(transitivity,[status(thm)],[2282, 2280])).
% 1.32/1.59 tff(2284,plain,
% 1.32/1.59 ((~![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(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))),
% 1.32/1.59 inference(quant_inst,[status(thm)],[])).
% 1.32/1.59 tff(2285,plain,
% 1.32/1.59 ((~![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(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(z))))))),
% 1.32/1.59 inference(modus_ponens,[status(thm)],[2284, 2283])).
% 1.32/1.59 tff(2286,plain,
% 1.32/1.59 (~r(s(z), s(s(z)))),
% 1.32/1.59 inference(unit_resolution,[status(thm)],[2285, 37, 2279, 468, 2277])).
% 1.32/1.59 tff(2287,plain,
% 1.32/1.59 (b(s(z), s(s(z)))),
% 1.32/1.59 inference(unit_resolution,[status(thm)],[416, 2286])).
% 1.32/1.59 tff(2288,plain,
% 1.32/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.32/1.59 inference(rewrite,[status(thm)],[])).
% 1.32/1.59 tff(2289,plain,
% 1.32/1.59 (((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.32/1.59 inference(rewrite,[status(thm)],[])).
% 1.32/1.59 tff(2290,plain,
% 1.32/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(elem!1))))))),
% 1.32/1.59 inference(monotonicity,[status(thm)],[2289])).
% 1.32/1.59 tff(2291,plain,
% 1.32/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.32/1.59 inference(transitivity,[status(thm)],[2290, 2288])).
% 1.32/1.59 tff(2292,plain,
% 1.32/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.32/1.59 inference(quant_inst,[status(thm)],[])).
% 1.32/1.59 tff(2293,plain,
% 1.32/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 1.32/1.59 inference(modus_ponens,[status(thm)],[2292, 2291])).
% 1.32/1.59 tff(2294,plain,
% 1.32/1.59 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.32/1.59 inference(unit_resolution,[status(thm)],[2293, 75, 2269, 2265, 2221])).
% 1.32/1.59 tff(2295,plain,
% 1.32/1.59 ((s(s(s(s(z)))) = s(s(z))) | r(s(s(s(s(z)))), s(s(z)))),
% 1.32/1.59 inference(unit_resolution,[status(thm)],[2167, 58, 2294])).
% 1.32/1.59 tff(2296,plain,
% 1.32/1.59 (r(s(s(s(s(z)))), s(s(z)))),
% 1.32/1.59 inference(unit_resolution,[status(thm)],[2295, 2153])).
% 1.32/1.59 tff(2297,plain,
% 1.32/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))))),
% 1.32/1.59 inference(rewrite,[status(thm)],[])).
% 1.32/1.59 tff(2298,plain,
% 1.32/1.59 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))))),
% 1.32/1.59 inference(rewrite,[status(thm)],[])).
% 1.32/1.59 tff(2299,plain,
% 1.32/1.59 (((~![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(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z))))))))),
% 1.32/1.59 inference(monotonicity,[status(thm)],[2298])).
% 1.32/1.59 tff(2300,plain,
% 1.32/1.59 (((~![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(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))))),
% 1.32/1.59 inference(transitivity,[status(thm)],[2299, 2297])).
% 1.32/1.59 tff(2301,plain,
% 1.32/1.59 ((~![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(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))))),
% 1.32/1.59 inference(quant_inst,[status(thm)],[])).
% 1.32/1.59 tff(2302,plain,
% 1.32/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z))))))),
% 1.32/1.59 inference(modus_ponens,[status(thm)],[2301, 2300])).
% 1.32/1.59 tff(2303,plain,
% 1.32/1.59 (~r(z, s(s(s(s(z)))))),
% 1.32/1.59 inference(unit_resolution,[status(thm)],[2302, 37, 2262, 2296])).
% 1.32/1.59 tff(2304,plain,
% 1.32/1.59 ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z)))))),
% 1.32/1.59 inference(unit_resolution,[status(thm)],[1515, 58, 2303])).
% 1.32/1.59 tff(2305,plain,
% 1.32/1.59 (b(z, s(s(s(s(z)))))),
% 1.32/1.59 inference(unit_resolution,[status(thm)],[2304, 1503])).
% 1.32/1.59 tff(2306,plain,
% 1.32/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.32/1.59 inference(rewrite,[status(thm)],[])).
% 1.32/1.59 tff(2307,plain,
% 1.32/1.59 (((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.32/1.59 inference(rewrite,[status(thm)],[])).
% 1.32/1.59 tff(2308,plain,
% 1.32/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))))),
% 1.32/1.59 inference(monotonicity,[status(thm)],[2307])).
% 1.32/1.59 tff(2309,plain,
% 1.32/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.32/1.59 inference(transitivity,[status(thm)],[2308, 2306])).
% 1.32/1.59 tff(2310,plain,
% 1.32/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), z)))),
% 1.32/1.59 inference(quant_inst,[status(thm)],[])).
% 1.32/1.59 tff(2311,plain,
% 1.32/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 1.32/1.59 inference(modus_ponens,[status(thm)],[2310, 2309])).
% 1.32/1.59 tff(2312,plain,
% 1.42/1.60 (~b(s(s(elem!1)), z)),
% 1.42/1.60 inference(unit_resolution,[status(thm)],[2311, 75, 2269, 2221, 2305])).
% 1.42/1.60 tff(2313,plain,
% 1.42/1.60 (r(s(s(elem!1)), z)),
% 1.42/1.60 inference(unit_resolution,[status(thm)],[518, 58, 515, 2312])).
% 1.42/1.60 tff(2314,plain,
% 1.42/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.42/1.60 inference(rewrite,[status(thm)],[])).
% 1.42/1.60 tff(2315,plain,
% 1.42/1.60 (((~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(z)), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.42/1.60 inference(rewrite,[status(thm)],[])).
% 1.42/1.60 tff(2316,plain,
% 1.42/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), 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(z)), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(z))))))),
% 1.42/1.60 inference(monotonicity,[status(thm)],[2315])).
% 1.42/1.60 tff(2317,plain,
% 1.42/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), 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(z)), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.42/1.60 inference(transitivity,[status(thm)],[2316, 2314])).
% 1.42/1.60 tff(2318,plain,
% 1.42/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.42/1.60 inference(quant_inst,[status(thm)],[])).
% 1.42/1.60 tff(2319,plain,
% 1.42/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(z))))),
% 1.42/1.60 inference(modus_ponens,[status(thm)],[2318, 2317])).
% 1.42/1.60 tff(2320,plain,
% 1.42/1.60 (~r(s(s(elem!1)), s(s(z)))),
% 1.42/1.60 inference(unit_resolution,[status(thm)],[2319, 37, 2279, 2313])).
% 1.42/1.60 tff(2321,plain,
% 1.42/1.60 (b(s(s(elem!1)), s(s(z)))),
% 1.42/1.60 inference(unit_resolution,[status(thm)],[1476, 2320, 266])).
% 1.42/1.60 tff(2322,plain,
% 1.42/1.60 (~b(s(z), s(s(elem!1)))),
% 1.42/1.60 inference(unit_resolution,[status(thm)],[1994, 2321, 2287, 2260])).
% 1.42/1.60 tff(2323,plain,
% 1.42/1.60 (s(s(elem!1)) = elem!1),
% 1.42/1.60 inference(symmetry,[status(thm)],[1602])).
% 1.42/1.60 tff(2324,plain,
% 1.42/1.60 (b(s(z), s(s(elem!1))) <=> b(s(z), elem!1)),
% 1.42/1.60 inference(monotonicity,[status(thm)],[2323])).
% 1.42/1.60 tff(2325,plain,
% 1.42/1.60 (b(s(z), elem!1) <=> b(s(z), s(s(elem!1)))),
% 1.42/1.60 inference(symmetry,[status(thm)],[2324])).
% 1.42/1.60 tff(2326,plain,
% 1.42/1.60 (b(s(z), s(s(elem!1)))),
% 1.42/1.60 inference(modus_ponens,[status(thm)],[107, 2325])).
% 1.42/1.60 tff(2327,assumption,(~b(s(z), s(s(elem!1)))), introduced(assumption)).
% 1.42/1.60 tff(2328,plain,
% 1.42/1.60 ($false),
% 1.42/1.60 inference(unit_resolution,[status(thm)],[2327, 2326])).
% 1.42/1.60 tff(2329,plain,((~(elem!1 = s(s(elem!1)))) | b(s(z), s(s(elem!1))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.42/1.60 tff(2330,plain,
% 1.42/1.60 (~b(s(z), elem!1)),
% 1.42/1.60 inference(unit_resolution,[status(thm)],[2329, 2322, 1602])).
% 1.42/1.60 tff(2331,plain,
% 1.42/1.60 (r(s(z), elem!1)),
% 1.42/1.60 inference(unit_resolution,[status(thm)],[601, 2330, 108])).
% 1.42/1.60 tff(2332,plain,
% 1.42/1.60 (~r(s(s(s(z))), elem!1)),
% 1.42/1.60 inference(unit_resolution,[status(thm)],[1362, 2331, 300])).
% 1.42/1.60 tff(2333,plain,
% 1.42/1.60 (b(s(s(s(z))), elem!1)),
% 1.42/1.60 inference(unit_resolution,[status(thm)],[1115, 2332, 2267])).
% 1.42/1.60 tff(2334,plain,
% 1.42/1.60 (b(s(s(s(z))), s(s(elem!1)))),
% 1.42/1.60 inference(modus_ponens,[status(thm)],[2333, 2266])).
% 1.42/1.60 tff(2335,plain,
% 1.42/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.42/1.60 inference(rewrite,[status(thm)],[])).
% 1.42/1.60 tff(2336,plain,
% 1.42/1.60 (((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.42/1.60 inference(rewrite,[status(thm)],[])).
% 1.42/1.60 tff(2337,plain,
% 1.42/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1))))))),
% 1.42/1.60 inference(monotonicity,[status(thm)],[2336])).
% 1.42/1.60 tff(2338,plain,
% 1.42/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.42/1.60 inference(transitivity,[status(thm)],[2337, 2335])).
% 1.42/1.60 tff(2339,plain,
% 1.42/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.42/1.60 inference(quant_inst,[status(thm)],[])).
% 1.42/1.60 tff(2340,plain,
% 1.42/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 1.42/1.60 inference(modus_ponens,[status(thm)],[2339, 2338])).
% 1.42/1.60 tff(2341,plain,
% 1.42/1.60 (~b(s(s(z)), s(s(s(z))))),
% 1.42/1.60 inference(unit_resolution,[status(thm)],[2340, 75, 2269, 2334, 2265, 2221])).
% 1.42/1.60 tff(2342,plain,
% 1.42/1.60 (r(s(s(z)), s(s(s(z))))),
% 1.42/1.60 inference(unit_resolution,[status(thm)],[1559, 58, 1556, 2341])).
% 1.42/1.60 tff(2343,plain,
% 1.42/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.42/1.60 inference(rewrite,[status(thm)],[])).
% 1.42/1.60 tff(2344,plain,
% 1.42/1.60 (((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.42/1.60 inference(rewrite,[status(thm)],[])).
% 1.42/1.60 tff(2345,plain,
% 1.42/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1))))))),
% 1.42/1.60 inference(monotonicity,[status(thm)],[2344])).
% 1.42/1.60 tff(2346,plain,
% 1.42/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.42/1.60 inference(transitivity,[status(thm)],[2345, 2343])).
% 1.42/1.60 tff(2347,plain,
% 1.42/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.42/1.60 inference(quant_inst,[status(thm)],[])).
% 1.42/1.60 tff(2348,plain,
% 1.42/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 1.42/1.60 inference(modus_ponens,[status(thm)],[2347, 2346])).
% 1.42/1.60 tff(2349,plain,
% 1.42/1.60 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.42/1.60 inference(unit_resolution,[status(thm)],[2348, 75, 2269, 2334, 2221])).
% 1.42/1.60 tff(2350,plain,
% 1.42/1.60 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.42/1.60 inference(unit_resolution,[status(thm)],[575, 2349])).
% 1.42/1.60 tff(2351,plain,
% 1.42/1.60 ($false),
% 1.42/1.60 inference(unit_resolution,[status(thm)],[1548, 37, 2350, 2277, 2342])).
% 1.42/1.60 tff(2352,plain,((~(elem!1 = s(s(elem!1)))) | (~r(z, elem!1)) | (s(z) = elem!1) | (s(s(elem!1)) = s(s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (s(s(z)) = elem!1) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.42/1.60 tff(2353,plain,
% 1.42/1.60 (~(elem!1 = s(s(elem!1)))),
% 1.42/1.60 inference(unit_resolution,[status(thm)],[2352, 2219, 108, 266, 468, 300, 371, 372, 286, 287, 494])).
% 1.42/1.60 tff(2354,plain,
% 1.42/1.60 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.42/1.60 inference(unit_resolution,[status(thm)],[1655, 494, 468])).
% 1.42/1.60 tff(2355,plain,
% 1.42/1.60 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.42/1.60 inference(unit_resolution,[status(thm)],[1660, 1011, 2354])).
% 1.42/1.60 tff(2356,plain,
% 1.42/1.60 (~b(elem!1, s(s(elem!1)))),
% 1.42/1.60 inference(unit_resolution,[status(thm)],[1628, 2355, 287, 286])).
% 1.42/1.60 tff(2357,plain,
% 1.42/1.60 ($false),
% 1.42/1.60 inference(unit_resolution,[status(thm)],[1617, 2356, 2353, 2217])).
% 1.42/1.60 tff(2358,plain,((s(s(elem!1)) = s(s(s(s(z))))) | r(elem!1, s(s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (s(z) = elem!1) | (s(s(elem!1)) = s(s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.42/1.60 tff(2359,plain,
% 1.42/1.60 (~r(s(s(elem!1)), s(z))),
% 1.42/1.60 inference(unit_resolution,[status(thm)],[2358, 2217, 1011, 108, 287, 266, 286, 300, 1440, 371, 372])).
% 1.42/1.60 tff(2360,plain,
% 1.42/1.60 (b(s(s(elem!1)), s(z))),
% 1.42/1.60 inference(unit_resolution,[status(thm)],[561, 2359])).
% 1.42/1.60 tff(2361,plain,
% 1.42/1.60 ($false),
% 1.42/1.60 inference(unit_resolution,[status(thm)],[1638, 2360, 2218, 1391, 107])).
% 1.42/1.60 tff(2362,plain,(r(elem!1, s(s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (elem!1 = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(s(z))))) | (s(z) = elem!1) | (~b(s(s(s(s(z)))), elem!1)) | (s(s(elem!1)) = s(s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~r(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.42/1.60 tff(2363,plain,
% 1.42/1.60 (r(elem!1, s(s(elem!1)))),
% 1.42/1.60 inference(unit_resolution,[status(thm)],[2362, 2095, 1391, 2216, 1011, 2094, 287, 266, 286, 299, 2215, 372])).
% 1.42/1.60 tff(2364,assumption,(r(z, s(s(elem!1)))), introduced(assumption)).
% 1.42/1.60 tff(2365,plain,
% 1.42/1.60 (((~![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)))))),
% 1.42/1.60 inference(rewrite,[status(thm)],[])).
% 1.42/1.60 tff(2366,plain,
% 1.42/1.60 (((~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)))))),
% 1.42/1.60 inference(rewrite,[status(thm)],[])).
% 1.42/1.60 tff(2367,plain,
% 1.42/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(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))))))),
% 1.42/1.60 inference(monotonicity,[status(thm)],[2366])).
% 1.42/1.60 tff(2368,plain,
% 1.42/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(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)))))),
% 1.42/1.60 inference(transitivity,[status(thm)],[2367, 2365])).
% 1.42/1.60 tff(2369,plain,
% 1.42/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)))),
% 1.42/1.60 inference(quant_inst,[status(thm)],[])).
% 1.42/1.60 tff(2370,plain,
% 1.42/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))),
% 1.42/1.60 inference(modus_ponens,[status(thm)],[2369, 2368])).
% 1.42/1.60 tff(2371,plain,
% 1.42/1.60 ($false),
% 1.42/1.60 inference(unit_resolution,[status(thm)],[2370, 37, 300, 1490, 2364])).
% 1.42/1.60 tff(2372,plain,((~r(z, s(s(elem!1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.42/1.60 tff(2373,plain,
% 1.42/1.60 (~r(z, s(s(elem!1)))),
% 1.42/1.60 inference(unit_resolution,[status(thm)],[2372, 2363, 299])).
% 1.42/1.60 tff(2374,plain,
% 1.42/1.60 (~r(z, s(s(s(s(s(z))))))),
% 1.42/1.60 inference(modus_ponens,[status(thm)],[2373, 2189])).
% 1.42/1.60 tff(2375,plain,
% 1.42/1.60 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.42/1.60 inference(monotonicity,[status(thm)],[2186])).
% 1.42/1.60 tff(2376,plain,
% 1.42/1.61 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 1.42/1.61 inference(symmetry,[status(thm)],[2375])).
% 1.42/1.61 tff(2377,plain,
% 1.42/1.61 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.42/1.61 inference(monotonicity,[status(thm)],[2186])).
% 1.42/1.61 tff(2378,plain,
% 1.42/1.61 ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) <=> (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 1.42/1.61 inference(monotonicity,[status(thm)],[2377])).
% 1.42/1.61 tff(2379,plain,
% 1.42/1.61 (~r(s(s(elem!1)), s(s(z)))),
% 1.42/1.61 inference(unit_resolution,[status(thm)],[1498, 2363, 1489])).
% 1.42/1.61 tff(2380,plain,
% 1.42/1.61 (b(s(s(elem!1)), s(s(z)))),
% 1.42/1.61 inference(unit_resolution,[status(thm)],[1476, 2379, 266])).
% 1.42/1.61 tff(2381,plain,
% 1.42/1.61 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.42/1.61 inference(monotonicity,[status(thm)],[2183])).
% 1.42/1.61 tff(2382,plain,
% 1.42/1.61 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.42/1.61 inference(modus_ponens,[status(thm)],[287, 2381])).
% 1.42/1.61 tff(2383,assumption,(b(s(s(s(s(s(z))))), s(s(s(s(z)))))), introduced(assumption)).
% 1.42/1.61 tff(2384,plain,
% 1.42/1.61 (s(elem!1) = s(s(s(s(z))))),
% 1.42/1.61 inference(monotonicity,[status(thm)],[1029])).
% 1.42/1.61 tff(2385,plain,
% 1.42/1.61 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 1.42/1.61 inference(monotonicity,[status(thm)],[2384])).
% 1.42/1.61 tff(2386,plain,
% 1.42/1.61 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 1.42/1.61 inference(symmetry,[status(thm)],[2385])).
% 1.42/1.61 tff(2387,plain,
% 1.42/1.61 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 1.42/1.61 inference(monotonicity,[status(thm)],[2386])).
% 1.42/1.61 tff(2388,plain,
% 1.42/1.61 (b(s(s(elem!1)), s(s(z))) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 1.42/1.61 inference(symmetry,[status(thm)],[2387])).
% 1.42/1.61 tff(2389,plain,
% 1.42/1.61 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.42/1.61 inference(modus_ponens,[status(thm)],[1283, 2388])).
% 1.42/1.61 tff(2390,assumption,(b(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 1.42/1.61 tff(2391,plain,
% 1.42/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.42/1.61 inference(rewrite,[status(thm)],[])).
% 1.42/1.61 tff(2392,plain,
% 1.42/1.61 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.42/1.61 inference(rewrite,[status(thm)],[])).
% 1.42/1.61 tff(2393,plain,
% 1.42/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 1.42/1.61 inference(monotonicity,[status(thm)],[2392])).
% 1.42/1.61 tff(2394,plain,
% 1.42/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.42/1.61 inference(transitivity,[status(thm)],[2393, 2391])).
% 1.42/1.61 tff(2395,plain,
% 1.42/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.42/1.61 inference(quant_inst,[status(thm)],[])).
% 1.42/1.61 tff(2396,plain,
% 1.42/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 1.42/1.61 inference(modus_ponens,[status(thm)],[2395, 2394])).
% 1.42/1.61 tff(2397,plain,
% 1.42/1.61 ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 1.42/1.61 inference(unit_resolution,[status(thm)],[2396, 75, 2390, 983, 895])).
% 1.42/1.61 tff(2398,plain,
% 1.42/1.61 ($false),
% 1.42/1.61 inference(unit_resolution,[status(thm)],[2397, 2389, 2383])).
% 1.42/1.61 tff(2399,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(z)))) | (~(elem!1 = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.42/1.61 tff(2400,plain,
% 1.42/1.61 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.42/1.61 inference(unit_resolution,[status(thm)],[2399, 2382, 2139, 895, 2380, 2183])).
% 1.42/1.61 tff(2401,plain,
% 1.42/1.61 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.42/1.61 inference(modus_ponens,[status(thm)],[2400, 2378])).
% 1.42/1.61 tff(2402,plain,
% 1.42/1.61 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.42/1.61 inference(unit_resolution,[status(thm)],[1660, 2401, 1011])).
% 1.42/1.61 tff(2403,plain,
% 1.42/1.61 (~r(s(s(elem!1)), s(z))),
% 1.42/1.61 inference(unit_resolution,[status(thm)],[1655, 2402, 1440])).
% 1.42/1.61 tff(2404,plain,
% 1.42/1.61 (b(s(s(elem!1)), s(z))),
% 1.42/1.61 inference(unit_resolution,[status(thm)],[561, 2403])).
% 1.42/1.61 tff(2405,plain,
% 1.42/1.61 (b(s(s(s(s(s(z))))), s(z))),
% 1.42/1.61 inference(modus_ponens,[status(thm)],[2404, 2376])).
% 1.42/1.61 tff(2406,plain,
% 1.42/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.42/1.61 inference(rewrite,[status(thm)],[])).
% 1.42/1.61 tff(2407,plain,
% 1.42/1.61 (((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.42/1.61 inference(rewrite,[status(thm)],[])).
% 1.42/1.61 tff(2408,plain,
% 1.42/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))), s(z))) | (~b(z, s(z))) | (~b(s(z), 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(X1, 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(z))))), s(z))) | (~b(z, s(s(s(s(s(z)))))))))),
% 1.42/1.61 inference(monotonicity,[status(thm)],[2407])).
% 1.42/1.61 tff(2409,plain,
% 1.42/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))), s(z))) | (~b(z, s(z))) | (~b(s(z), 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(X1, 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(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.42/1.61 inference(transitivity,[status(thm)],[2408, 2406])).
% 1.42/1.61 tff(2410,plain,
% 1.42/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.42/1.61 inference(quant_inst,[status(thm)],[])).
% 1.42/1.61 tff(2411,plain,
% 1.42/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))), s(z))) | (~b(z, s(s(s(s(s(z)))))))),
% 1.42/1.61 inference(modus_ponens,[status(thm)],[2410, 2409])).
% 1.42/1.61 tff(2412,plain,
% 1.42/1.61 ((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z)))))))),
% 1.42/1.61 inference(unit_resolution,[status(thm)],[2411, 75, 372, 2215])).
% 1.42/1.61 tff(2413,plain,
% 1.42/1.61 (~b(z, s(s(s(s(s(z))))))),
% 1.42/1.61 inference(unit_resolution,[status(thm)],[2412, 2405])).
% 1.42/1.61 tff(2414,plain,
% 1.42/1.61 (((~![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)))))))),
% 1.42/1.61 inference(rewrite,[status(thm)],[])).
% 1.42/1.61 tff(2415,plain,
% 1.42/1.61 ((~![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)))))))),
% 1.42/1.61 inference(quant_inst,[status(thm)],[])).
% 1.42/1.61 tff(2416,plain,
% 1.42/1.61 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z))))))),
% 1.42/1.61 inference(modus_ponens,[status(thm)],[2415, 2414])).
% 1.42/1.61 tff(2417,plain,
% 1.42/1.61 ((z = s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z))))))),
% 1.42/1.61 inference(unit_resolution,[status(thm)],[2416, 58, 2413])).
% 1.42/1.61 tff(2418,plain,
% 1.42/1.61 ($false),
% 1.42/1.61 inference(unit_resolution,[status(thm)],[2417, 2374, 2064])).
% 1.42/1.61 tff(2419,plain,((~b(z, s(z))) | (s(s(elem!1)) = s(s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (s(s(elem!1)) = s(s(z))) | (~r(elem!1, s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.42/1.61 tff(2420,plain,
% 1.42/1.61 (~r(elem!1, s(s(z)))),
% 1.42/1.61 inference(unit_resolution,[status(thm)],[2419, 2060, 372, 266, 1426, 1391, 287, 286, 889, 285])).
% 1.42/1.61 tff(2421,plain,
% 1.42/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(z)))))),
% 1.42/1.61 inference(rewrite,[status(thm)],[])).
% 1.42/1.61 tff(2422,plain,
% 1.42/1.61 (((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z))))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(z)))))),
% 1.42/1.61 inference(rewrite,[status(thm)],[])).
% 1.42/1.61 tff(2423,plain,
% 1.42/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, 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(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(z))))))),
% 1.42/1.61 inference(monotonicity,[status(thm)],[2422])).
% 1.42/1.61 tff(2424,plain,
% 1.42/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, 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(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(z)))))),
% 1.42/1.61 inference(transitivity,[status(thm)],[2423, 2421])).
% 1.42/1.61 tff(2425,plain,
% 1.42/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))))),
% 1.42/1.61 inference(quant_inst,[status(thm)],[])).
% 1.42/1.61 tff(2426,plain,
% 1.42/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(z))))),
% 1.42/1.61 inference(modus_ponens,[status(thm)],[2425, 2424])).
% 1.42/1.61 tff(2427,plain,
% 1.42/1.61 (~b(elem!1, s(s(z)))),
% 1.42/1.61 inference(unit_resolution,[status(thm)],[2426, 75, 286, 287, 2060])).
% 1.42/1.61 tff(2428,plain,
% 1.42/1.61 (elem!1 = s(s(z))),
% 1.42/1.61 inference(unit_resolution,[status(thm)],[398, 58, 2427, 2420])).
% 1.42/1.61 tff(2429,plain,
% 1.42/1.61 (s(s(z)) = elem!1),
% 1.42/1.61 inference(symmetry,[status(thm)],[2428])).
% 1.42/1.61 tff(2430,plain,
% 1.42/1.61 ($false),
% 1.42/1.61 inference(unit_resolution,[status(thm)],[15, 2429])).
% 1.42/1.61 tff(2431,plain,((s(s(z)) = elem!1) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(z))) | (s(s(elem!1)) = s(s(z))) | (~b(elem!1, s(z))) | b(z, elem!1) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.42/1.61 tff(2432,plain,
% 1.42/1.61 (s(s(z)) = elem!1),
% 1.42/1.61 inference(unit_resolution,[status(thm)],[2431, 2058, 287, 286, 266, 1376, 285, 99])).
% 1.42/1.61 tff(2433,plain,
% 1.42/1.61 ((s(s(s(s(s(s(s(z))))))) = s(s(z))) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.42/1.61 inference(monotonicity,[status(thm)],[2432])).
% 1.42/1.61 tff(2434,plain,
% 1.42/1.61 ((~(s(s(s(s(s(s(s(z))))))) = s(s(z)))) <=> (~(s(s(s(s(s(s(s(z))))))) = elem!1))),
% 1.42/1.61 inference(monotonicity,[status(thm)],[2433])).
% 1.42/1.61 tff(2435,plain,
% 1.42/1.61 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.42/1.61 inference(modus_ponens,[status(thm)],[1045, 2434])).
% 1.42/1.61 tff(2436,plain,
% 1.42/1.61 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.42/1.61 inference(unit_resolution,[status(thm)],[1145, 2432])).
% 1.42/1.61 tff(2437,plain,
% 1.42/1.61 (s(s(s(z))) = s(elem!1)),
% 1.42/1.61 inference(monotonicity,[status(thm)],[2432])).
% 1.42/1.61 tff(2438,plain,
% 1.42/1.61 (s(elem!1) = s(s(s(z)))),
% 1.42/1.61 inference(symmetry,[status(thm)],[2437])).
% 1.42/1.61 tff(2439,plain,
% 1.42/1.61 (r(s(elem!1), elem!1) <=> r(s(s(s(z))), elem!1)),
% 1.42/1.61 inference(monotonicity,[status(thm)],[2438])).
% 1.42/1.61 tff(2440,plain,
% 1.42/1.61 (r(s(s(s(z))), elem!1) <=> r(s(elem!1), elem!1)),
% 1.42/1.61 inference(symmetry,[status(thm)],[2439])).
% 1.42/1.61 tff(2441,plain,
% 1.42/1.61 (~b(s(z), s(s(s(s(z)))))),
% 1.42/1.61 inference(unit_resolution,[status(thm)],[1438, 1376, 286, 287])).
% 1.42/1.61 tff(2442,plain,
% 1.42/1.61 (r(s(z), s(s(s(s(z)))))),
% 1.42/1.61 inference(unit_resolution,[status(thm)],[489, 2441])).
% 1.42/1.61 tff(2443,plain,
% 1.42/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.42/1.61 inference(rewrite,[status(thm)],[])).
% 1.42/1.61 tff(2444,plain,
% 1.42/1.61 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.42/1.61 inference(rewrite,[status(thm)],[])).
% 1.42/1.61 tff(2445,plain,
% 1.42/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.42/1.61 inference(monotonicity,[status(thm)],[2444])).
% 1.42/1.61 tff(2446,plain,
% 1.42/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.42/1.61 inference(transitivity,[status(thm)],[2445, 2443])).
% 1.42/1.61 tff(2447,plain,
% 1.42/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))),
% 1.42/1.61 inference(quant_inst,[status(thm)],[])).
% 1.42/1.61 tff(2448,plain,
% 1.42/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.42/1.61 inference(modus_ponens,[status(thm)],[2447, 2446])).
% 1.42/1.61 tff(2449,plain,
% 1.42/1.61 (~r(s(s(s(z))), s(z))),
% 1.42/1.61 inference(unit_resolution,[status(thm)],[2448, 37, 468, 2105])).
% 1.42/1.61 tff(2450,plain,
% 1.42/1.61 (b(s(s(s(z))), s(z))),
% 1.42/1.61 inference(unit_resolution,[status(thm)],[1081, 2449])).
% 1.42/1.61 tff(2451,plain,
% 1.42/1.61 (~b(s(s(s(z))), elem!1)),
% 1.42/1.61 inference(unit_resolution,[status(thm)],[1718, 75, 1391, 2450, 2122])).
% 1.42/1.61 tff(2452,plain,
% 1.42/1.61 (~b(s(s(s(z))), z)),
% 1.42/1.61 inference(unit_resolution,[status(thm)],[1091, 2450, 372, 2122])).
% 1.42/1.61 tff(2453,plain,
% 1.42/1.61 (r(s(s(s(z))), z)),
% 1.42/1.61 inference(unit_resolution,[status(thm)],[1334, 58, 221, 2452])).
% 1.42/1.61 tff(2454,plain,
% 1.42/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(z))))),
% 1.42/1.61 inference(rewrite,[status(thm)],[])).
% 1.42/1.61 tff(2455,plain,
% 1.42/1.61 (((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(z))))),
% 1.42/1.61 inference(rewrite,[status(thm)],[])).
% 1.42/1.61 tff(2456,plain,
% 1.42/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~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(X1, 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(z))))) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(z)))))),
% 1.42/1.62 inference(monotonicity,[status(thm)],[2455])).
% 1.42/1.62 tff(2457,plain,
% 1.42/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~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(X1, 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(z))))) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(z))))),
% 1.42/1.62 inference(transitivity,[status(thm)],[2456, 2454])).
% 1.42/1.62 tff(2458,plain,
% 1.42/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))),
% 1.42/1.62 inference(quant_inst,[status(thm)],[])).
% 1.42/1.62 tff(2459,plain,
% 1.42/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(z)))),
% 1.42/1.62 inference(modus_ponens,[status(thm)],[2458, 2457])).
% 1.42/1.62 tff(2460,plain,
% 1.42/1.62 (~b(elem!1, z)),
% 1.42/1.62 inference(unit_resolution,[status(thm)],[2459, 75, 372, 1391, 2450, 2122])).
% 1.42/1.62 tff(2461,plain,
% 1.42/1.62 (r(elem!1, z)),
% 1.42/1.62 inference(unit_resolution,[status(thm)],[387, 2460, 353])).
% 1.42/1.62 tff(2462,plain,
% 1.42/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))),
% 1.42/1.62 inference(rewrite,[status(thm)],[])).
% 1.42/1.62 tff(2463,plain,
% 1.42/1.62 (((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))),
% 1.42/1.62 inference(rewrite,[status(thm)],[])).
% 1.42/1.62 tff(2464,plain,
% 1.42/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z))))),
% 1.42/1.62 inference(monotonicity,[status(thm)],[2463])).
% 1.42/1.62 tff(2465,plain,
% 1.42/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))),
% 1.42/1.62 inference(transitivity,[status(thm)],[2464, 2462])).
% 1.42/1.62 tff(2466,plain,
% 1.42/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)))),
% 1.42/1.62 inference(quant_inst,[status(thm)],[])).
% 1.42/1.62 tff(2467,plain,
% 1.42/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z))),
% 1.42/1.62 inference(modus_ponens,[status(thm)],[2466, 2465])).
% 1.42/1.62 tff(2468,plain,
% 1.42/1.62 (~r(s(s(s(z))), elem!1)),
% 1.42/1.62 inference(unit_resolution,[status(thm)],[2467, 37, 2461, 2453])).
% 1.42/1.62 tff(2469,plain,
% 1.42/1.62 (s(s(s(z))) = elem!1),
% 1.42/1.62 inference(unit_resolution,[status(thm)],[1115, 2468, 2451])).
% 1.42/1.62 tff(2470,plain,
% 1.42/1.62 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 1.42/1.62 inference(unit_resolution,[status(thm)],[1026, 2469, 860])).
% 1.42/1.62 tff(2471,plain,
% 1.42/1.62 (~(s(s(z)) = elem!1)),
% 1.42/1.62 inference(unit_resolution,[status(thm)],[1013, 2470])).
% 1.42/1.62 tff(2472,plain,
% 1.42/1.62 (r(s(s(z)), elem!1)),
% 1.42/1.62 inference(unit_resolution,[status(thm)],[104, 2471, 99])).
% 1.42/1.62 tff(2473,plain,
% 1.42/1.62 (~r(s(s(z)), z)),
% 1.42/1.62 inference(unit_resolution,[status(thm)],[328, 2472, 300])).
% 1.42/1.62 tff(2474,plain,
% 1.42/1.62 (b(s(s(z)), z)),
% 1.42/1.62 inference(unit_resolution,[status(thm)],[202, 2473])).
% 1.42/1.62 tff(2475,plain,
% 1.42/1.62 (~r(z, s(s(z)))),
% 1.42/1.62 inference(unit_resolution,[status(thm)],[339, 2472, 300])).
% 1.42/1.62 tff(2476,plain,
% 1.42/1.62 (b(z, s(s(z)))),
% 1.42/1.62 inference(unit_resolution,[status(thm)],[351, 2475])).
% 1.42/1.62 tff(2477,plain,
% 1.42/1.62 (~b(s(z), s(s(z)))),
% 1.42/1.62 inference(unit_resolution,[status(thm)],[410, 2476, 372, 2474])).
% 1.42/1.62 tff(2478,plain,
% 1.42/1.62 (~(s(z) = elem!1)),
% 1.42/1.62 inference(unit_resolution,[status(thm)],[1393, 1391])).
% 1.42/1.62 tff(2479,plain,
% 1.42/1.62 (~r(s(z), elem!1)),
% 1.42/1.62 inference(unit_resolution,[status(thm)],[2086, 2472, 300])).
% 1.42/1.62 tff(2480,plain,
% 1.42/1.62 (b(s(z), elem!1)),
% 1.42/1.62 inference(unit_resolution,[status(thm)],[601, 2479, 2478])).
% 1.42/1.62 tff(2481,plain,
% 1.42/1.62 (~r(s(z), s(s(z)))),
% 1.42/1.62 inference(unit_resolution,[status(thm)],[2138, 2480, 286, 372, 1391, 2104, 2461, 468])).
% 1.42/1.62 tff(2482,plain,
% 1.42/1.62 ($false),
% 1.42/1.62 inference(unit_resolution,[status(thm)],[416, 2481, 2477])).
% 1.42/1.62 tff(2483,plain,(b(s(s(s(z))), s(s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, elem!1)) | b(s(s(z)), elem!1) | (elem!1 = s(s(s(s(z))))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.42/1.62 tff(2484,plain,
% 1.42/1.62 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.42/1.62 inference(unit_resolution,[status(thm)],[2483, 2058, 286, 1376, 2442, 299, 99, 274, 305])).
% 1.42/1.62 tff(2485,plain,
% 1.42/1.62 (~b(s(s(s(z))), elem!1)),
% 1.42/1.62 inference(unit_resolution,[status(thm)],[1596, 75, 286, 2484, 287])).
% 1.42/1.62 tff(2486,plain,
% 1.42/1.62 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.42/1.62 inference(unit_resolution,[status(thm)],[1013, 2432])).
% 1.42/1.62 tff(2487,plain,
% 1.42/1.62 (~(s(s(s(z))) = elem!1)),
% 1.42/1.62 inference(unit_resolution,[status(thm)],[1026, 2486, 274])).
% 1.42/1.62 tff(2488,plain,
% 1.42/1.62 (r(s(s(s(z))), elem!1)),
% 1.42/1.62 inference(unit_resolution,[status(thm)],[1115, 2487, 2485])).
% 1.42/1.62 tff(2489,plain,
% 1.42/1.62 (r(s(elem!1), elem!1)),
% 1.42/1.62 inference(modus_ponens,[status(thm)],[2488, 2440])).
% 1.42/1.62 tff(2490,plain,
% 1.42/1.62 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.42/1.62 inference(unit_resolution,[status(thm)],[808, 2489, 299, 2436])).
% 1.42/1.62 tff(2491,plain,
% 1.42/1.62 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.42/1.62 inference(unit_resolution,[status(thm)],[813, 2490, 2435])).
% 1.42/1.62 tff(2492,plain,
% 1.42/1.62 (~(s(z) = elem!1)),
% 1.42/1.62 inference(unit_resolution,[status(thm)],[1393, 1376])).
% 1.42/1.62 tff(2493,plain,
% 1.42/1.62 (~r(s(s(z)), elem!1)),
% 1.42/1.62 inference(unit_resolution,[status(thm)],[2083, 588, 300, 372])).
% 1.42/1.62 tff(2494,plain,
% 1.42/1.62 (s(s(z)) = elem!1),
% 1.42/1.62 inference(unit_resolution,[status(thm)],[104, 2493, 99])).
% 1.42/1.62 tff(2495,plain,
% 1.42/1.62 (~r(s(s(s(z))), elem!1)),
% 1.42/1.62 inference(unit_resolution,[status(thm)],[1362, 588, 300])).
% 1.42/1.62 tff(2496,plain,
% 1.42/1.62 (s(s(s(z))) = elem!1),
% 1.42/1.62 inference(unit_resolution,[status(thm)],[1115, 2495, 100])).
% 1.42/1.62 tff(2497,plain,
% 1.42/1.62 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 1.42/1.62 inference(unit_resolution,[status(thm)],[1026, 2496, 860])).
% 1.42/1.62 tff(2498,plain,
% 1.42/1.62 ($false),
% 1.42/1.62 inference(unit_resolution,[status(thm)],[1013, 2497, 2494])).
% 1.42/1.62 tff(2499,plain,((~r(s(z), elem!1)) | (elem!1 = s(s(s(s(z))))) | b(s(s(z)), elem!1) | b(s(s(s(z))), elem!1) | (~r(z, elem!1)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.42/1.62 tff(2500,plain,
% 1.42/1.62 (~r(s(z), elem!1)),
% 1.42/1.62 inference(unit_resolution,[status(thm)],[2499, 2485, 99, 274, 299, 2058])).
% 1.42/1.62 tff(2501,plain,
% 1.42/1.62 (b(s(z), elem!1)),
% 1.42/1.62 inference(unit_resolution,[status(thm)],[601, 2500, 2492])).
% 1.42/1.62 tff(2502,plain,
% 1.42/1.62 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.42/1.62 inference(unit_resolution,[status(thm)],[2037, 75, 2501, 1376, 2491])).
% 1.42/1.62 tff(2503,plain,
% 1.42/1.62 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.42/1.62 inference(unit_resolution,[status(thm)],[1230, 58, 1227, 2502])).
% 1.42/1.62 tff(2504,plain,
% 1.42/1.62 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 1.42/1.62 inference(unit_resolution,[status(thm)],[2045, 75, 2501, 1376, 287, 2491])).
% 1.42/1.62 tff(2505,plain,
% 1.42/1.62 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(z)))))),
% 1.42/1.62 inference(unit_resolution,[status(thm)],[1134, 2432])).
% 1.42/1.62 tff(2506,plain,
% 1.42/1.62 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 1.42/1.62 inference(unit_resolution,[status(thm)],[1179, 58, 2505, 2504])).
% 1.42/1.62 tff(2507,plain,
% 1.42/1.62 (~b(s(s(s(s(z)))), s(z))),
% 1.42/1.62 inference(unit_resolution,[status(thm)],[1402, 75, 2501, 1376, 287])).
% 1.42/1.62 tff(2508,plain,
% 1.42/1.62 (r(s(s(s(s(z)))), s(z))),
% 1.42/1.62 inference(unit_resolution,[status(thm)],[1406, 58, 2507, 483])).
% 1.42/1.62 tff(2509,plain,
% 1.42/1.62 ($false),
% 1.42/1.62 inference(unit_resolution,[status(thm)],[2054, 37, 2508, 2506, 2503])).
% 1.42/1.62 tff(2510,plain,(b(z, elem!1) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (s(s(elem!1)) = s(s(z))) | b(s(s(z)), elem!1) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.42/1.62 tff(2511,plain,
% 1.42/1.62 (b(z, elem!1)),
% 1.42/1.62 inference(unit_resolution,[status(thm)],[2510, 284, 279, 266, 99, 267])).
% 1.42/1.62 tff(2512,plain,
% 1.42/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)))),
% 1.42/1.62 inference(rewrite,[status(thm)],[])).
% 1.42/1.62 tff(2513,plain,
% 1.42/1.62 (((~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)))),
% 1.42/1.62 inference(rewrite,[status(thm)],[])).
% 1.42/1.62 tff(2514,plain,
% 1.42/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z))))),
% 1.42/1.62 inference(monotonicity,[status(thm)],[2513])).
% 1.42/1.62 tff(2515,plain,
% 1.42/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)))),
% 1.42/1.62 inference(transitivity,[status(thm)],[2514, 2512])).
% 1.42/1.62 tff(2516,plain,
% 1.42/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))),
% 1.42/1.62 inference(quant_inst,[status(thm)],[])).
% 1.42/1.62 tff(2517,plain,
% 1.42/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z))),
% 1.42/1.62 inference(modus_ponens,[status(thm)],[2516, 2515])).
% 1.42/1.62 tff(2518,plain,
% 1.42/1.62 (~b(s(s(s(z))), z)),
% 1.42/1.62 inference(unit_resolution,[status(thm)],[2517, 75, 1518, 1119, 286, 287])).
% 1.42/1.62 tff(2519,plain,
% 1.42/1.62 (r(s(s(s(z))), z)),
% 1.42/1.62 inference(unit_resolution,[status(thm)],[1334, 58, 221, 2518])).
% 1.42/1.62 tff(2520,plain,
% 1.42/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))))),
% 1.42/1.62 inference(rewrite,[status(thm)],[])).
% 1.42/1.62 tff(2521,plain,
% 1.42/1.62 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z))))))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))))),
% 1.42/1.62 inference(rewrite,[status(thm)],[])).
% 1.42/1.62 tff(2522,plain,
% 1.42/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, elem!1)) | (~b(elem!1, s(s(s(s(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(X1, 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(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z))))))))),
% 1.42/1.62 inference(monotonicity,[status(thm)],[2521])).
% 1.42/1.62 tff(2523,plain,
% 1.42/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, elem!1)) | (~b(elem!1, s(s(s(s(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(X1, 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(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))))),
% 1.42/1.62 inference(transitivity,[status(thm)],[2522, 2520])).
% 1.42/1.62 tff(2524,plain,
% 1.42/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))))),
% 1.42/1.62 inference(quant_inst,[status(thm)],[])).
% 1.42/1.62 tff(2525,plain,
% 1.42/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z))))))),
% 1.42/1.62 inference(modus_ponens,[status(thm)],[2524, 2523])).
% 1.42/1.62 tff(2526,plain,
% 1.42/1.62 (~b(z, s(s(s(s(z)))))),
% 1.42/1.62 inference(unit_resolution,[status(thm)],[2525, 75, 1518, 286, 287])).
% 1.42/1.62 tff(2527,plain,
% 1.42/1.62 ((z = s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 1.42/1.62 inference(unit_resolution,[status(thm)],[1515, 58, 2526])).
% 1.42/1.62 tff(2528,plain,
% 1.42/1.62 (r(z, s(s(s(s(z)))))),
% 1.42/1.62 inference(unit_resolution,[status(thm)],[2527, 1503])).
% 1.42/1.62 tff(2529,plain,
% 1.42/1.62 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.42/1.62 inference(rewrite,[status(thm)],[])).
% 1.42/1.62 tff(2530,plain,
% 1.42/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.42/1.62 inference(monotonicity,[status(thm)],[2529])).
% 1.42/1.62 tff(2531,plain,
% 1.42/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.42/1.62 inference(transitivity,[status(thm)],[2530, 1591])).
% 1.42/1.62 tff(2532,plain,
% 1.42/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.42/1.62 inference(quant_inst,[status(thm)],[])).
% 1.42/1.62 tff(2533,plain,
% 1.42/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.42/1.62 inference(modus_ponens,[status(thm)],[2532, 2531])).
% 1.42/1.62 tff(2534,plain,
% 1.42/1.62 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.42/1.62 inference(unit_resolution,[status(thm)],[2533, 75, 1119, 286, 287])).
% 1.42/1.62 tff(2535,plain,
% 1.42/1.62 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.42/1.62 inference(unit_resolution,[status(thm)],[575, 2534])).
% 1.42/1.62 tff(2536,plain,
% 1.42/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))),
% 1.42/1.62 inference(rewrite,[status(thm)],[])).
% 1.42/1.62 tff(2537,plain,
% 1.42/1.62 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))),
% 1.42/1.62 inference(rewrite,[status(thm)],[])).
% 1.42/1.62 tff(2538,plain,
% 1.42/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z))))),
% 1.42/1.62 inference(monotonicity,[status(thm)],[2537])).
% 1.42/1.62 tff(2539,plain,
% 1.42/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))),
% 1.42/1.62 inference(transitivity,[status(thm)],[2538, 2536])).
% 1.42/1.62 tff(2540,plain,
% 1.42/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))),
% 1.42/1.63 inference(quant_inst,[status(thm)],[])).
% 1.42/1.63 tff(2541,plain,
% 1.42/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z))),
% 1.42/1.63 inference(modus_ponens,[status(thm)],[2540, 2539])).
% 1.42/1.63 tff(2542,plain,
% 1.42/1.63 ($false),
% 1.42/1.63 inference(unit_resolution,[status(thm)],[2541, 37, 2535, 2528, 2519])).
% 1.42/1.63 tff(2543,plain,((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.42/1.63 tff(2544,plain,
% 1.42/1.63 (~b(s(s(s(z))), elem!1)),
% 1.42/1.63 inference(unit_resolution,[status(thm)],[2543, 284, 279, 2511])).
% 1.42/1.63 tff(2545,plain,
% 1.42/1.63 (r(s(s(z)), elem!1)),
% 1.42/1.63 inference(unit_resolution,[status(thm)],[104, 2219, 99])).
% 1.42/1.63 tff(2546,plain,
% 1.42/1.63 (r(s(s(s(s(z)))), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.42/1.63 inference(monotonicity,[status(thm)],[214])).
% 1.42/1.63 tff(2547,plain,
% 1.42/1.63 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.42/1.63 inference(symmetry,[status(thm)],[2546])).
% 1.42/1.63 tff(2548,plain,
% 1.42/1.63 (~(s(elem!1) = s(s(elem!1)))),
% 1.42/1.63 inference(unit_resolution,[status(thm)],[1771, 213, 1011])).
% 1.42/1.63 tff(2549,plain,
% 1.42/1.63 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(s(z)))))),
% 1.42/1.63 inference(monotonicity,[status(thm)],[1019])).
% 1.42/1.63 tff(2550,plain,
% 1.42/1.63 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(elem!1))),
% 1.42/1.63 inference(symmetry,[status(thm)],[2549])).
% 1.42/1.63 tff(2551,plain,
% 1.42/1.63 (b(elem!1, s(elem!1))),
% 1.42/1.63 inference(modus_ponens,[status(thm)],[279, 2550])).
% 1.42/1.63 tff(2552,assumption,(s(s(elem!1)) = elem!1), introduced(assumption)).
% 1.42/1.63 tff(2553,plain,
% 1.42/1.63 (elem!1 = s(s(elem!1))),
% 1.42/1.63 inference(symmetry,[status(thm)],[2552])).
% 1.42/1.63 tff(2554,plain,
% 1.42/1.63 ($false),
% 1.42/1.63 inference(unit_resolution,[status(thm)],[1630, 2553])).
% 1.42/1.63 tff(2555,plain,((~(s(s(elem!1)) = elem!1)) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.42/1.63 tff(2556,plain,
% 1.42/1.63 (~(s(s(elem!1)) = elem!1)),
% 1.42/1.63 inference(unit_resolution,[status(thm)],[2555, 1908])).
% 1.42/1.63 tff(2557,plain,
% 1.42/1.63 ((s(s(s(z))) = s(z)) <=> (elem!1 = s(z))),
% 1.42/1.63 inference(monotonicity,[status(thm)],[213])).
% 1.42/1.63 tff(2558,plain,
% 1.42/1.63 ((s(s(s(z))) = s(z)) <=> (s(z) = elem!1)),
% 1.42/1.63 inference(transitivity,[status(thm)],[2557, 91])).
% 1.42/1.63 tff(2559,plain,
% 1.42/1.63 ((~(s(s(s(z))) = s(z))) <=> (~(s(z) = elem!1))),
% 1.42/1.63 inference(monotonicity,[status(thm)],[2558])).
% 1.42/1.63 tff(2560,plain,
% 1.42/1.63 (~(s(z) = elem!1)),
% 1.42/1.63 inference(modus_ponens,[status(thm)],[457, 2559])).
% 1.42/1.63 tff(2561,plain,
% 1.42/1.63 (b(s(s(s(s(z)))), elem!1)),
% 1.42/1.63 inference(unit_resolution,[status(thm)],[283, 267, 12])).
% 1.42/1.63 tff(2562,plain,
% 1.42/1.63 (b(elem!1, s(s(s(s(z)))))),
% 1.42/1.63 inference(unit_resolution,[status(thm)],[278, 274, 268])).
% 1.42/1.63 tff(2563,plain,
% 1.42/1.63 (~b(z, s(s(s(s(z)))))),
% 1.42/1.63 inference(unit_resolution,[status(thm)],[2525, 75, 1518, 2562, 2561])).
% 1.42/1.63 tff(2564,plain,
% 1.42/1.63 ((z = s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 1.42/1.63 inference(unit_resolution,[status(thm)],[1515, 58, 2563])).
% 1.42/1.63 tff(2565,plain,
% 1.42/1.63 (r(z, s(s(s(s(z)))))),
% 1.42/1.63 inference(unit_resolution,[status(thm)],[2564, 1503])).
% 1.42/1.63 tff(2566,plain,
% 1.42/1.63 ((~(s(z) = elem!1)) <=> (~(elem!1 = s(z)))),
% 1.42/1.63 inference(monotonicity,[status(thm)],[92])).
% 1.42/1.63 tff(2567,plain,
% 1.42/1.63 (~(elem!1 = s(z))),
% 1.42/1.63 inference(modus_ponens,[status(thm)],[108, 2566])).
% 1.42/1.63 tff(2568,plain,
% 1.42/1.63 (b(elem!1, s(z))),
% 1.42/1.63 inference(unit_resolution,[status(thm)],[89, 2567, 1711])).
% 1.42/1.63 tff(2569,plain,
% 1.42/1.63 (~b(s(z), s(s(s(s(z)))))),
% 1.42/1.63 inference(unit_resolution,[status(thm)],[1438, 2568, 2562, 2561])).
% 1.42/1.63 tff(2570,plain,
% 1.42/1.63 (r(s(z), s(s(s(s(z)))))),
% 1.42/1.63 inference(unit_resolution,[status(thm)],[489, 2569])).
% 1.42/1.63 tff(2571,plain,
% 1.42/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)))),
% 1.42/1.63 inference(rewrite,[status(thm)],[])).
% 1.42/1.63 tff(2572,plain,
% 1.42/1.63 (((~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)))),
% 1.42/1.63 inference(rewrite,[status(thm)],[])).
% 1.42/1.63 tff(2573,plain,
% 1.42/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z))))),
% 1.42/1.63 inference(monotonicity,[status(thm)],[2572])).
% 1.42/1.63 tff(2574,plain,
% 1.42/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)))),
% 1.42/1.63 inference(transitivity,[status(thm)],[2573, 2571])).
% 1.42/1.63 tff(2575,plain,
% 1.42/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))),
% 1.42/1.63 inference(quant_inst,[status(thm)],[])).
% 1.42/1.63 tff(2576,plain,
% 1.42/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z))),
% 1.42/1.63 inference(modus_ponens,[status(thm)],[2575, 2574])).
% 1.42/1.63 tff(2577,plain,
% 1.42/1.63 (~b(s(s(s(s(z)))), z)),
% 1.42/1.63 inference(unit_resolution,[status(thm)],[2576, 75, 1518, 2562, 2561])).
% 1.42/1.63 tff(2578,plain,
% 1.42/1.63 (r(s(s(s(s(z)))), z)),
% 1.42/1.63 inference(unit_resolution,[status(thm)],[1421, 58, 1143, 2577])).
% 1.42/1.63 tff(2579,plain,
% 1.42/1.63 (((~![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)))),
% 1.42/1.63 inference(rewrite,[status(thm)],[])).
% 1.42/1.63 tff(2580,plain,
% 1.42/1.63 (((~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)))),
% 1.42/1.63 inference(rewrite,[status(thm)],[])).
% 1.42/1.63 tff(2581,plain,
% 1.42/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), 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))))),
% 1.42/1.63 inference(monotonicity,[status(thm)],[2580])).
% 1.42/1.63 tff(2582,plain,
% 1.42/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), 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)))),
% 1.42/1.63 inference(transitivity,[status(thm)],[2581, 2579])).
% 1.42/1.63 tff(2583,plain,
% 1.42/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 1.42/1.63 inference(quant_inst,[status(thm)],[])).
% 1.42/1.63 tff(2584,plain,
% 1.42/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 1.42/1.63 inference(modus_ponens,[status(thm)],[2583, 2582])).
% 1.42/1.63 tff(2585,plain,
% 1.42/1.63 ($false),
% 1.42/1.63 inference(unit_resolution,[status(thm)],[2584, 37, 1561, 468, 1408])).
% 1.42/1.63 tff(2586,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.42/1.63 tff(2587,plain,
% 1.42/1.63 (~r(s(z), z)),
% 1.42/1.63 inference(unit_resolution,[status(thm)],[2586, 2570, 2578])).
% 1.42/1.63 tff(2588,plain,
% 1.42/1.63 (b(s(z), z)),
% 1.42/1.63 inference(unit_resolution,[status(thm)],[169, 2587])).
% 1.42/1.63 tff(2589,plain,
% 1.42/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))) | (~b(z, elem!1)))),
% 1.42/1.63 inference(rewrite,[status(thm)],[])).
% 1.42/1.63 tff(2590,plain,
% 1.42/1.63 (((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)))),
% 1.42/1.63 inference(rewrite,[status(thm)],[])).
% 1.42/1.63 tff(2591,plain,
% 1.42/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))) | (~b(z, elem!1))))),
% 1.42/1.63 inference(monotonicity,[status(thm)],[2590])).
% 1.42/1.63 tff(2592,plain,
% 1.42/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))) | (~b(z, elem!1)))),
% 1.42/1.63 inference(transitivity,[status(thm)],[2591, 2589])).
% 1.42/1.63 tff(2593,plain,
% 1.42/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))),
% 1.42/1.63 inference(quant_inst,[status(thm)],[])).
% 1.42/1.63 tff(2594,plain,
% 1.42/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1))),
% 1.42/1.63 inference(modus_ponens,[status(thm)],[2593, 2592])).
% 1.42/1.63 tff(2595,plain,
% 1.42/1.63 ($false),
% 1.42/1.63 inference(unit_resolution,[status(thm)],[2594, 75, 1518, 372, 371, 1391])).
% 1.42/1.63 tff(2596,plain,((~b(s(z), z)) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.42/1.63 tff(2597,plain,
% 1.42/1.63 (~b(z, s(z))),
% 1.42/1.63 inference(unit_resolution,[status(thm)],[2596, 2588, 1518, 2568])).
% 1.42/1.63 tff(2598,plain,
% 1.42/1.63 (r(z, s(z))),
% 1.42/1.63 inference(unit_resolution,[status(thm)],[187, 2597])).
% 1.42/1.63 tff(2599,plain,
% 1.42/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(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)))))))),
% 1.42/1.63 inference(rewrite,[status(thm)],[])).
% 1.42/1.63 tff(2600,plain,
% 1.42/1.63 (((~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)))))))),
% 1.42/1.63 inference(rewrite,[status(thm)],[])).
% 1.42/1.63 tff(2601,plain,
% 1.42/1.63 (((~![X0: $i, 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))))))))),
% 1.42/1.63 inference(monotonicity,[status(thm)],[2600])).
% 1.42/1.63 tff(2602,plain,
% 1.42/1.63 (((~![X0: $i, 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)))))))),
% 1.42/1.63 inference(transitivity,[status(thm)],[2601, 2599])).
% 1.42/1.63 tff(2603,plain,
% 1.42/1.63 ((~![X0: $i, 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))))),
% 1.42/1.63 inference(quant_inst,[status(thm)],[])).
% 1.42/1.63 tff(2604,plain,
% 1.42/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))),
% 1.42/1.63 inference(modus_ponens,[status(thm)],[2603, 2602])).
% 1.42/1.63 tff(2605,plain,
% 1.42/1.63 ($false),
% 1.42/1.63 inference(unit_resolution,[status(thm)],[2604, 37, 2598, 2570, 2565])).
% 1.42/1.63 tff(2606,plain,((s(s(s(s(z)))) = elem!1) | (~b(z, elem!1)) | r(elem!1, s(z)) | (s(z) = elem!1) | r(elem!1, s(s(s(s(z))))) | r(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.42/1.63 tff(2607,plain,
% 1.42/1.63 (r(elem!1, s(z))),
% 1.42/1.63 inference(unit_resolution,[status(thm)],[2606, 2560, 1518, 12, 268, 267])).
% 1.42/1.63 tff(2608,plain,
% 1.42/1.63 (b(s(elem!1), elem!1)),
% 1.42/1.63 inference(unit_resolution,[status(thm)],[1983, 213, 284])).
% 1.42/1.63 tff(2609,assumption,(b(elem!1, s(elem!1))), introduced(assumption)).
% 1.42/1.63 tff(2610,plain,
% 1.42/1.63 (~b(s(s(s(s(z)))), z)),
% 1.42/1.63 inference(unit_resolution,[status(thm)],[2576, 75, 1518, 286, 287])).
% 1.42/1.63 tff(2611,plain,
% 1.42/1.63 (r(s(s(s(s(z)))), z)),
% 1.42/1.63 inference(unit_resolution,[status(thm)],[1421, 58, 1143, 2610])).
% 1.42/1.63 tff(2612,plain,
% 1.42/1.63 (~b(s(z), s(s(s(s(z)))))),
% 1.42/1.63 inference(unit_resolution,[status(thm)],[586, 107, 286, 287])).
% 1.42/1.63 tff(2613,plain,
% 1.42/1.63 (r(s(z), s(s(s(s(z)))))),
% 1.42/1.63 inference(unit_resolution,[status(thm)],[489, 2612])).
% 1.42/1.63 tff(2614,assumption,(~r(elem!1, z)), introduced(assumption)).
% 1.42/1.63 tff(2615,plain,
% 1.42/1.63 (~(elem!1 = z)),
% 1.42/1.63 inference(unit_resolution,[status(thm)],[304, 235])).
% 1.42/1.63 tff(2616,plain,
% 1.42/1.63 (b(elem!1, z)),
% 1.42/1.63 inference(unit_resolution,[status(thm)],[387, 2615, 2614])).
% 1.42/1.63 tff(2617,plain,
% 1.42/1.63 (b(z, elem!1)),
% 1.42/1.63 inference(unit_resolution,[status(thm)],[298, 235, 13])).
% 1.42/1.63 tff(2618,plain,
% 1.42/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)))),
% 1.42/1.63 inference(rewrite,[status(thm)],[])).
% 1.42/1.63 tff(2619,plain,
% 1.42/1.63 (((~b(elem!1, z)) | (~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), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)))),
% 1.42/1.63 inference(rewrite,[status(thm)],[])).
% 1.42/1.63 tff(2620,plain,
% 1.42/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), 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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z))))),
% 1.42/1.63 inference(monotonicity,[status(thm)],[2619])).
% 1.42/1.63 tff(2621,plain,
% 1.42/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), 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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)))),
% 1.42/1.63 inference(transitivity,[status(thm)],[2620, 2618])).
% 1.42/1.63 tff(2622,plain,
% 1.42/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 1.42/1.63 inference(quant_inst,[status(thm)],[])).
% 1.42/1.63 tff(2623,plain,
% 1.42/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z))),
% 1.42/1.63 inference(modus_ponens,[status(thm)],[2622, 2621])).
% 1.42/1.63 tff(2624,plain,
% 1.42/1.63 ($false),
% 1.42/1.63 inference(unit_resolution,[status(thm)],[2623, 75, 2617, 2616, 107, 371])).
% 1.42/1.63 tff(2625,plain,((z = elem!1) | (~b(s(z), elem!1)) | (~b(s(z), z)) | r(elem!1, z) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.42/1.63 tff(2626,plain,
% 1.42/1.63 (~b(s(z), z)),
% 1.42/1.63 inference(unit_resolution,[status(thm)],[2625, 107, 235, 13, 2614])).
% 1.42/1.63 tff(2627,plain,
% 1.42/1.63 (r(s(z), z)),
% 1.42/1.63 inference(unit_resolution,[status(thm)],[169, 2626])).
% 1.42/1.63 tff(2628,plain,
% 1.42/1.63 ($false),
% 1.42/1.63 inference(unit_resolution,[status(thm)],[2586, 2627, 2613, 1408])).
% 1.42/1.63 tff(2629,plain,((~b(s(z), elem!1)) | (~r(s(s(s(s(z)))), z)) | (z = elem!1) | r(z, elem!1) | r(elem!1, z) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.42/1.63 tff(2630,plain,
% 1.42/1.63 (r(elem!1, z)),
% 1.42/1.63 inference(unit_resolution,[status(thm)],[2629, 107, 235, 13, 2611, 286, 287])).
% 1.42/1.63 tff(2631,plain,
% 1.42/1.63 (~r(s(z), z)),
% 1.42/1.63 inference(unit_resolution,[status(thm)],[162, 2630, 114])).
% 1.42/1.63 tff(2632,plain,
% 1.42/1.63 (b(s(z), z)),
% 1.42/1.63 inference(unit_resolution,[status(thm)],[169, 2631])).
% 1.42/1.63 tff(2633,plain,
% 1.42/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.42/1.63 inference(rewrite,[status(thm)],[])).
% 1.42/1.63 tff(2634,plain,
% 1.42/1.63 (((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.42/1.63 inference(rewrite,[status(thm)],[])).
% 1.42/1.63 tff(2635,plain,
% 1.42/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1)))))),
% 1.42/1.64 inference(monotonicity,[status(thm)],[2634])).
% 1.42/1.64 tff(2636,plain,
% 1.42/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.42/1.64 inference(transitivity,[status(thm)],[2635, 2633])).
% 1.42/1.64 tff(2637,plain,
% 1.42/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 1.42/1.64 inference(quant_inst,[status(thm)],[])).
% 1.42/1.64 tff(2638,plain,
% 1.42/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1)))),
% 1.42/1.64 inference(modus_ponens,[status(thm)],[2637, 2636])).
% 1.42/1.64 tff(2639,plain,
% 1.42/1.64 ($false),
% 1.42/1.64 inference(unit_resolution,[status(thm)],[2638, 75, 1518, 107, 2632, 921, 2609])).
% 1.42/1.64 tff(2640,plain,((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (z = elem!1) | r(z, elem!1) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.42/1.64 tff(2641,plain,
% 1.42/1.64 (~b(s(z), elem!1)),
% 1.42/1.64 inference(unit_resolution,[status(thm)],[2640, 2608, 1518, 2551, 2607, 294, 13, 279, 284])).
% 1.42/1.64 tff(2642,plain,
% 1.42/1.64 (r(s(z), elem!1)),
% 1.42/1.64 inference(unit_resolution,[status(thm)],[601, 2641, 2560])).
% 1.42/1.64 tff(2643,plain,
% 1.42/1.64 (~r(s(z), s(s(z)))),
% 1.42/1.64 inference(unit_resolution,[status(thm)],[2081, 37, 588, 106])).
% 1.42/1.64 tff(2644,plain,
% 1.42/1.64 (b(s(z), s(s(z)))),
% 1.42/1.64 inference(unit_resolution,[status(thm)],[416, 2643])).
% 1.42/1.64 tff(2645,plain,
% 1.42/1.64 (~r(s(s(z)), s(z))),
% 1.42/1.64 inference(unit_resolution,[status(thm)],[594, 37, 588, 106])).
% 1.42/1.64 tff(2646,plain,
% 1.42/1.64 (b(s(s(z)), s(z))),
% 1.42/1.64 inference(unit_resolution,[status(thm)],[153, 2645])).
% 1.42/1.64 tff(2647,assumption,(r(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.42/1.64 tff(2648,plain,
% 1.42/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(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(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 1.42/1.64 inference(rewrite,[status(thm)],[])).
% 1.42/1.64 tff(2649,plain,
% 1.42/1.64 (((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 1.42/1.64 inference(rewrite,[status(thm)],[])).
% 1.42/1.64 tff(2650,plain,
% 1.42/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))))),
% 1.42/1.64 inference(monotonicity,[status(thm)],[2649])).
% 1.42/1.64 tff(2651,plain,
% 1.42/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 1.42/1.64 inference(transitivity,[status(thm)],[2650, 2648])).
% 1.42/1.64 tff(2652,plain,
% 1.42/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 1.42/1.64 inference(quant_inst,[status(thm)],[])).
% 1.42/1.64 tff(2653,plain,
% 1.42/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))),
% 1.42/1.64 inference(modus_ponens,[status(thm)],[2652, 2651])).
% 1.42/1.64 tff(2654,plain,
% 1.42/1.64 (~r(s(z), s(s(elem!1)))),
% 1.42/1.64 inference(unit_resolution,[status(thm)],[2653, 37, 588, 2647])).
% 1.42/1.64 tff(2655,plain,
% 1.42/1.64 (b(s(z), s(s(elem!1)))),
% 1.42/1.64 inference(unit_resolution,[status(thm)],[1890, 2654])).
% 1.42/1.64 tff(2656,plain,
% 1.42/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), 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)), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 1.42/1.64 inference(rewrite,[status(thm)],[])).
% 1.42/1.64 tff(2657,plain,
% 1.42/1.64 (((~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)), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 1.42/1.64 inference(rewrite,[status(thm)],[])).
% 1.42/1.64 tff(2658,plain,
% 1.42/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(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)), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), elem!1))))),
% 1.42/1.64 inference(monotonicity,[status(thm)],[2657])).
% 1.42/1.64 tff(2659,plain,
% 1.42/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(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)), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 1.42/1.64 inference(transitivity,[status(thm)],[2658, 2656])).
% 1.42/1.64 tff(2660,plain,
% 1.42/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.42/1.64 inference(quant_inst,[status(thm)],[])).
% 1.42/1.64 tff(2661,plain,
% 1.42/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), elem!1))),
% 1.42/1.64 inference(modus_ponens,[status(thm)],[2660, 2659])).
% 1.42/1.64 tff(2662,plain,
% 1.42/1.64 (~r(s(s(elem!1)), s(s(z)))),
% 1.42/1.64 inference(unit_resolution,[status(thm)],[2661, 37, 106, 2647])).
% 1.42/1.64 tff(2663,plain,
% 1.42/1.64 (b(s(s(elem!1)), s(s(z)))),
% 1.42/1.64 inference(unit_resolution,[status(thm)],[1476, 2662, 266])).
% 1.42/1.64 tff(2664,plain,
% 1.42/1.64 ($false),
% 1.42/1.64 inference(unit_resolution,[status(thm)],[1994, 2663, 2655, 2646, 2644])).
% 1.42/1.64 tff(2665,plain,((~r(s(s(elem!1)), elem!1)) | (s(s(elem!1)) = s(s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.42/1.64 tff(2666,plain,
% 1.42/1.64 (~r(s(s(elem!1)), elem!1)),
% 1.42/1.64 inference(unit_resolution,[status(thm)],[2665, 2642, 266, 106])).
% 1.42/1.64 tff(2667,assumption,(~(s(s(elem!1)) = elem!1)), introduced(assumption)).
% 1.42/1.64 tff(2668,assumption,(~r(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.42/1.64 tff(2669,plain,
% 1.42/1.64 (((~![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))),
% 1.42/1.64 inference(rewrite,[status(thm)],[])).
% 1.42/1.64 tff(2670,plain,
% 1.42/1.64 ((~![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))),
% 1.42/1.64 inference(quant_inst,[status(thm)],[])).
% 1.42/1.64 tff(2671,plain,
% 1.42/1.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1)),
% 1.42/1.64 inference(modus_ponens,[status(thm)],[2670, 2669])).
% 1.42/1.64 tff(2672,plain,
% 1.42/1.64 ($false),
% 1.42/1.64 inference(unit_resolution,[status(thm)],[2671, 58, 1, 2668, 2667])).
% 1.42/1.64 tff(2673,plain,(r(s(s(elem!1)), elem!1) | b(s(s(elem!1)), elem!1) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.42/1.64 tff(2674,plain,
% 1.42/1.64 (b(s(s(elem!1)), elem!1)),
% 1.42/1.64 inference(unit_resolution,[status(thm)],[2673, 2666, 2556])).
% 1.42/1.64 tff(2675,plain,
% 1.42/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(elem!1))))),
% 1.42/1.64 inference(rewrite,[status(thm)],[])).
% 1.42/1.64 tff(2676,plain,
% 1.42/1.64 (((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), 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(elem!1, s(elem!1))))),
% 1.42/1.64 inference(rewrite,[status(thm)],[])).
% 1.42/1.64 tff(2677,plain,
% 1.42/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(elem!1)))))),
% 1.42/1.64 inference(monotonicity,[status(thm)],[2676])).
% 1.42/1.64 tff(2678,plain,
% 1.42/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(elem!1))))),
% 1.42/1.64 inference(transitivity,[status(thm)],[2677, 2675])).
% 1.42/1.64 tff(2679,plain,
% 1.42/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.42/1.64 inference(quant_inst,[status(thm)],[])).
% 1.42/1.64 tff(2680,plain,
% 1.42/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(elem!1)))),
% 1.42/1.64 inference(modus_ponens,[status(thm)],[2679, 2678])).
% 1.42/1.64 tff(2681,plain,
% 1.42/1.64 (~b(s(elem!1), s(s(elem!1)))),
% 1.42/1.64 inference(unit_resolution,[status(thm)],[2680, 75, 2608, 2674, 2551])).
% 1.42/1.64 tff(2682,plain,
% 1.42/1.64 (r(s(elem!1), s(s(elem!1)))),
% 1.42/1.64 inference(unit_resolution,[status(thm)],[1851, 2681, 2548])).
% 1.42/1.64 tff(2683,plain,
% 1.42/1.64 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.42/1.64 inference(modus_ponens,[status(thm)],[2682, 2547])).
% 1.42/1.64 tff(2684,plain,
% 1.42/1.64 (~b(s(s(s(s(z)))), z)),
% 1.42/1.64 inference(unit_resolution,[status(thm)],[2576, 75, 1518, 279, 284])).
% 1.42/1.64 tff(2685,plain,
% 1.42/1.64 (r(s(s(s(s(z)))), z)),
% 1.42/1.64 inference(unit_resolution,[status(thm)],[1421, 58, 1143, 2684])).
% 1.42/1.64 tff(2686,plain,
% 1.42/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.42/1.64 inference(rewrite,[status(thm)],[])).
% 1.42/1.64 tff(2687,plain,
% 1.42/1.64 (((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.42/1.64 inference(rewrite,[status(thm)],[])).
% 1.42/1.64 tff(2688,plain,
% 1.42/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1)))))),
% 1.42/1.64 inference(monotonicity,[status(thm)],[2687])).
% 1.42/1.64 tff(2689,plain,
% 1.42/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.42/1.64 inference(transitivity,[status(thm)],[2688, 2686])).
% 1.42/1.64 tff(2690,plain,
% 1.42/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))),
% 1.42/1.64 inference(quant_inst,[status(thm)],[])).
% 1.42/1.64 tff(2691,plain,
% 1.42/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1)))),
% 1.42/1.64 inference(modus_ponens,[status(thm)],[2690, 2689])).
% 1.42/1.64 tff(2692,plain,
% 1.42/1.64 (~b(s(s(elem!1)), z)),
% 1.42/1.64 inference(unit_resolution,[status(thm)],[2691, 75, 1518, 2608, 2674, 2551])).
% 1.42/1.64 tff(2693,assumption,(~r(s(s(elem!1)), z)), introduced(assumption)).
% 1.42/1.64 tff(2694,assumption,(~b(s(s(elem!1)), z)), introduced(assumption)).
% 1.42/1.64 tff(2695,plain,
% 1.42/1.64 ($false),
% 1.42/1.64 inference(unit_resolution,[status(thm)],[518, 58, 515, 2694, 2693])).
% 1.42/1.64 tff(2696,plain,(b(s(s(elem!1)), z) | r(s(s(elem!1)), z)), inference(lemma,lemma(discharge,[]))).
% 1.42/1.64 tff(2697,plain,
% 1.42/1.64 (r(s(s(elem!1)), z)),
% 1.42/1.64 inference(unit_resolution,[status(thm)],[2696, 2692])).
% 1.42/1.64 tff(2698,assumption,(r(s(s(elem!1)), z)), introduced(assumption)).
% 1.42/1.64 tff(2699,assumption,(r(s(s(s(s(z)))), s(s(elem!1)))), introduced(assumption)).
% 1.42/1.64 tff(2700,plain,
% 1.42/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)))),
% 1.42/1.64 inference(rewrite,[status(thm)],[])).
% 1.42/1.64 tff(2701,plain,
% 1.42/1.64 (((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)))),
% 1.42/1.64 inference(rewrite,[status(thm)],[])).
% 1.42/1.64 tff(2702,plain,
% 1.42/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), z))))),
% 1.42/1.64 inference(monotonicity,[status(thm)],[2701])).
% 1.42/1.64 tff(2703,plain,
% 1.42/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)))),
% 1.42/1.64 inference(transitivity,[status(thm)],[2702, 2700])).
% 1.42/1.64 tff(2704,plain,
% 1.42/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.42/1.64 inference(quant_inst,[status(thm)],[])).
% 1.42/1.64 tff(2705,plain,
% 1.42/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), z))),
% 1.42/1.64 inference(modus_ponens,[status(thm)],[2704, 2703])).
% 1.42/1.64 tff(2706,plain,
% 1.42/1.64 ($false),
% 1.42/1.64 inference(unit_resolution,[status(thm)],[2705, 37, 1408, 2699, 2698])).
% 1.42/1.64 tff(2707,plain,((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.42/1.64 tff(2708,plain,
% 1.42/1.64 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.42/1.64 inference(unit_resolution,[status(thm)],[2707, 2697, 2685])).
% 1.42/1.64 tff(2709,plain,
% 1.42/1.64 ($false),
% 1.42/1.64 inference(unit_resolution,[status(thm)],[2708, 2683])).
% 1.42/1.64 tff(2710,plain,((~(s(s(s(z))) = elem!1)) | (~b(z, elem!1)) | (s(s(elem!1)) = s(s(z))) | (~r(s(s(z)), elem!1)) | r(z, elem!1) | r(s(s(s(s(z)))), elem!1) | r(elem!1, s(s(s(s(z))))) | (s(s(s(s(z)))) = elem!1) | (s(s(elem!1)) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.42/1.64 tff(2711,plain,
% 1.42/1.64 (~(s(s(s(z))) = elem!1)),
% 1.42/1.64 inference(unit_resolution,[status(thm)],[2710, 2545, 266, 2511, 13, 12, 268, 267, 1011])).
% 1.42/1.64 tff(2712,plain,
% 1.42/1.64 (r(s(s(s(z))), elem!1)),
% 1.42/1.64 inference(unit_resolution,[status(thm)],[1115, 2711, 2544])).
% 1.42/1.64 tff(2713,plain,
% 1.42/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), 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(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), elem!1)))),
% 1.42/1.65 inference(rewrite,[status(thm)],[])).
% 1.42/1.65 tff(2714,plain,
% 1.42/1.65 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), elem!1)))),
% 1.42/1.65 inference(rewrite,[status(thm)],[])).
% 1.42/1.65 tff(2715,plain,
% 1.42/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), elem!1))))),
% 1.42/1.65 inference(monotonicity,[status(thm)],[2714])).
% 1.42/1.65 tff(2716,plain,
% 1.42/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), elem!1)))),
% 1.42/1.65 inference(transitivity,[status(thm)],[2715, 2713])).
% 1.42/1.65 tff(2717,plain,
% 1.42/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))))),
% 1.42/1.65 inference(quant_inst,[status(thm)],[])).
% 1.42/1.65 tff(2718,plain,
% 1.42/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), elem!1))),
% 1.42/1.65 inference(modus_ponens,[status(thm)],[2717, 2716])).
% 1.42/1.65 tff(2719,plain,
% 1.42/1.65 (~r(s(s(z)), s(s(s(z))))),
% 1.42/1.65 inference(unit_resolution,[status(thm)],[2718, 37, 2545, 2712])).
% 1.42/1.65 tff(2720,plain,
% 1.42/1.65 (b(s(s(z)), s(s(s(z))))),
% 1.42/1.65 inference(unit_resolution,[status(thm)],[1559, 58, 1556, 2719])).
% 1.42/1.65 tff(2721,plain,
% 1.42/1.65 ((~r(z, elem!1)) <=> (~r(z, s(z)))),
% 1.42/1.65 inference(monotonicity,[status(thm)],[907])).
% 1.42/1.65 tff(2722,plain,
% 1.42/1.65 (~r(z, s(z))),
% 1.42/1.65 inference(modus_ponens,[status(thm)],[13, 2721])).
% 1.42/1.65 tff(2723,plain,
% 1.42/1.65 ($false),
% 1.42/1.65 inference(unit_resolution,[status(thm)],[506, 2722])).
% 1.42/1.65 tff(2724,plain,((~(s(z) = elem!1)) | (~r(z, s(z))) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.42/1.65 tff(2725,plain,
% 1.42/1.65 (~(s(z) = elem!1)),
% 1.42/1.65 inference(unit_resolution,[status(thm)],[2724, 506, 13])).
% 1.42/1.65 tff(2726,plain,
% 1.42/1.65 (r(elem!1, s(z))),
% 1.42/1.65 inference(unit_resolution,[status(thm)],[2606, 2725, 2511, 12, 268, 267])).
% 1.42/1.65 tff(2727,plain,
% 1.42/1.65 (~b(s(s(s(s(z)))), z)),
% 1.42/1.65 inference(unit_resolution,[status(thm)],[2576, 75, 2511, 279, 284])).
% 1.42/1.65 tff(2728,plain,
% 1.42/1.65 (r(s(s(s(s(z)))), z)),
% 1.42/1.65 inference(unit_resolution,[status(thm)],[1421, 58, 1143, 2727])).
% 1.42/1.65 tff(2729,plain,
% 1.42/1.65 (~r(elem!1, z)),
% 1.42/1.65 inference(unit_resolution,[status(thm)],[177, 2726, 506])).
% 1.42/1.65 tff(2730,plain,
% 1.42/1.65 (~b(s(z), elem!1)),
% 1.42/1.65 inference(unit_resolution,[status(thm)],[2629, 2729, 294, 13, 2728, 279, 284])).
% 1.42/1.65 tff(2731,plain,
% 1.42/1.65 (r(s(z), elem!1)),
% 1.42/1.65 inference(unit_resolution,[status(thm)],[601, 2730, 2725])).
% 1.42/1.65 tff(2732,plain,
% 1.42/1.65 (~r(s(s(z)), s(s(s(z))))),
% 1.42/1.65 inference(unit_resolution,[status(thm)],[2718, 37, 106, 1061])).
% 1.42/1.65 tff(2733,plain,
% 1.42/1.65 (~r(s(s(z)), s(z))),
% 1.42/1.65 inference(unit_resolution,[status(thm)],[123, 106, 114])).
% 1.42/1.65 tff(2734,plain,
% 1.42/1.65 (b(s(s(z)), s(z))),
% 1.42/1.65 inference(unit_resolution,[status(thm)],[153, 2733])).
% 1.42/1.65 tff(2735,plain,
% 1.42/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.42/1.65 inference(rewrite,[status(thm)],[])).
% 1.42/1.65 tff(2736,plain,
% 1.42/1.65 (((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.42/1.65 inference(rewrite,[status(thm)],[])).
% 1.42/1.65 tff(2737,plain,
% 1.42/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z)))))))),
% 1.42/1.65 inference(monotonicity,[status(thm)],[2736])).
% 1.42/1.65 tff(2738,plain,
% 1.42/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.42/1.65 inference(transitivity,[status(thm)],[2737, 2735])).
% 1.42/1.65 tff(2739,plain,
% 1.42/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.42/1.65 inference(quant_inst,[status(thm)],[])).
% 1.42/1.65 tff(2740,plain,
% 1.42/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z)))))),
% 1.42/1.65 inference(modus_ponens,[status(thm)],[2739, 2738])).
% 1.42/1.65 tff(2741,plain,
% 1.42/1.65 (~b(s(s(z)), s(s(s(z))))),
% 1.42/1.65 inference(unit_resolution,[status(thm)],[2740, 75, 2734, 402, 1082])).
% 1.42/1.65 tff(2742,plain,
% 1.42/1.65 ($false),
% 1.42/1.65 inference(unit_resolution,[status(thm)],[1559, 58, 1556, 2741, 2732])).
% 1.42/1.65 tff(2743,plain,((~r(s(s(s(z))), elem!1)) | (~b(s(z), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.42/1.65 tff(2744,plain,
% 1.42/1.65 (~r(s(s(s(z))), elem!1)),
% 1.42/1.65 inference(unit_resolution,[status(thm)],[2743, 2644, 106, 114])).
% 1.42/1.65 tff(2745,plain,
% 1.42/1.65 (~r(elem!1, z)),
% 1.42/1.65 inference(unit_resolution,[status(thm)],[177, 114, 506])).
% 1.42/1.65 tff(2746,plain,
% 1.42/1.65 (b(elem!1, z)),
% 1.42/1.65 inference(unit_resolution,[status(thm)],[387, 2745, 305])).
% 1.42/1.65 tff(2747,assumption,(r(z, s(s(s(s(z)))))), introduced(assumption)).
% 1.42/1.65 tff(2748,plain,
% 1.42/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))),
% 1.42/1.65 inference(rewrite,[status(thm)],[])).
% 1.42/1.65 tff(2749,plain,
% 1.42/1.65 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(z))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))),
% 1.42/1.65 inference(rewrite,[status(thm)],[])).
% 1.42/1.65 tff(2750,plain,
% 1.42/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z))))),
% 1.42/1.65 inference(monotonicity,[status(thm)],[2749])).
% 1.42/1.65 tff(2751,plain,
% 1.42/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))),
% 1.42/1.65 inference(transitivity,[status(thm)],[2750, 2748])).
% 1.42/1.65 tff(2752,plain,
% 1.42/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)))),
% 1.42/1.65 inference(quant_inst,[status(thm)],[])).
% 1.42/1.65 tff(2753,plain,
% 1.42/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z))),
% 1.42/1.65 inference(modus_ponens,[status(thm)],[2752, 2751])).
% 1.42/1.65 tff(2754,plain,
% 1.42/1.65 (~r(s(s(s(z))), z)),
% 1.42/1.65 inference(unit_resolution,[status(thm)],[2753, 37, 506, 2105, 2747])).
% 1.42/1.65 tff(2755,plain,
% 1.42/1.65 (b(s(s(s(z))), z)),
% 1.42/1.65 inference(unit_resolution,[status(thm)],[1334, 58, 221, 2754])).
% 1.42/1.65 tff(2756,plain,
% 1.42/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)))),
% 1.42/1.65 inference(rewrite,[status(thm)],[])).
% 1.42/1.65 tff(2757,plain,
% 1.42/1.65 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)))),
% 1.42/1.65 inference(rewrite,[status(thm)],[])).
% 1.42/1.65 tff(2758,plain,
% 1.42/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z))))),
% 1.42/1.65 inference(monotonicity,[status(thm)],[2757])).
% 1.42/1.65 tff(2759,plain,
% 1.42/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)))),
% 1.42/1.65 inference(transitivity,[status(thm)],[2758, 2756])).
% 1.42/1.65 tff(2760,plain,
% 1.42/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 1.42/1.65 inference(quant_inst,[status(thm)],[])).
% 1.42/1.65 tff(2761,plain,
% 1.42/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z))),
% 1.42/1.65 inference(modus_ponens,[status(thm)],[2760, 2759])).
% 1.42/1.65 tff(2762,plain,
% 1.42/1.65 (~b(s(s(s(z))), elem!1)),
% 1.42/1.65 inference(unit_resolution,[status(thm)],[2761, 75, 1518, 1958, 2755])).
% 1.42/1.65 tff(2763,plain,
% 1.42/1.65 (s(s(s(z))) = elem!1),
% 1.42/1.65 inference(unit_resolution,[status(thm)],[1115, 2762, 1710])).
% 1.42/1.65 tff(2764,plain,
% 1.42/1.65 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.42/1.65 inference(monotonicity,[status(thm)],[2763])).
% 1.42/1.65 tff(2765,plain,
% 1.42/1.65 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 1.42/1.65 inference(symmetry,[status(thm)],[2764])).
% 1.42/1.65 tff(2766,plain,
% 1.42/1.65 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.42/1.65 inference(modus_ponens,[status(thm)],[286, 2765])).
% 1.42/1.65 tff(2767,plain,
% 1.42/1.65 ($false),
% 1.42/1.65 inference(unit_resolution,[status(thm)],[2104, 2766])).
% 1.42/1.65 tff(2768,plain,(b(s(s(s(z))), s(s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | r(s(s(s(z))), elem!1) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(z, s(z))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.42/1.65 tff(2769,plain,
% 1.42/1.65 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.42/1.65 inference(unit_resolution,[status(thm)],[2768, 2744, 286, 1518, 2746, 506, 2528])).
% 1.42/1.65 tff(2770,plain,
% 1.42/1.65 (~b(s(s(s(z))), elem!1)),
% 1.42/1.65 inference(unit_resolution,[status(thm)],[1596, 75, 286, 2769, 287])).
% 1.42/1.65 tff(2771,plain,
% 1.42/1.65 (s(s(s(z))) = elem!1),
% 1.42/1.65 inference(unit_resolution,[status(thm)],[1115, 2770, 2744])).
% 1.42/1.65 tff(2772,plain,
% 1.42/1.65 (s(s(s(s(z)))) = s(elem!1)),
% 1.42/1.65 inference(monotonicity,[status(thm)],[2771])).
% 1.42/1.65 tff(2773,plain,
% 1.42/1.65 (r(s(s(s(s(z)))), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.42/1.65 inference(monotonicity,[status(thm)],[2772])).
% 1.42/1.65 tff(2774,plain,
% 1.42/1.65 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.42/1.65 inference(symmetry,[status(thm)],[2773])).
% 1.42/1.65 tff(2775,plain,
% 1.42/1.65 (~(s(elem!1) = s(s(elem!1)))),
% 1.42/1.65 inference(unit_resolution,[status(thm)],[1771, 2771, 1011])).
% 1.42/1.65 tff(2776,plain,
% 1.42/1.65 (~r(s(s(elem!1)), elem!1)),
% 1.42/1.65 inference(unit_resolution,[status(thm)],[2665, 588, 266, 106])).
% 1.42/1.65 tff(2777,plain,
% 1.42/1.65 (~(elem!1 = s(s(elem!1)))),
% 1.42/1.65 inference(unit_resolution,[status(thm)],[1612, 2771])).
% 1.42/1.65 tff(2778,plain,
% 1.42/1.65 (~(s(s(elem!1)) = elem!1)),
% 1.42/1.65 inference(unit_resolution,[status(thm)],[2555, 2777])).
% 1.42/1.65 tff(2779,plain,
% 1.42/1.65 (b(s(s(elem!1)), elem!1)),
% 1.42/1.65 inference(unit_resolution,[status(thm)],[2673, 2778, 2776])).
% 1.42/1.65 tff(2780,plain,
% 1.42/1.65 (b(s(elem!1), elem!1)),
% 1.42/1.65 inference(unit_resolution,[status(thm)],[1983, 2771, 287])).
% 1.42/1.65 tff(2781,plain,
% 1.42/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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, z)) | (~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(X1, 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, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.42/1.65 inference(rewrite,[status(thm)],[])).
% 1.42/1.65 tff(2782,plain,
% 1.42/1.65 (((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.42/1.65 inference(rewrite,[status(thm)],[])).
% 1.42/1.65 tff(2783,plain,
% 1.42/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1))))))),
% 1.42/1.66 inference(monotonicity,[status(thm)],[2782])).
% 1.42/1.66 tff(2784,plain,
% 1.42/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.42/1.66 inference(transitivity,[status(thm)],[2783, 2781])).
% 1.42/1.66 tff(2785,plain,
% 1.42/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.42/1.66 inference(quant_inst,[status(thm)],[])).
% 1.42/1.66 tff(2786,plain,
% 1.42/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1))))),
% 1.42/1.66 inference(modus_ponens,[status(thm)],[2785, 2784])).
% 1.42/1.66 tff(2787,plain,
% 1.42/1.66 (~b(s(elem!1), s(s(elem!1)))),
% 1.42/1.66 inference(unit_resolution,[status(thm)],[2786, 75, 1518, 2746, 2780, 2779])).
% 1.42/1.66 tff(2788,plain,
% 1.42/1.66 (r(s(elem!1), s(s(elem!1)))),
% 1.42/1.66 inference(unit_resolution,[status(thm)],[1851, 2787, 2775])).
% 1.42/1.66 tff(2789,plain,
% 1.42/1.66 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.42/1.66 inference(modus_ponens,[status(thm)],[2788, 2774])).
% 1.42/1.66 tff(2790,plain,
% 1.42/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), z)) | (~b(z, elem!1)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), z)) | (~b(z, elem!1)) | (~b(elem!1, z)))),
% 1.42/1.66 inference(rewrite,[status(thm)],[])).
% 1.42/1.66 tff(2791,plain,
% 1.42/1.66 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(elem!1, z)))),
% 1.42/1.66 inference(rewrite,[status(thm)],[])).
% 1.42/1.66 tff(2792,plain,
% 1.42/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), z)) | (~b(z, elem!1)) | (~b(elem!1, z))))),
% 1.42/1.66 inference(monotonicity,[status(thm)],[2791])).
% 1.42/1.66 tff(2793,plain,
% 1.42/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), z)) | (~b(z, elem!1)) | (~b(elem!1, z)))),
% 1.42/1.66 inference(transitivity,[status(thm)],[2792, 2790])).
% 1.42/1.66 tff(2794,plain,
% 1.42/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))),
% 1.42/1.66 inference(quant_inst,[status(thm)],[])).
% 1.42/1.66 tff(2795,plain,
% 1.42/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(elem!1, z))),
% 1.42/1.66 inference(modus_ponens,[status(thm)],[2794, 2793])).
% 1.42/1.66 tff(2796,plain,
% 1.42/1.66 (~b(s(s(elem!1)), z)),
% 1.42/1.66 inference(unit_resolution,[status(thm)],[2795, 75, 1518, 2746, 2779])).
% 1.42/1.66 tff(2797,plain,
% 1.42/1.66 (r(s(s(elem!1)), z)),
% 1.42/1.66 inference(unit_resolution,[status(thm)],[2696, 2796])).
% 1.42/1.66 tff(2798,plain,
% 1.42/1.66 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.42/1.66 inference(unit_resolution,[status(thm)],[2707, 2797, 2611])).
% 1.42/1.66 tff(2799,plain,
% 1.42/1.66 ($false),
% 1.42/1.66 inference(unit_resolution,[status(thm)],[2798, 2789])).
% 1.42/1.66 tff(2800,plain,((~r(s(z), elem!1)) | (~b(z, elem!1)) | (s(s(elem!1)) = s(s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(z))) | (s(s(elem!1)) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.42/1.66 tff(2801,plain,
% 1.42/1.66 (~r(s(s(z)), elem!1)),
% 1.42/1.66 inference(unit_resolution,[status(thm)],[2800, 1011, 1518, 287, 286, 506, 588, 114, 266])).
% 1.42/1.66 tff(2802,plain,
% 1.42/1.66 ($false),
% 1.42/1.66 inference(unit_resolution,[status(thm)],[104, 2801, 2219, 99])).
% 1.42/1.66 tff(2803,plain,((s(s(elem!1)) = s(s(s(s(z))))) | b(s(s(z)), elem!1) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (s(s(elem!1)) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.42/1.66 tff(2804,plain,
% 1.42/1.66 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.42/1.66 inference(unit_resolution,[status(thm)],[2803, 506, 2511, 284, 279, 99, 2731, 2726, 266])).
% 1.42/1.66 tff(2805,plain,
% 1.42/1.66 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(z)))))),
% 1.42/1.66 inference(monotonicity,[status(thm)],[2804])).
% 1.42/1.66 tff(2806,plain,
% 1.42/1.66 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 1.42/1.66 inference(symmetry,[status(thm)],[2805])).
% 1.42/1.66 tff(2807,plain,
% 1.42/1.66 (s(s(s(z))) = s(elem!1)),
% 1.42/1.66 inference(transitivity,[status(thm)],[451, 2806, 228])).
% 1.42/1.66 tff(2808,plain,
% 1.42/1.66 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.42/1.66 inference(monotonicity,[status(thm)],[2807])).
% 1.42/1.66 tff(2809,plain,
% 1.42/1.66 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.42/1.66 inference(transitivity,[status(thm)],[2808, 269])).
% 1.42/1.66 tff(2810,plain,
% 1.42/1.66 ((s(elem!1) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(z))))),
% 1.42/1.66 inference(symmetry,[status(thm)],[2809])).
% 1.42/1.66 tff(2811,plain,
% 1.42/1.66 ((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(s(s(z)))))),
% 1.42/1.66 inference(monotonicity,[status(thm)],[2810])).
% 1.42/1.66 tff(2812,plain,
% 1.42/1.66 (s(s(z)) = elem!1),
% 1.42/1.66 inference(unit_resolution,[status(thm)],[1425, 2804])).
% 1.42/1.66 tff(2813,plain,
% 1.42/1.66 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.42/1.66 inference(unit_resolution,[status(thm)],[1145, 2812])).
% 1.42/1.66 tff(2814,plain,
% 1.42/1.66 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))),
% 1.42/1.66 inference(modus_ponens,[status(thm)],[2813, 2811])).
% 1.42/1.66 tff(2815,plain,
% 1.42/1.66 ((s(s(s(s(s(s(s(z))))))) = s(s(z))) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.42/1.66 inference(monotonicity,[status(thm)],[2812])).
% 1.42/1.66 tff(2816,plain,
% 1.42/1.66 ((~(s(s(s(s(s(s(s(z))))))) = s(s(z)))) <=> (~(s(s(s(s(s(s(s(z))))))) = elem!1))),
% 1.42/1.66 inference(monotonicity,[status(thm)],[2815])).
% 1.42/1.66 tff(2817,plain,
% 1.42/1.66 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.42/1.66 inference(modus_ponens,[status(thm)],[1045, 2816])).
% 1.42/1.66 tff(2818,plain,
% 1.42/1.66 (b(elem!1, z)),
% 1.42/1.66 inference(unit_resolution,[status(thm)],[387, 2729, 305])).
% 1.42/1.66 tff(2819,plain,
% 1.42/1.66 (~b(z, s(s(s(s(z)))))),
% 1.42/1.66 inference(unit_resolution,[status(thm)],[2525, 75, 2511, 279, 284])).
% 1.42/1.66 tff(2820,plain,
% 1.42/1.66 ((z = s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 1.42/1.66 inference(unit_resolution,[status(thm)],[1515, 58, 2819])).
% 1.42/1.66 tff(2821,plain,
% 1.42/1.66 (r(z, s(s(s(s(z)))))),
% 1.42/1.66 inference(unit_resolution,[status(thm)],[2820, 1503])).
% 1.42/1.66 tff(2822,plain,
% 1.42/1.66 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(z)))))),
% 1.42/1.66 inference(unit_resolution,[status(thm)],[1134, 2812])).
% 1.42/1.66 tff(2823,plain,
% 1.42/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 1.42/1.66 inference(rewrite,[status(thm)],[])).
% 1.42/1.66 tff(2824,plain,
% 1.42/1.66 (((~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 1.42/1.66 inference(rewrite,[status(thm)],[])).
% 1.42/1.66 tff(2825,plain,
% 1.42/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 1.42/1.66 inference(monotonicity,[status(thm)],[2824])).
% 1.42/1.66 tff(2826,plain,
% 1.42/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 1.42/1.66 inference(transitivity,[status(thm)],[2825, 2823])).
% 1.42/1.66 tff(2827,plain,
% 1.42/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 1.42/1.66 inference(quant_inst,[status(thm)],[])).
% 1.42/1.66 tff(2828,plain,
% 1.42/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 1.42/1.66 inference(modus_ponens,[status(thm)],[2827, 2826])).
% 1.42/1.66 tff(2829,plain,
% 1.42/1.66 (~b(z, s(s(s(s(s(s(s(z))))))))),
% 1.42/1.66 inference(unit_resolution,[status(thm)],[2828, 75, 1518, 1958, 1168])).
% 1.42/1.66 tff(2830,plain,
% 1.42/1.66 (r(z, s(s(s(s(s(s(s(z))))))))),
% 1.42/1.66 inference(unit_resolution,[status(thm)],[781, 58, 2829, 778])).
% 1.42/1.66 tff(2831,plain,
% 1.42/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.42/1.66 inference(rewrite,[status(thm)],[])).
% 1.42/1.66 tff(2832,plain,
% 1.42/1.66 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z))) <=> ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.42/1.66 inference(rewrite,[status(thm)],[])).
% 1.42/1.66 tff(2833,plain,
% 1.42/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 1.42/1.66 inference(monotonicity,[status(thm)],[2832])).
% 1.42/1.66 tff(2834,plain,
% 1.42/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.42/1.66 inference(transitivity,[status(thm)],[2833, 2831])).
% 1.42/1.66 tff(2835,plain,
% 1.42/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.42/1.66 inference(quant_inst,[status(thm)],[])).
% 1.42/1.66 tff(2836,plain,
% 1.42/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 1.42/1.66 inference(modus_ponens,[status(thm)],[2835, 2834])).
% 1.42/1.66 tff(2837,plain,
% 1.42/1.66 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 1.42/1.66 inference(unit_resolution,[status(thm)],[2836, 75, 1518, 1958, 1168])).
% 1.42/1.66 tff(2838,plain,
% 1.42/1.66 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.42/1.66 inference(unit_resolution,[status(thm)],[750, 58, 747, 2837])).
% 1.42/1.66 tff(2839,plain,
% 1.42/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.42/1.66 inference(rewrite,[status(thm)],[])).
% 1.42/1.66 tff(2840,plain,
% 1.42/1.66 (((~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(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(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.42/1.66 inference(rewrite,[status(thm)],[])).
% 1.42/1.66 tff(2841,plain,
% 1.42/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(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(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 1.42/1.66 inference(monotonicity,[status(thm)],[2840])).
% 1.42/1.66 tff(2842,plain,
% 1.42/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(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(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.42/1.66 inference(transitivity,[status(thm)],[2841, 2839])).
% 1.42/1.66 tff(2843,plain,
% 1.42/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(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(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.42/1.66 inference(quant_inst,[status(thm)],[])).
% 1.42/1.66 tff(2844,plain,
% 1.42/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 1.42/1.66 inference(modus_ponens,[status(thm)],[2843, 2842])).
% 1.42/1.66 tff(2845,plain,
% 1.42/1.66 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 1.42/1.66 inference(unit_resolution,[status(thm)],[2844, 75, 1518, 1958, 287, 1168])).
% 1.42/1.66 tff(2846,plain,
% 1.42/1.66 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 1.42/1.66 inference(unit_resolution,[status(thm)],[1179, 58, 1176, 2845])).
% 1.42/1.66 tff(2847,plain,
% 1.42/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, 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(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.42/1.66 inference(rewrite,[status(thm)],[])).
% 1.42/1.66 tff(2848,plain,
% 1.42/1.66 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.42/1.66 inference(rewrite,[status(thm)],[])).
% 1.42/1.66 tff(2849,plain,
% 1.42/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 1.42/1.66 inference(monotonicity,[status(thm)],[2848])).
% 1.42/1.66 tff(2850,plain,
% 1.42/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.42/1.67 inference(transitivity,[status(thm)],[2849, 2847])).
% 1.42/1.67 tff(2851,plain,
% 1.42/1.67 ((~![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(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.42/1.67 inference(quant_inst,[status(thm)],[])).
% 1.42/1.67 tff(2852,plain,
% 1.42/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 1.42/1.67 inference(modus_ponens,[status(thm)],[2851, 2850])).
% 1.42/1.67 tff(2853,plain,
% 1.42/1.67 ($false),
% 1.42/1.67 inference(unit_resolution,[status(thm)],[2852, 37, 2747, 2846, 2838, 2830])).
% 1.42/1.67 tff(2854,plain,((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(z, s(s(s(s(z)))))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.42/1.67 tff(2855,plain,
% 1.42/1.67 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.42/1.67 inference(unit_resolution,[status(thm)],[2854, 2822, 2821, 2511, 2818, 284])).
% 1.42/1.67 tff(2856,plain,
% 1.42/1.67 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.42/1.67 inference(unit_resolution,[status(thm)],[813, 2855, 2817])).
% 1.42/1.67 tff(2857,plain,
% 1.42/1.67 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.42/1.67 inference(unit_resolution,[status(thm)],[1219, 37, 2731, 2856])).
% 1.42/1.67 tff(2858,plain,
% 1.42/1.67 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.42/1.67 inference(unit_resolution,[status(thm)],[1230, 58, 1227, 2857])).
% 1.42/1.67 tff(2859,plain,
% 1.42/1.67 (~(s(s(s(z))) = elem!1)),
% 1.42/1.67 inference(unit_resolution,[status(thm)],[1026, 2804, 274])).
% 1.42/1.67 tff(2860,plain,
% 1.42/1.67 (r(z, s(s(elem!1))) <=> r(z, s(s(s(s(z)))))),
% 1.42/1.67 inference(monotonicity,[status(thm)],[2804])).
% 1.42/1.67 tff(2861,plain,
% 1.42/1.67 (r(z, s(s(s(s(z))))) <=> r(z, s(s(elem!1)))),
% 1.42/1.67 inference(symmetry,[status(thm)],[2860])).
% 1.42/1.67 tff(2862,plain,
% 1.42/1.67 (r(z, s(s(elem!1)))),
% 1.42/1.67 inference(modus_ponens,[status(thm)],[2821, 2861])).
% 1.42/1.67 tff(2863,plain,
% 1.42/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)))),
% 1.42/1.67 inference(rewrite,[status(thm)],[])).
% 1.42/1.67 tff(2864,plain,
% 1.42/1.67 (((~b(z, elem!1)) | (~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(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)))),
% 1.42/1.67 inference(rewrite,[status(thm)],[])).
% 1.42/1.67 tff(2865,plain,
% 1.42/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z))))),
% 1.42/1.67 inference(monotonicity,[status(thm)],[2864])).
% 1.42/1.67 tff(2866,plain,
% 1.42/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)))),
% 1.42/1.67 inference(transitivity,[status(thm)],[2865, 2863])).
% 1.42/1.67 tff(2867,plain,
% 1.42/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))),
% 1.42/1.67 inference(quant_inst,[status(thm)],[])).
% 1.42/1.67 tff(2868,plain,
% 1.42/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z))),
% 1.42/1.67 inference(modus_ponens,[status(thm)],[2867, 2866])).
% 1.42/1.67 tff(2869,plain,
% 1.42/1.67 (~b(s(s(s(s(z)))), z)),
% 1.42/1.67 inference(unit_resolution,[status(thm)],[2868, 75, 1518, 1958, 287])).
% 1.42/1.67 tff(2870,plain,
% 1.42/1.67 (r(s(s(s(s(z)))), z)),
% 1.42/1.67 inference(unit_resolution,[status(thm)],[1421, 58, 1143, 2869])).
% 1.42/1.67 tff(2871,plain,
% 1.42/1.67 ((z = s(s(s(z)))) <=> (s(s(s(z))) = z)),
% 1.42/1.67 inference(commutativity,[status(thm)],[])).
% 1.42/1.67 tff(2872,plain,
% 1.42/1.67 ((s(s(s(z))) = z) <=> (z = s(s(s(z))))),
% 1.42/1.67 inference(symmetry,[status(thm)],[2871])).
% 1.42/1.67 tff(2873,plain,
% 1.42/1.67 ((~(s(s(s(z))) = z)) <=> (~(z = s(s(s(z)))))),
% 1.42/1.67 inference(monotonicity,[status(thm)],[2872])).
% 1.42/1.67 tff(2874,plain,
% 1.42/1.67 (~(z = s(s(s(z))))),
% 1.42/1.67 inference(modus_ponens,[status(thm)],[221, 2873])).
% 1.42/1.67 tff(2875,plain,
% 1.42/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))))),
% 1.42/1.67 inference(rewrite,[status(thm)],[])).
% 1.42/1.67 tff(2876,plain,
% 1.42/1.67 (((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z)))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))))),
% 1.42/1.67 inference(rewrite,[status(thm)],[])).
% 1.42/1.67 tff(2877,plain,
% 1.42/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(z)))))))),
% 1.42/1.67 inference(monotonicity,[status(thm)],[2876])).
% 1.42/1.67 tff(2878,plain,
% 1.42/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))))),
% 1.42/1.67 inference(transitivity,[status(thm)],[2877, 2875])).
% 1.42/1.67 tff(2879,plain,
% 1.42/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))))),
% 1.42/1.67 inference(quant_inst,[status(thm)],[])).
% 1.42/1.67 tff(2880,plain,
% 1.42/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(z)))))),
% 1.42/1.67 inference(modus_ponens,[status(thm)],[2879, 2878])).
% 1.42/1.67 tff(2881,plain,
% 1.42/1.67 (~b(z, s(s(s(z))))),
% 1.42/1.67 inference(unit_resolution,[status(thm)],[2880, 75, 1518, 1958, 1119])).
% 1.42/1.67 tff(2882,plain,
% 1.42/1.67 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z)))))),
% 1.42/1.67 inference(rewrite,[status(thm)],[])).
% 1.42/1.67 tff(2883,plain,
% 1.42/1.67 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z)))))),
% 1.42/1.67 inference(quant_inst,[status(thm)],[])).
% 1.42/1.67 tff(2884,plain,
% 1.42/1.67 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z))))),
% 1.42/1.67 inference(modus_ponens,[status(thm)],[2883, 2882])).
% 1.42/1.67 tff(2885,plain,
% 1.42/1.67 ((z = s(s(s(z)))) | r(z, s(s(s(z))))),
% 1.42/1.67 inference(unit_resolution,[status(thm)],[2884, 58, 2881])).
% 1.42/1.67 tff(2886,plain,
% 1.42/1.67 (r(z, s(s(s(z))))),
% 1.42/1.67 inference(unit_resolution,[status(thm)],[2885, 2874])).
% 1.42/1.67 tff(2887,plain,
% 1.42/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, 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(X1, 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(z)))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.42/1.67 inference(rewrite,[status(thm)],[])).
% 1.42/1.67 tff(2888,plain,
% 1.42/1.67 (((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.42/1.67 inference(rewrite,[status(thm)],[])).
% 1.42/1.67 tff(2889,plain,
% 1.42/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.42/1.67 inference(monotonicity,[status(thm)],[2888])).
% 1.42/1.67 tff(2890,plain,
% 1.42/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.42/1.67 inference(transitivity,[status(thm)],[2889, 2887])).
% 1.42/1.67 tff(2891,plain,
% 1.42/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.42/1.67 inference(quant_inst,[status(thm)],[])).
% 1.42/1.67 tff(2892,plain,
% 1.42/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.42/1.67 inference(modus_ponens,[status(thm)],[2891, 2890])).
% 1.42/1.67 tff(2893,plain,
% 1.42/1.67 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.42/1.67 inference(unit_resolution,[status(thm)],[2892, 75, 1518, 1958, 1119, 287])).
% 1.42/1.67 tff(2894,plain,
% 1.42/1.67 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.42/1.67 inference(rewrite,[status(thm)],[])).
% 1.42/1.67 tff(2895,plain,
% 1.42/1.67 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.42/1.67 inference(quant_inst,[status(thm)],[])).
% 1.42/1.67 tff(2896,plain,
% 1.42/1.67 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 1.42/1.67 inference(modus_ponens,[status(thm)],[2895, 2894])).
% 1.42/1.67 tff(2897,plain,
% 1.42/1.67 ((s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 1.42/1.67 inference(unit_resolution,[status(thm)],[2896, 58])).
% 1.42/1.67 tff(2898,plain,
% 1.42/1.67 (b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 1.42/1.67 inference(unit_resolution,[status(thm)],[2897, 264])).
% 1.42/1.67 tff(2899,plain,
% 1.42/1.67 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.42/1.67 inference(unit_resolution,[status(thm)],[2898, 2893])).
% 1.42/1.67 tff(2900,plain,
% 1.42/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, 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(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.42/1.67 inference(rewrite,[status(thm)],[])).
% 1.42/1.67 tff(2901,plain,
% 1.42/1.67 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.42/1.67 inference(rewrite,[status(thm)],[])).
% 1.42/1.67 tff(2902,plain,
% 1.42/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))))),
% 1.42/1.67 inference(monotonicity,[status(thm)],[2901])).
% 1.42/1.67 tff(2903,plain,
% 1.42/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.42/1.67 inference(transitivity,[status(thm)],[2902, 2900])).
% 1.42/1.67 tff(2904,plain,
% 1.42/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)))),
% 1.42/1.67 inference(quant_inst,[status(thm)],[])).
% 1.42/1.67 tff(2905,plain,
% 1.42/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))),
% 1.42/1.68 inference(modus_ponens,[status(thm)],[2904, 2903])).
% 1.42/1.68 tff(2906,plain,
% 1.42/1.68 ($false),
% 1.42/1.68 inference(unit_resolution,[status(thm)],[2905, 37, 2899, 2364, 2886, 2870])).
% 1.42/1.68 tff(2907,plain,((~b(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.42/1.68 tff(2908,plain,
% 1.42/1.68 (~b(s(s(s(z))), elem!1)),
% 1.42/1.68 inference(unit_resolution,[status(thm)],[2907, 2862, 284, 2511, 2818])).
% 1.42/1.68 tff(2909,plain,
% 1.42/1.68 (r(s(s(s(z))), elem!1)),
% 1.42/1.68 inference(unit_resolution,[status(thm)],[1115, 2908, 2859])).
% 1.42/1.68 tff(2910,plain,
% 1.42/1.68 (~r(s(z), s(s(s(z))))),
% 1.42/1.68 inference(unit_resolution,[status(thm)],[1341, 37, 2731, 2909])).
% 1.42/1.68 tff(2911,plain,
% 1.42/1.68 (b(s(z), s(s(s(z))))),
% 1.42/1.68 inference(unit_resolution,[status(thm)],[1263, 2910])).
% 1.42/1.68 tff(2912,plain,
% 1.42/1.68 (~r(s(s(s(z))), s(z))),
% 1.42/1.68 inference(unit_resolution,[status(thm)],[1075, 2909, 2726])).
% 1.42/1.68 tff(2913,plain,
% 1.42/1.68 (b(s(s(s(z))), s(z))),
% 1.42/1.68 inference(unit_resolution,[status(thm)],[1081, 2912])).
% 1.42/1.68 tff(2914,plain,
% 1.42/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.42/1.68 inference(rewrite,[status(thm)],[])).
% 1.42/1.68 tff(2915,plain,
% 1.42/1.68 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.42/1.68 inference(rewrite,[status(thm)],[])).
% 1.42/1.68 tff(2916,plain,
% 1.42/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))))),
% 1.42/1.68 inference(monotonicity,[status(thm)],[2915])).
% 1.42/1.68 tff(2917,plain,
% 1.42/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.42/1.68 inference(transitivity,[status(thm)],[2916, 2914])).
% 1.42/1.68 tff(2918,plain,
% 1.42/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.42/1.68 inference(quant_inst,[status(thm)],[])).
% 1.42/1.68 tff(2919,plain,
% 1.42/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 1.42/1.68 inference(modus_ponens,[status(thm)],[2918, 2917])).
% 1.42/1.68 tff(2920,plain,
% 1.42/1.68 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.42/1.68 inference(unit_resolution,[status(thm)],[2919, 75, 2913, 2911, 2858])).
% 1.42/1.68 tff(2921,plain,
% 1.42/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, 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(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.42/1.68 inference(rewrite,[status(thm)],[])).
% 1.42/1.68 tff(2922,plain,
% 1.42/1.68 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.42/1.68 inference(rewrite,[status(thm)],[])).
% 1.42/1.68 tff(2923,plain,
% 1.42/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(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(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))))),
% 1.42/1.68 inference(monotonicity,[status(thm)],[2922])).
% 1.42/1.68 tff(2924,plain,
% 1.42/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(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(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.42/1.68 inference(transitivity,[status(thm)],[2923, 2921])).
% 1.42/1.68 tff(2925,plain,
% 1.42/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.42/1.68 inference(quant_inst,[status(thm)],[])).
% 1.42/1.68 tff(2926,plain,
% 1.42/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 1.42/1.68 inference(modus_ponens,[status(thm)],[2925, 2924])).
% 1.42/1.68 tff(2927,plain,
% 1.42/1.68 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.42/1.68 inference(unit_resolution,[status(thm)],[2926, 37, 2909, 2856])).
% 1.42/1.68 tff(2928,plain,
% 1.42/1.68 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 1.42/1.68 inference(rewrite,[status(thm)],[])).
% 1.42/1.68 tff(2929,plain,
% 1.42/1.68 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 1.42/1.68 inference(quant_inst,[status(thm)],[])).
% 1.42/1.68 tff(2930,plain,
% 1.42/1.68 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.42/1.68 inference(modus_ponens,[status(thm)],[2929, 2928])).
% 1.42/1.68 tff(2931,plain,
% 1.42/1.68 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.42/1.68 inference(unit_resolution,[status(thm)],[2930, 58, 2927])).
% 1.42/1.68 tff(2932,plain,
% 1.42/1.68 ($false),
% 1.42/1.68 inference(unit_resolution,[status(thm)],[2931, 2920, 2814])).
% 1.42/1.68 tff(2933,plain,((~r(z, s(z))) | b(s(s(z)), elem!1) | (s(s(elem!1)) = s(s(z))) | r(z, elem!1) | r(s(s(s(s(z)))), elem!1) | r(elem!1, s(s(s(s(z))))) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.42/1.68 tff(2934,plain,
% 1.42/1.68 (~r(z, s(z))),
% 1.42/1.68 inference(unit_resolution,[status(thm)],[2933, 13, 266, 99, 12, 268, 267])).
% 1.42/1.68 tff(2935,plain,
% 1.42/1.68 (b(z, s(z))),
% 1.42/1.68 inference(unit_resolution,[status(thm)],[187, 2934])).
% 1.42/1.68 tff(2936,plain,
% 1.42/1.68 (~b(s(s(s(z))), elem!1)),
% 1.42/1.68 inference(unit_resolution,[status(thm)],[2543, 284, 279, 1518])).
% 1.42/1.68 tff(2937,plain,
% 1.42/1.68 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.42/1.68 inference(monotonicity,[status(thm)],[213])).
% 1.42/1.68 tff(2938,plain,
% 1.42/1.68 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 1.42/1.68 inference(symmetry,[status(thm)],[2937])).
% 1.42/1.68 tff(2939,plain,
% 1.42/1.68 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.42/1.68 inference(modus_ponens,[status(thm)],[286, 2938])).
% 1.42/1.68 tff(2940,plain,
% 1.42/1.68 ($false),
% 1.42/1.68 inference(unit_resolution,[status(thm)],[2104, 2939])).
% 1.42/1.68 tff(2941,plain,((~(s(s(s(z))) = elem!1)) | b(s(s(s(z))), s(s(s(s(z))))) | (~b(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.42/1.68 tff(2942,plain,
% 1.42/1.68 (~(s(s(s(z))) = elem!1)),
% 1.42/1.68 inference(unit_resolution,[status(thm)],[2941, 2104, 279])).
% 1.42/1.68 tff(2943,plain,
% 1.42/1.68 (r(s(s(s(z))), elem!1)),
% 1.42/1.68 inference(unit_resolution,[status(thm)],[1115, 2942, 2936])).
% 1.42/1.68 tff(2944,plain,
% 1.42/1.68 (~b(z, s(s(s(s(z)))))),
% 1.42/1.68 inference(unit_resolution,[status(thm)],[2525, 75, 1518, 279, 284])).
% 1.42/1.68 tff(2945,plain,
% 1.42/1.68 ((z = s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 1.42/1.68 inference(unit_resolution,[status(thm)],[1515, 58, 2944])).
% 1.42/1.68 tff(2946,plain,
% 1.42/1.68 (r(z, s(s(s(s(z)))))),
% 1.42/1.68 inference(unit_resolution,[status(thm)],[2945, 1503])).
% 1.42/1.68 tff(2947,plain,
% 1.42/1.68 (~r(s(s(s(z))), z)),
% 1.42/1.68 inference(unit_resolution,[status(thm)],[2541, 37, 2105, 2946])).
% 1.42/1.68 tff(2948,plain,
% 1.42/1.68 (b(s(s(s(z))), z)),
% 1.42/1.68 inference(unit_resolution,[status(thm)],[1334, 58, 221, 2947])).
% 1.42/1.68 tff(2949,plain,
% 1.42/1.68 (~(s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))),
% 1.42/1.68 inference(unit_resolution,[status(thm)],[862, 274])).
% 1.42/1.68 tff(2950,plain,
% 1.42/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(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(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 1.42/1.68 inference(rewrite,[status(thm)],[])).
% 1.42/1.68 tff(2951,plain,
% 1.42/1.68 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 1.42/1.68 inference(rewrite,[status(thm)],[])).
% 1.42/1.68 tff(2952,plain,
% 1.42/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))))),
% 1.42/1.68 inference(monotonicity,[status(thm)],[2951])).
% 1.42/1.68 tff(2953,plain,
% 1.42/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 1.42/1.68 inference(transitivity,[status(thm)],[2952, 2950])).
% 1.42/1.68 tff(2954,plain,
% 1.42/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))),
% 1.42/1.68 inference(quant_inst,[status(thm)],[])).
% 1.42/1.68 tff(2955,plain,
% 1.42/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))),
% 1.42/1.68 inference(modus_ponens,[status(thm)],[2954, 2953])).
% 1.42/1.68 tff(2956,plain,
% 1.42/1.68 (~r(z, s(s(s(z))))),
% 1.42/1.68 inference(unit_resolution,[status(thm)],[2955, 37, 2105, 2946])).
% 1.42/1.68 tff(2957,plain,
% 1.42/1.68 ((s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))),
% 1.42/1.68 inference(commutativity,[status(thm)],[])).
% 1.42/1.68 tff(2958,plain,
% 1.42/1.68 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 1.42/1.68 inference(monotonicity,[status(thm)],[611])).
% 1.42/1.68 tff(2959,plain,
% 1.42/1.68 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))),
% 1.42/1.68 inference(transitivity,[status(thm)],[2958, 2957])).
% 1.42/1.68 tff(2960,plain,
% 1.42/1.68 ((s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(s(z)))))),
% 1.42/1.68 inference(symmetry,[status(thm)],[2959])).
% 1.42/1.68 tff(2961,plain,
% 1.42/1.68 ((~(s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))))),
% 1.42/1.68 inference(monotonicity,[status(thm)],[2960])).
% 1.42/1.68 tff(2962,plain,
% 1.42/1.68 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(z)))))),
% 1.42/1.68 inference(modus_ponens,[status(thm)],[868, 2961])).
% 1.42/1.68 tff(2963,plain,
% 1.42/1.68 (b(s(s(s(z))), z) <=> b(s(s(elem!1)), z)),
% 1.42/1.68 inference(monotonicity,[status(thm)],[610])).
% 1.42/1.68 tff(2964,plain,
% 1.42/1.68 (b(s(s(elem!1)), z)),
% 1.42/1.68 inference(modus_ponens,[status(thm)],[1083, 2963])).
% 1.42/1.68 tff(2965,plain,
% 1.42/1.68 (r(z, s(s(s(z)))) <=> r(z, s(s(elem!1)))),
% 1.42/1.68 inference(monotonicity,[status(thm)],[610])).
% 1.42/1.68 tff(2966,plain,
% 1.42/1.68 ((~r(z, s(s(s(z))))) <=> (~r(z, s(s(elem!1))))),
% 1.42/1.68 inference(monotonicity,[status(thm)],[2965])).
% 1.42/1.68 tff(2967,assumption,(~r(z, s(s(s(z))))), introduced(assumption)).
% 1.42/1.68 tff(2968,plain,
% 1.42/1.68 (~r(z, s(s(elem!1)))),
% 1.42/1.68 inference(modus_ponens,[status(thm)],[2967, 2966])).
% 1.42/1.68 tff(2969,plain,
% 1.42/1.68 ((z = s(s(elem!1))) | b(z, s(s(elem!1)))),
% 1.42/1.68 inference(unit_resolution,[status(thm)],[1834, 58, 2968])).
% 1.42/1.68 tff(2970,plain,
% 1.42/1.68 (b(z, s(s(elem!1)))),
% 1.42/1.68 inference(unit_resolution,[status(thm)],[2969, 1824])).
% 1.42/1.68 tff(2971,plain,
% 1.42/1.68 (b(s(s(z)), s(s(s(z)))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.42/1.68 inference(monotonicity,[status(thm)],[609, 610])).
% 1.42/1.68 tff(2972,plain,
% 1.42/1.68 (b(s(s(z)), s(s(s(z))))),
% 1.42/1.68 inference(unit_resolution,[status(thm)],[1559, 58, 1556, 2732])).
% 1.42/1.68 tff(2973,plain,
% 1.42/1.68 (b(s(elem!1), s(s(elem!1)))),
% 1.42/1.68 inference(modus_ponens,[status(thm)],[2972, 2971])).
% 1.42/1.68 tff(2974,plain,
% 1.42/1.68 (((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.42/1.68 inference(rewrite,[status(thm)],[])).
% 1.42/1.68 tff(2975,plain,
% 1.42/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1), s(s(elem!1))))))),
% 1.42/1.68 inference(monotonicity,[status(thm)],[2974])).
% 1.42/1.68 tff(2976,plain,
% 1.42/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1), s(s(elem!1)))))),
% 1.42/1.68 inference(transitivity,[status(thm)],[2975, 1837])).
% 1.42/1.68 tff(2977,plain,
% 1.42/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))),
% 1.42/1.68 inference(quant_inst,[status(thm)],[])).
% 1.42/1.68 tff(2978,plain,
% 1.42/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1), s(s(elem!1))))),
% 1.42/1.68 inference(modus_ponens,[status(thm)],[2977, 2976])).
% 1.42/1.68 tff(2979,plain,
% 1.42/1.68 (~b(s(elem!1), z)),
% 1.42/1.68 inference(unit_resolution,[status(thm)],[2978, 75, 2973, 2970, 2964])).
% 1.42/1.68 tff(2980,plain,
% 1.42/1.68 (r(s(elem!1), z)),
% 1.42/1.68 inference(unit_resolution,[status(thm)],[766, 2979])).
% 1.42/1.68 tff(2981,plain,
% 1.42/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 1.42/1.68 inference(rewrite,[status(thm)],[])).
% 1.42/1.68 tff(2982,plain,
% 1.42/1.68 (((~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 1.42/1.68 inference(rewrite,[status(thm)],[])).
% 1.42/1.68 tff(2983,plain,
% 1.42/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))))),
% 1.42/1.68 inference(monotonicity,[status(thm)],[2982])).
% 1.42/1.68 tff(2984,plain,
% 1.42/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 1.42/1.68 inference(transitivity,[status(thm)],[2983, 2981])).
% 1.42/1.68 tff(2985,plain,
% 1.42/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)))),
% 1.42/1.68 inference(quant_inst,[status(thm)],[])).
% 1.42/1.68 tff(2986,plain,
% 1.42/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))),
% 1.42/1.68 inference(modus_ponens,[status(thm)],[2985, 2984])).
% 1.42/1.68 tff(2987,plain,
% 1.42/1.68 ($false),
% 1.42/1.68 inference(unit_resolution,[status(thm)],[2986, 37, 155, 752, 1752])).
% 1.42/1.68 tff(2988,plain,((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.42/1.68 tff(2989,plain,
% 1.42/1.68 (~r(elem!1, z)),
% 1.42/1.68 inference(unit_resolution,[status(thm)],[2988, 627, 2980])).
% 1.42/1.68 tff(2990,plain,
% 1.42/1.68 (b(elem!1, z)),
% 1.42/1.68 inference(unit_resolution,[status(thm)],[387, 2989, 353])).
% 1.42/1.68 tff(2991,plain,
% 1.42/1.68 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.42/1.68 inference(unit_resolution,[status(thm)],[2854, 2990, 2747, 1518, 2962, 287])).
% 1.42/1.68 tff(2992,plain,
% 1.42/1.68 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.42/1.68 inference(unit_resolution,[status(thm)],[813, 2991, 720])).
% 1.42/1.68 tff(2993,plain,
% 1.42/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(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(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.42/1.69 inference(rewrite,[status(thm)],[])).
% 1.42/1.69 tff(2994,plain,
% 1.42/1.69 (((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.42/1.69 inference(rewrite,[status(thm)],[])).
% 1.42/1.69 tff(2995,plain,
% 1.42/1.69 (((~![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(s(z))))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(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(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 1.42/1.69 inference(monotonicity,[status(thm)],[2994])).
% 1.42/1.69 tff(2996,plain,
% 1.42/1.69 (((~![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(s(z))))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(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(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.42/1.69 inference(transitivity,[status(thm)],[2995, 2993])).
% 1.42/1.69 tff(2997,plain,
% 1.42/1.69 ((~![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(s(z))))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.42/1.69 inference(quant_inst,[status(thm)],[])).
% 1.42/1.69 tff(2998,plain,
% 1.42/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 1.42/1.69 inference(modus_ponens,[status(thm)],[2997, 2996])).
% 1.42/1.69 tff(2999,plain,
% 1.42/1.69 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.42/1.69 inference(unit_resolution,[status(thm)],[2998, 37, 2992, 627])).
% 1.42/1.69 tff(3000,plain,
% 1.42/1.69 ((s(s(s(s(s(s(s(z))))))) = s(elem!1)) <=> (s(s(s(s(s(s(s(z))))))) = s(s(z)))),
% 1.42/1.69 inference(monotonicity,[status(thm)],[619])).
% 1.42/1.69 tff(3001,assumption,(s(s(s(s(s(s(s(z))))))) = s(elem!1)), introduced(assumption)).
% 1.42/1.69 tff(3002,plain,
% 1.42/1.69 (s(s(s(s(s(s(s(z))))))) = s(s(z))),
% 1.42/1.69 inference(modus_ponens,[status(thm)],[3001, 3000])).
% 1.42/1.69 tff(3003,assumption,(~(s(s(s(s(s(s(s(z))))))) = s(s(z)))), introduced(assumption)).
% 1.42/1.69 tff(3004,plain,
% 1.42/1.69 ($false),
% 1.42/1.69 inference(unit_resolution,[status(thm)],[3003, 3002])).
% 1.42/1.69 tff(3005,plain,((~(s(s(s(s(s(s(s(z))))))) = s(elem!1))) | (s(s(s(s(s(s(s(z))))))) = s(s(z))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.42/1.69 tff(3006,plain,
% 1.42/1.69 ((~(s(s(s(s(s(s(s(z))))))) = s(elem!1))) | (~(s(z) = elem!1))),
% 1.42/1.69 inference(unit_resolution,[status(thm)],[3005, 1045])).
% 1.42/1.69 tff(3007,plain,
% 1.42/1.69 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.42/1.69 inference(unit_resolution,[status(thm)],[3006, 93])).
% 1.42/1.69 tff(3008,plain,
% 1.42/1.69 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(elem!1)) | b(s(s(s(s(s(s(s(z))))))), s(elem!1)) | r(s(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(s(z))))))) = s(elem!1)) | b(s(s(s(s(s(s(s(z))))))), s(elem!1)) | r(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 1.42/1.69 inference(rewrite,[status(thm)],[])).
% 1.42/1.69 tff(3009,plain,
% 1.42/1.69 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(elem!1)) | b(s(s(s(s(s(s(s(z))))))), s(elem!1)) | r(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 1.42/1.69 inference(quant_inst,[status(thm)],[])).
% 1.42/1.69 tff(3010,plain,
% 1.42/1.69 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | b(s(s(s(s(s(s(s(z))))))), s(elem!1)) | r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.42/1.69 inference(modus_ponens,[status(thm)],[3009, 3008])).
% 1.42/1.69 tff(3011,plain,
% 1.42/1.69 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.42/1.69 inference(unit_resolution,[status(thm)],[3010, 58, 3007, 2999])).
% 1.42/1.69 tff(3012,plain,
% 1.42/1.69 (r(s(s(s(z))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 1.42/1.69 inference(monotonicity,[status(thm)],[610])).
% 1.42/1.69 tff(3013,plain,
% 1.42/1.69 (r(s(s(elem!1)), elem!1)),
% 1.42/1.69 inference(modus_ponens,[status(thm)],[1061, 3012])).
% 1.42/1.69 tff(3014,plain,
% 1.42/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.42/1.69 inference(rewrite,[status(thm)],[])).
% 1.42/1.69 tff(3015,plain,
% 1.42/1.69 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.42/1.69 inference(rewrite,[status(thm)],[])).
% 1.42/1.69 tff(3016,plain,
% 1.42/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), s(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(s(z))))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 1.42/1.69 inference(monotonicity,[status(thm)],[3015])).
% 1.42/1.69 tff(3017,plain,
% 1.42/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), s(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(s(z))))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.42/1.69 inference(transitivity,[status(thm)],[3016, 3014])).
% 1.42/1.69 tff(3018,plain,
% 1.42/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.42/1.69 inference(quant_inst,[status(thm)],[])).
% 1.42/1.69 tff(3019,plain,
% 1.42/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 1.42/1.69 inference(modus_ponens,[status(thm)],[3018, 3017])).
% 1.42/1.69 tff(3020,plain,
% 1.42/1.69 (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.42/1.69 inference(unit_resolution,[status(thm)],[3019, 37, 2992, 3013])).
% 1.42/1.69 tff(3021,plain,
% 1.42/1.69 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.42/1.69 inference(unit_resolution,[status(thm)],[840, 58, 837, 3020])).
% 1.42/1.69 tff(3022,plain,
% 1.42/1.69 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.42/1.69 inference(unit_resolution,[status(thm)],[788, 37, 2992, 627])).
% 1.42/1.69 tff(3023,plain,
% 1.42/1.69 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.42/1.69 inference(unit_resolution,[status(thm)],[793, 58, 737, 3022])).
% 1.42/1.69 tff(3024,plain,
% 1.42/1.69 (b(s(s(s(z))), s(s(z))) <=> b(s(s(elem!1)), s(elem!1))),
% 1.42/1.69 inference(monotonicity,[status(thm)],[610, 609])).
% 1.42/1.69 tff(3025,plain,
% 1.42/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(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(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), elem!1)))),
% 1.42/1.69 inference(rewrite,[status(thm)],[])).
% 1.42/1.69 tff(3026,plain,
% 1.42/1.69 (((~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), elem!1)))),
% 1.42/1.69 inference(rewrite,[status(thm)],[])).
% 1.42/1.69 tff(3027,plain,
% 1.42/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), elem!1))))),
% 1.42/1.69 inference(monotonicity,[status(thm)],[3026])).
% 1.42/1.69 tff(3028,plain,
% 1.42/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), elem!1)))),
% 1.42/1.69 inference(transitivity,[status(thm)],[3027, 3025])).
% 1.42/1.69 tff(3029,plain,
% 1.42/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), s(s(z)))))),
% 1.42/1.69 inference(quant_inst,[status(thm)],[])).
% 1.42/1.69 tff(3030,plain,
% 1.42/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), elem!1))),
% 1.42/1.69 inference(modus_ponens,[status(thm)],[3029, 3028])).
% 1.42/1.69 tff(3031,plain,
% 1.42/1.69 (~r(s(s(s(z))), s(s(z)))),
% 1.42/1.69 inference(unit_resolution,[status(thm)],[3030, 37, 106, 1061])).
% 1.42/1.69 tff(3032,plain,
% 1.42/1.69 ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z)))),
% 1.42/1.69 inference(unit_resolution,[status(thm)],[2173, 58, 3031])).
% 1.42/1.69 tff(3033,plain,
% 1.42/1.69 (b(s(s(s(z))), s(s(z)))),
% 1.42/1.69 inference(unit_resolution,[status(thm)],[3032, 2150])).
% 1.42/1.69 tff(3034,plain,
% 1.42/1.69 (b(s(s(elem!1)), s(elem!1))),
% 1.42/1.69 inference(modus_ponens,[status(thm)],[3033, 3024])).
% 1.42/1.69 tff(3035,plain,
% 1.42/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.42/1.69 inference(rewrite,[status(thm)],[])).
% 1.42/1.69 tff(3036,plain,
% 1.42/1.69 (((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.42/1.69 inference(rewrite,[status(thm)],[])).
% 1.42/1.69 tff(3037,plain,
% 1.42/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 1.42/1.69 inference(monotonicity,[status(thm)],[3036])).
% 1.42/1.69 tff(3038,plain,
% 1.42/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.42/1.69 inference(transitivity,[status(thm)],[3037, 3035])).
% 1.42/1.69 tff(3039,plain,
% 1.42/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.42/1.69 inference(quant_inst,[status(thm)],[])).
% 1.42/1.69 tff(3040,plain,
% 1.42/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 1.42/1.69 inference(modus_ponens,[status(thm)],[3039, 3038])).
% 1.42/1.69 tff(3041,plain,
% 1.42/1.69 ($false),
% 1.42/1.69 inference(unit_resolution,[status(thm)],[3040, 75, 3034, 3023, 3021, 3011])).
% 1.42/1.69 tff(3042,plain,((~(s(z) = elem!1)) | (~r(z, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (elem!1 = z) | (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))) | r(z, s(s(s(z)))) | (~b(s(s(s(z))), z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.42/1.69 tff(3043,plain,
% 1.42/1.69 (~(s(z) = elem!1)),
% 1.42/1.69 inference(unit_resolution,[status(thm)],[3042, 2956, 1518, 284, 353, 2949, 2946, 2948, 2943, 106])).
% 1.42/1.69 tff(3044,plain,
% 1.42/1.69 (r(elem!1, s(z))),
% 1.42/1.69 inference(unit_resolution,[status(thm)],[2606, 3043, 1518, 12, 268, 267])).
% 1.42/1.69 tff(3045,plain,
% 1.42/1.69 (~b(s(z), s(s(z)))),
% 1.42/1.69 inference(unit_resolution,[status(thm)],[2743, 3044, 106, 2943])).
% 1.42/1.69 tff(3046,plain,
% 1.42/1.69 (r(s(z), s(s(z)))),
% 1.42/1.69 inference(unit_resolution,[status(thm)],[416, 3045])).
% 1.42/1.69 tff(3047,plain,
% 1.42/1.69 (~r(s(s(s(z))), s(z))),
% 1.42/1.69 inference(unit_resolution,[status(thm)],[1075, 3044, 2943])).
% 1.42/1.69 tff(3048,plain,
% 1.42/1.69 (b(s(s(s(z))), s(z))),
% 1.42/1.69 inference(unit_resolution,[status(thm)],[1081, 3047])).
% 1.42/1.69 tff(3049,plain,
% 1.42/1.69 (~b(s(z), s(s(s(z))))),
% 1.42/1.69 inference(unit_resolution,[status(thm)],[1091, 3048, 372, 2948])).
% 1.42/1.69 tff(3050,plain,
% 1.42/1.69 (r(s(z), s(s(s(z))))),
% 1.42/1.69 inference(unit_resolution,[status(thm)],[1263, 3049])).
% 1.42/1.69 tff(3051,plain,
% 1.42/1.69 (~r(s(z), s(s(s(s(z)))))),
% 1.42/1.69 inference(unit_resolution,[status(thm)],[1316, 3050, 2105])).
% 1.42/1.69 tff(3052,plain,
% 1.42/1.69 (b(s(z), s(s(s(s(z)))))),
% 1.42/1.69 inference(unit_resolution,[status(thm)],[489, 3051])).
% 1.42/1.69 tff(3053,plain,
% 1.42/1.69 (~b(s(z), elem!1)),
% 1.42/1.69 inference(unit_resolution,[status(thm)],[586, 3052, 279, 284])).
% 1.42/1.69 tff(3054,plain,
% 1.42/1.69 (r(s(z), elem!1)),
% 1.42/1.69 inference(unit_resolution,[status(thm)],[601, 3053, 3043])).
% 1.42/1.69 tff(3055,plain,
% 1.42/1.69 ($false),
% 1.42/1.69 inference(unit_resolution,[status(thm)],[2081, 37, 3054, 106, 3046])).
% 1.42/1.69 tff(3056,plain,(b(s(s(s(z))), s(s(s(s(z))))) | (~r(s(s(z)), elem!1)) | (~b(z, s(z))) | (~b(z, elem!1)) | r(s(s(s(s(z)))), elem!1) | r(elem!1, s(s(s(s(z))))) | (s(s(s(s(z)))) = elem!1) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.42/1.69 tff(3057,plain,
% 1.42/1.69 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.42/1.69 inference(unit_resolution,[status(thm)],[3056, 2545, 2935, 2511, 12, 268, 267, 305])).
% 1.42/1.69 tff(3058,plain,
% 1.42/1.69 (~b(elem!1, s(s(s(z))))),
% 1.42/1.69 inference(unit_resolution,[status(thm)],[2145, 75, 279, 3057, 284])).
% 1.42/1.69 tff(3059,plain,
% 1.42/1.69 (~(elem!1 = s(s(s(z))))),
% 1.42/1.69 inference(unit_resolution,[status(thm)],[1033, 2711])).
% 1.42/1.69 tff(3060,plain,
% 1.42/1.69 (r(elem!1, s(s(s(z))))),
% 1.42/1.69 inference(unit_resolution,[status(thm)],[1279, 3059, 3058])).
% 1.42/1.69 tff(3061,plain,
% 1.42/1.69 (b(s(s(s(elem!1))), elem!1)),
% 1.42/1.69 inference(unit_resolution,[status(thm)],[935, 93, 287])).
% 1.42/1.69 tff(3062,plain,
% 1.42/1.69 (b(elem!1, s(s(s(elem!1))))),
% 1.42/1.69 inference(modus_ponens,[status(thm)],[286, 916])).
% 1.42/1.69 tff(3063,plain,
% 1.42/1.69 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.42/1.69 inference(unit_resolution,[status(thm)],[2998, 37, 738, 752])).
% 1.42/1.69 tff(3064,assumption,(~(s(s(s(s(s(s(s(z))))))) = s(elem!1))), introduced(assumption)).
% 1.42/1.69 tff(3065,plain,
% 1.42/1.69 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.42/1.69 inference(unit_resolution,[status(thm)],[3010, 58, 3064, 3063])).
% 1.42/1.69 tff(3066,plain,
% 1.42/1.69 (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.42/1.69 inference(unit_resolution,[status(thm)],[3019, 37, 738, 2647])).
% 1.42/1.69 tff(3067,assumption,(~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.42/1.69 tff(3068,plain,
% 1.42/1.69 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.42/1.69 inference(unit_resolution,[status(thm)],[840, 58, 3067, 3066])).
% 1.42/1.69 tff(3069,assumption,(b(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 1.42/1.69 tff(3070,plain,
% 1.42/1.69 ($false),
% 1.42/1.69 inference(unit_resolution,[status(thm)],[3040, 75, 3069, 794, 3068, 3065])).
% 1.42/1.69 tff(3071,plain,((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.42/1.69 tff(3072,plain,
% 1.42/1.69 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.42/1.69 inference(unit_resolution,[status(thm)],[3071, 3034, 3007, 837, 737, 627, 3013])).
% 1.42/1.69 tff(3073,plain,
% 1.42/1.69 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.42/1.69 inference(unit_resolution,[status(thm)],[813, 3072, 720])).
% 1.42/1.69 tff(3074,plain,
% 1.42/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 1.42/1.69 inference(rewrite,[status(thm)],[])).
% 1.42/1.69 tff(3075,plain,
% 1.42/1.69 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 1.42/1.69 inference(rewrite,[status(thm)],[])).
% 1.42/1.69 tff(3076,plain,
% 1.42/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))), 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(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))))),
% 1.42/1.69 inference(monotonicity,[status(thm)],[3075])).
% 1.42/1.69 tff(3077,plain,
% 1.42/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))), 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(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 1.42/1.70 inference(transitivity,[status(thm)],[3076, 3074])).
% 1.42/1.70 tff(3078,plain,
% 1.42/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))), 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(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 1.42/1.70 inference(quant_inst,[status(thm)],[])).
% 1.42/1.70 tff(3079,plain,
% 1.42/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))),
% 1.42/1.70 inference(modus_ponens,[status(thm)],[3078, 3077])).
% 1.42/1.70 tff(3080,plain,
% 1.42/1.70 (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 1.42/1.70 inference(unit_resolution,[status(thm)],[3079, 75, 3073, 3062, 3061])).
% 1.42/1.70 tff(3081,plain,
% 1.42/1.70 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))),
% 1.42/1.70 inference(rewrite,[status(thm)],[])).
% 1.42/1.70 tff(3082,plain,
% 1.42/1.70 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))),
% 1.42/1.70 inference(quant_inst,[status(thm)],[])).
% 1.42/1.70 tff(3083,plain,
% 1.42/1.70 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 1.42/1.70 inference(modus_ponens,[status(thm)],[3082, 3081])).
% 1.42/1.70 tff(3084,plain,
% 1.42/1.70 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 1.42/1.70 inference(unit_resolution,[status(thm)],[3083, 58, 868, 3080])).
% 1.42/1.70 tff(3085,plain,
% 1.42/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, 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(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, 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(s(z))))))), elem!1)))),
% 1.42/1.70 inference(rewrite,[status(thm)],[])).
% 1.42/1.70 tff(3086,plain,
% 1.42/1.70 (((~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z))) <=> ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, 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(s(z))))))), elem!1)))),
% 1.42/1.70 inference(rewrite,[status(thm)],[])).
% 1.42/1.70 tff(3087,plain,
% 1.42/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, 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(s(z))))))), elem!1))))),
% 1.52/1.70 inference(monotonicity,[status(thm)],[3086])).
% 1.52/1.70 tff(3088,plain,
% 1.52/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, 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(s(z))))))), elem!1)))),
% 1.52/1.70 inference(transitivity,[status(thm)],[3087, 3085])).
% 1.52/1.70 tff(3089,plain,
% 1.52/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.52/1.70 inference(quant_inst,[status(thm)],[])).
% 1.52/1.70 tff(3090,plain,
% 1.52/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, 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(s(z))))))), elem!1))),
% 1.52/1.70 inference(modus_ponens,[status(thm)],[3089, 3088])).
% 1.52/1.70 tff(3091,plain,
% 1.52/1.70 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[3090, 75, 1518, 3073, 3062, 3061])).
% 1.52/1.70 tff(3092,plain,
% 1.52/1.70 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[750, 58, 747, 3091])).
% 1.52/1.70 tff(3093,plain,
% 1.52/1.70 (r(s(s(s(elem!1))), z) <=> r(s(s(s(s(z)))), z)),
% 1.52/1.70 inference(monotonicity,[status(thm)],[612])).
% 1.52/1.70 tff(3094,plain,
% 1.52/1.70 (r(s(s(s(s(z)))), z) <=> r(s(s(s(elem!1))), z)),
% 1.52/1.70 inference(symmetry,[status(thm)],[3093])).
% 1.52/1.70 tff(3095,plain,
% 1.52/1.70 (r(s(s(s(elem!1))), z)),
% 1.52/1.70 inference(modus_ponens,[status(thm)],[2611, 3094])).
% 1.52/1.70 tff(3096,plain,
% 1.52/1.70 (((~![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(s(z))))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(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(s(z))))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 1.52/1.70 inference(rewrite,[status(thm)],[])).
% 1.52/1.70 tff(3097,plain,
% 1.52/1.70 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 1.52/1.70 inference(rewrite,[status(thm)],[])).
% 1.52/1.70 tff(3098,plain,
% 1.52/1.70 (((~![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(s(z))))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(elem!1))), s(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(s(z))))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))))),
% 1.52/1.70 inference(monotonicity,[status(thm)],[3097])).
% 1.52/1.70 tff(3099,plain,
% 1.52/1.70 (((~![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(s(z))))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(elem!1))), s(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(s(z))))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 1.52/1.70 inference(transitivity,[status(thm)],[3098, 3096])).
% 1.52/1.70 tff(3100,plain,
% 1.52/1.70 ((~![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(s(z))))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 1.52/1.70 inference(quant_inst,[status(thm)],[])).
% 1.52/1.70 tff(3101,plain,
% 1.52/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))),
% 1.52/1.70 inference(modus_ponens,[status(thm)],[3100, 3099])).
% 1.52/1.70 tff(3102,plain,
% 1.52/1.70 ($false),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[3101, 37, 3095, 3092, 3084])).
% 1.52/1.70 tff(3103,plain,((~(s(z) = elem!1)) | (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.70 tff(3104,plain,
% 1.52/1.70 (~(s(z) = elem!1)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[3103, 2712, 2511, 279, 2949, 2545, 284])).
% 1.52/1.70 tff(3105,plain,
% 1.52/1.70 (r(elem!1, s(z))),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[2606, 3104, 2511, 12, 268, 267])).
% 1.52/1.70 tff(3106,plain,
% 1.52/1.70 (~r(s(z), s(s(s(z))))),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[1274, 3105, 3060])).
% 1.52/1.70 tff(3107,plain,
% 1.52/1.70 (b(s(z), s(s(s(z))))),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[1263, 3106])).
% 1.52/1.70 tff(3108,plain,
% 1.52/1.70 (~r(s(s(s(z))), s(z))),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[1075, 3105, 2712])).
% 1.52/1.70 tff(3109,plain,
% 1.52/1.70 (b(s(s(s(z))), s(z))),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[1081, 3108])).
% 1.52/1.70 tff(3110,plain,
% 1.52/1.70 (~r(s(s(z)), s(z))),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[123, 3105, 2545])).
% 1.52/1.70 tff(3111,plain,
% 1.52/1.70 (b(s(s(z)), s(z))),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[153, 3110])).
% 1.52/1.70 tff(3112,plain,
% 1.52/1.70 ($false),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[1745, 75, 3111, 3109, 3107, 2720])).
% 1.52/1.70 tff(3113,plain,((s(s(elem!1)) = s(s(s(s(z))))) | r(s(s(s(s(z)))), elem!1) | r(elem!1, s(s(s(s(z))))) | (s(s(s(s(z)))) = elem!1) | (s(s(elem!1)) = s(s(z))) | r(z, elem!1) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.52/1.70 tff(3114,plain,
% 1.52/1.70 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[3113, 13, 268, 267, 266, 12, 99])).
% 1.52/1.70 tff(3115,plain,
% 1.52/1.70 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(z)))))),
% 1.52/1.70 inference(monotonicity,[status(thm)],[3114])).
% 1.52/1.70 tff(3116,plain,
% 1.52/1.70 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 1.52/1.70 inference(symmetry,[status(thm)],[3115])).
% 1.52/1.70 tff(3117,plain,
% 1.52/1.70 (s(s(s(z))) = s(elem!1)),
% 1.52/1.70 inference(transitivity,[status(thm)],[451, 3116, 228])).
% 1.52/1.70 tff(3118,plain,
% 1.52/1.70 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.52/1.70 inference(monotonicity,[status(thm)],[3117])).
% 1.52/1.70 tff(3119,plain,
% 1.52/1.70 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.52/1.70 inference(transitivity,[status(thm)],[3118, 269])).
% 1.52/1.70 tff(3120,plain,
% 1.52/1.70 ((s(elem!1) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(z))))),
% 1.52/1.70 inference(symmetry,[status(thm)],[3119])).
% 1.52/1.70 tff(3121,plain,
% 1.52/1.70 ((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(s(s(z)))))),
% 1.52/1.70 inference(monotonicity,[status(thm)],[3120])).
% 1.52/1.70 tff(3122,plain,
% 1.52/1.70 (s(s(z)) = elem!1),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[1425, 3114])).
% 1.52/1.70 tff(3123,plain,
% 1.52/1.70 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[1145, 3122])).
% 1.52/1.70 tff(3124,plain,
% 1.52/1.70 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))),
% 1.52/1.70 inference(modus_ponens,[status(thm)],[3123, 3121])).
% 1.52/1.70 tff(3125,plain,
% 1.52/1.70 ((s(s(s(s(s(s(s(z))))))) = s(s(z))) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.52/1.70 inference(monotonicity,[status(thm)],[3122])).
% 1.52/1.70 tff(3126,plain,
% 1.52/1.70 ((~(s(s(s(s(s(s(s(z))))))) = s(s(z)))) <=> (~(s(s(s(s(s(s(s(z))))))) = elem!1))),
% 1.52/1.70 inference(monotonicity,[status(thm)],[3125])).
% 1.52/1.70 tff(3127,plain,
% 1.52/1.70 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.52/1.70 inference(modus_ponens,[status(thm)],[1045, 3126])).
% 1.52/1.70 tff(3128,plain,
% 1.52/1.70 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(z)))))),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[1134, 3122])).
% 1.52/1.70 tff(3129,plain,
% 1.52/1.70 (s(elem!1) = s(s(s(z)))),
% 1.52/1.70 inference(transitivity,[status(thm)],[229, 3115, 250])).
% 1.52/1.70 tff(3130,plain,
% 1.52/1.70 (r(s(elem!1), elem!1) <=> r(s(s(s(z))), elem!1)),
% 1.52/1.70 inference(monotonicity,[status(thm)],[3129])).
% 1.52/1.70 tff(3131,plain,
% 1.52/1.70 (r(s(s(s(z))), elem!1) <=> r(s(elem!1), elem!1)),
% 1.52/1.70 inference(symmetry,[status(thm)],[3130])).
% 1.52/1.70 tff(3132,plain,
% 1.52/1.70 (~(s(s(s(z))) = elem!1)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[1026, 3114, 274])).
% 1.52/1.70 tff(3133,plain,
% 1.52/1.70 (r(s(s(s(z))), elem!1)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[1115, 3132, 2544])).
% 1.52/1.70 tff(3134,plain,
% 1.52/1.70 (r(s(elem!1), elem!1)),
% 1.52/1.70 inference(modus_ponens,[status(thm)],[3133, 3131])).
% 1.52/1.70 tff(3135,plain,
% 1.52/1.70 ((s(s(z)) = s(z)) <=> (elem!1 = s(z))),
% 1.52/1.70 inference(monotonicity,[status(thm)],[3122])).
% 1.52/1.70 tff(3136,plain,
% 1.52/1.70 ((s(s(z)) = s(z)) <=> (s(z) = elem!1)),
% 1.52/1.70 inference(transitivity,[status(thm)],[3135, 91])).
% 1.52/1.70 tff(3137,plain,
% 1.52/1.70 ((~(s(s(z)) = s(z))) <=> (~(s(z) = elem!1))),
% 1.52/1.70 inference(monotonicity,[status(thm)],[3136])).
% 1.52/1.70 tff(3138,plain,
% 1.52/1.70 (~(s(z) = elem!1)),
% 1.52/1.70 inference(modus_ponens,[status(thm)],[148, 3137])).
% 1.52/1.70 tff(3139,plain,
% 1.52/1.70 (r(elem!1, s(z))),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[2606, 3138, 2511, 12, 268, 267])).
% 1.52/1.70 tff(3140,plain,
% 1.52/1.70 (~r(s(s(s(z))), s(z))),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[1075, 3139, 3133])).
% 1.52/1.70 tff(3141,plain,
% 1.52/1.70 (b(s(s(s(z))), s(z))),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[1081, 3140])).
% 1.52/1.70 tff(3142,plain,
% 1.52/1.70 (~(elem!1 = s(s(s(z))))),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[1033, 3132])).
% 1.52/1.70 tff(3143,plain,
% 1.52/1.70 (s(s(z)) = elem!1),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[1425, 1020])).
% 1.52/1.70 tff(3144,plain,
% 1.52/1.70 ((s(s(z)) = s(z)) <=> (elem!1 = s(z))),
% 1.52/1.70 inference(monotonicity,[status(thm)],[3143])).
% 1.52/1.70 tff(3145,plain,
% 1.52/1.70 ((s(s(z)) = s(z)) <=> (s(z) = elem!1)),
% 1.52/1.70 inference(transitivity,[status(thm)],[3144, 91])).
% 1.52/1.70 tff(3146,plain,
% 1.52/1.70 ((~(s(s(z)) = s(z))) <=> (~(s(z) = elem!1))),
% 1.52/1.70 inference(monotonicity,[status(thm)],[3145])).
% 1.52/1.70 tff(3147,plain,
% 1.52/1.70 (~(s(z) = elem!1)),
% 1.52/1.70 inference(modus_ponens,[status(thm)],[148, 3146])).
% 1.52/1.70 tff(3148,plain,
% 1.52/1.70 (b(s(s(elem!1)), s(s(z))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 1.52/1.70 inference(monotonicity,[status(thm)],[1020])).
% 1.52/1.70 tff(3149,plain,
% 1.52/1.70 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 1.52/1.70 inference(symmetry,[status(thm)],[3148])).
% 1.52/1.70 tff(3150,plain,
% 1.52/1.70 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(z)))), elem!1)),
% 1.52/1.70 inference(monotonicity,[status(thm)],[3143])).
% 1.52/1.70 tff(3151,plain,
% 1.52/1.70 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(z)))),
% 1.52/1.70 inference(symmetry,[status(thm)],[3150])).
% 1.52/1.70 tff(3152,plain,
% 1.52/1.70 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(elem!1)), s(s(z)))),
% 1.52/1.70 inference(transitivity,[status(thm)],[3151, 3149])).
% 1.52/1.70 tff(3153,plain,
% 1.52/1.70 (b(s(s(elem!1)), s(s(z)))),
% 1.52/1.70 inference(modus_ponens,[status(thm)],[287, 3152])).
% 1.52/1.70 tff(3154,plain,
% 1.52/1.70 (b(s(s(z)), s(s(s(s(z)))))),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[433, 3143, 286])).
% 1.52/1.70 tff(3155,plain,
% 1.52/1.70 (~r(s(z), s(s(s(s(z)))))),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[1320, 1265, 3154, 114, 1020, 1305, 3153])).
% 1.52/1.70 tff(3156,plain,
% 1.52/1.70 (b(s(z), s(s(s(s(z)))))),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[489, 3155])).
% 1.52/1.70 tff(3157,plain,
% 1.52/1.70 (~b(s(z), elem!1)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[586, 3156, 286, 287])).
% 1.52/1.70 tff(3158,plain,
% 1.52/1.70 (r(s(z), elem!1)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[601, 3157, 3147])).
% 1.52/1.70 tff(3159,plain,
% 1.52/1.70 ($false),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[1341, 37, 3158, 1061, 1265])).
% 1.52/1.70 tff(3160,plain,((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(z))) | (~(s(s(elem!1)) = s(s(s(s(z)))))) | (elem!1 = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.70 tff(3161,plain,
% 1.52/1.70 (~r(s(z), s(s(s(z))))),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[3160, 3133, 279, 284, 3139, 3114, 3142])).
% 1.52/1.70 tff(3162,plain,
% 1.52/1.70 (b(s(z), s(s(s(z))))),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[1263, 3161])).
% 1.52/1.70 tff(3163,plain,
% 1.52/1.70 (~b(s(s(s(z))), z)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[1091, 3162, 2935, 3141])).
% 1.52/1.70 tff(3164,plain,
% 1.52/1.70 (~b(s(elem!1), z)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[1098, 3163, 3114])).
% 1.52/1.70 tff(3165,plain,
% 1.52/1.70 (r(s(elem!1), z)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[766, 3164])).
% 1.52/1.70 tff(3166,plain,
% 1.52/1.70 (~r(elem!1, z)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[2988, 3165, 3134])).
% 1.52/1.70 tff(3167,plain,
% 1.52/1.70 (b(elem!1, z)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[387, 3166, 305])).
% 1.52/1.70 tff(3168,plain,
% 1.52/1.70 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[2854, 3167, 2821, 2511, 3128, 284])).
% 1.52/1.70 tff(3169,plain,
% 1.52/1.70 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[813, 3168, 3127])).
% 1.52/1.70 tff(3170,plain,
% 1.52/1.70 (~b(s(z), elem!1)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[2629, 3166, 294, 13, 2728, 279, 284])).
% 1.52/1.70 tff(3171,plain,
% 1.52/1.70 (r(s(z), elem!1)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[601, 3170, 3138])).
% 1.52/1.70 tff(3172,plain,
% 1.52/1.70 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[1219, 37, 3171, 3169])).
% 1.52/1.70 tff(3173,plain,
% 1.52/1.70 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[1230, 58, 1227, 3172])).
% 1.52/1.70 tff(3174,plain,
% 1.52/1.70 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[2919, 75, 3141, 3162, 3173])).
% 1.52/1.70 tff(3175,plain,
% 1.52/1.70 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[2926, 37, 3133, 3169])).
% 1.52/1.70 tff(3176,plain,
% 1.52/1.70 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[2930, 58, 3175])).
% 1.52/1.70 tff(3177,plain,
% 1.52/1.70 ($false),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[3176, 3174, 3124])).
% 1.52/1.70 tff(3178,plain,(r(z, elem!1) | r(s(s(s(s(z)))), elem!1) | r(elem!1, s(s(s(s(z))))) | (s(s(s(s(z)))) = elem!1) | (s(s(elem!1)) = s(s(z))) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.52/1.70 tff(3179,plain,
% 1.52/1.70 (r(z, elem!1)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[3178, 12, 268, 267, 266, 99])).
% 1.52/1.70 tff(3180,plain,
% 1.52/1.70 (~r(z, s(z))),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[2056, 3179, 284, 99, 266, 267, 279])).
% 1.52/1.70 tff(3181,plain,
% 1.52/1.70 (b(z, s(z))),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[187, 3180])).
% 1.52/1.70 tff(3182,plain,
% 1.52/1.70 (b(elem!1, s(z))),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[1375, 3179, 284, 279, 274, 266, 99])).
% 1.52/1.70 tff(3183,plain,
% 1.52/1.70 (~(s(z) = elem!1)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[1393, 3182])).
% 1.52/1.70 tff(3184,plain,
% 1.52/1.70 (~b(s(z), z)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[1526, 107, 1391, 1518])).
% 1.52/1.70 tff(3185,plain,
% 1.52/1.70 (r(s(z), z)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[169, 3184])).
% 1.52/1.70 tff(3186,plain,
% 1.52/1.70 (~b(s(z), s(s(s(s(z)))))),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[586, 107, 287, 286])).
% 1.52/1.70 tff(3187,plain,
% 1.52/1.70 (r(s(z), s(s(s(s(z)))))),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[489, 3186])).
% 1.52/1.70 tff(3188,plain,
% 1.52/1.70 ($false),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[2586, 3187, 3185, 2611])).
% 1.52/1.70 tff(3189,plain,((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.70 tff(3190,plain,
% 1.52/1.70 (~b(s(z), elem!1)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[3189, 3182, 279, 284, 2511])).
% 1.52/1.70 tff(3191,plain,
% 1.52/1.70 (r(s(z), elem!1)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[601, 3190, 3183])).
% 1.52/1.70 tff(3192,plain,
% 1.52/1.70 ($false),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[2499, 3191, 3181, 99, 274, 2544, 3179])).
% 1.52/1.70 tff(3193,plain,(r(s(s(s(s(z)))), elem!1) | b(s(s(z)), elem!1) | (s(s(elem!1)) = s(s(z))) | (s(s(s(s(z)))) = elem!1) | r(elem!1, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.70 tff(3194,plain,
% 1.52/1.70 (r(elem!1, s(s(s(s(z)))))),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[3193, 265, 12, 238, 99])).
% 1.52/1.70 tff(3195,assumption,(r(elem!1, s(s(s(s(z)))))), introduced(assumption)).
% 1.52/1.70 tff(3196,plain,
% 1.52/1.70 (((~![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(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(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.52/1.70 inference(rewrite,[status(thm)],[])).
% 1.52/1.70 tff(3197,plain,
% 1.52/1.70 (((~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.52/1.70 inference(rewrite,[status(thm)],[])).
% 1.52/1.70 tff(3198,plain,
% 1.52/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(z), s(s(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(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))))),
% 1.52/1.70 inference(monotonicity,[status(thm)],[3197])).
% 1.52/1.70 tff(3199,plain,
% 1.52/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(z), s(s(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(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.52/1.70 inference(transitivity,[status(thm)],[3198, 3196])).
% 1.52/1.70 tff(3200,plain,
% 1.52/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(z))))),
% 1.52/1.70 inference(quant_inst,[status(thm)],[])).
% 1.52/1.70 tff(3201,plain,
% 1.52/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))),
% 1.52/1.70 inference(modus_ponens,[status(thm)],[3200, 3199])).
% 1.52/1.70 tff(3202,plain,
% 1.52/1.70 ($false),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[3201, 37, 114, 468, 3195])).
% 1.52/1.70 tff(3203,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.70 tff(3204,plain,
% 1.52/1.70 (~r(s(z), s(s(s(s(z)))))),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[3203, 3194, 114])).
% 1.52/1.70 tff(3205,plain,
% 1.52/1.70 (b(s(z), s(s(s(s(z)))))),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[489, 3204])).
% 1.52/1.70 tff(3206,plain,
% 1.52/1.70 (b(s(z), s(elem!1))),
% 1.52/1.70 inference(modus_ponens,[status(thm)],[3205, 215])).
% 1.52/1.70 tff(3207,plain,
% 1.52/1.70 (b(z, elem!1)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[298, 222, 13])).
% 1.52/1.70 tff(3208,plain,
% 1.52/1.70 (b(elem!1, z)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[387, 1942, 2614])).
% 1.52/1.70 tff(3209,plain,
% 1.52/1.70 (b(s(s(s(s(z)))), elem!1)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[283, 265, 12])).
% 1.52/1.70 tff(3210,plain,
% 1.52/1.70 (b(s(elem!1), elem!1)),
% 1.52/1.70 inference(unit_resolution,[status(thm)],[1983, 3209, 213])).
% 1.52/1.70 tff(3211,assumption,(b(s(z), s(elem!1))), introduced(assumption)).
% 1.52/1.70 tff(3212,plain,
% 1.52/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)))),
% 1.52/1.70 inference(rewrite,[status(thm)],[])).
% 1.52/1.70 tff(3213,plain,
% 1.52/1.70 (((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1)))) <=> ((~b(s(z), s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)))),
% 1.52/1.71 inference(rewrite,[status(thm)],[])).
% 1.52/1.71 tff(3214,plain,
% 1.52/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1))))),
% 1.52/1.71 inference(monotonicity,[status(thm)],[3213])).
% 1.52/1.71 tff(3215,plain,
% 1.52/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)))),
% 1.52/1.71 inference(transitivity,[status(thm)],[3214, 3212])).
% 1.52/1.71 tff(3216,plain,
% 1.52/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))),
% 1.52/1.71 inference(quant_inst,[status(thm)],[])).
% 1.52/1.71 tff(3217,plain,
% 1.52/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1))),
% 1.52/1.71 inference(modus_ponens,[status(thm)],[3216, 3215])).
% 1.52/1.71 tff(3218,plain,
% 1.52/1.71 ($false),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[3217, 75, 1518, 1958, 107, 921, 3211])).
% 1.52/1.71 tff(3219,plain,((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.71 tff(3220,plain,
% 1.52/1.71 (~b(s(z), s(elem!1))),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[3219, 3210, 107, 3208, 3207])).
% 1.52/1.71 tff(3221,plain,
% 1.52/1.71 ($false),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[3220, 3206])).
% 1.52/1.71 tff(3222,plain,((~(s(s(s(z))) = elem!1)) | (~b(s(z), elem!1)) | (~r(elem!1, s(z))) | r(s(s(s(s(z)))), elem!1) | b(s(s(z)), elem!1) | r(elem!1, z) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.52/1.71 tff(3223,plain,
% 1.52/1.71 (~(s(s(s(z))) = elem!1)),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[3222, 113, 107, 12, 99, 212, 13])).
% 1.52/1.71 tff(3224,plain,
% 1.52/1.71 (r(s(s(s(z))), elem!1)),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[1115, 3223, 100])).
% 1.52/1.71 tff(3225,plain,
% 1.52/1.71 (~r(s(z), s(s(s(s(z)))))),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[3203, 3195, 114])).
% 1.52/1.71 tff(3226,plain,
% 1.52/1.71 ((s(z) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(z))),
% 1.52/1.71 inference(symmetry,[status(thm)],[247])).
% 1.52/1.71 tff(3227,plain,
% 1.52/1.71 ((~(s(z) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(z)))),
% 1.52/1.71 inference(monotonicity,[status(thm)],[3226])).
% 1.52/1.71 tff(3228,assumption,(~(s(z) = s(s(s(s(z)))))), introduced(assumption)).
% 1.52/1.71 tff(3229,plain,
% 1.52/1.71 (~(s(s(s(s(z)))) = s(z))),
% 1.52/1.71 inference(modus_ponens,[status(thm)],[3228, 3227])).
% 1.52/1.71 tff(3230,assumption,(~(s(s(s(z))) = s(s(s(s(z)))))), introduced(assumption)).
% 1.52/1.71 tff(3231,plain,
% 1.52/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(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(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.52/1.71 inference(rewrite,[status(thm)],[])).
% 1.52/1.71 tff(3232,plain,
% 1.52/1.71 (((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.52/1.71 inference(rewrite,[status(thm)],[])).
% 1.52/1.71 tff(3233,plain,
% 1.52/1.71 (((~![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(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(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))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))))),
% 1.52/1.71 inference(monotonicity,[status(thm)],[3232])).
% 1.52/1.71 tff(3234,plain,
% 1.52/1.71 (((~![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(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(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))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.52/1.71 inference(transitivity,[status(thm)],[3233, 3231])).
% 1.52/1.71 tff(3235,plain,
% 1.52/1.71 ((~![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(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)))),
% 1.52/1.71 inference(quant_inst,[status(thm)],[])).
% 1.52/1.71 tff(3236,plain,
% 1.52/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))),
% 1.52/1.71 inference(modus_ponens,[status(thm)],[3235, 3234])).
% 1.52/1.71 tff(3237,plain,
% 1.52/1.71 ($false),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[3236, 37, 114, 1061, 3195, 1308])).
% 1.52/1.71 tff(3238,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.71 tff(3239,plain,
% 1.52/1.71 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[3238, 3195, 1061, 114])).
% 1.52/1.71 tff(3240,plain,
% 1.52/1.71 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[574, 3239, 3230])).
% 1.52/1.71 tff(3241,plain,
% 1.52/1.71 (~b(s(s(s(s(z)))), s(z))),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[991, 3240, 578, 984])).
% 1.52/1.71 tff(3242,plain,
% 1.52/1.71 ((s(s(s(s(z)))) = s(z)) | r(s(s(s(s(z)))), s(z))),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[1406, 58, 3241])).
% 1.52/1.71 tff(3243,plain,
% 1.52/1.71 (r(s(s(s(s(z)))), s(z))),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[3242, 3229])).
% 1.52/1.71 tff(3244,plain,
% 1.52/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.52/1.71 inference(rewrite,[status(thm)],[])).
% 1.52/1.71 tff(3245,plain,
% 1.52/1.71 (((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.52/1.71 inference(rewrite,[status(thm)],[])).
% 1.52/1.71 tff(3246,plain,
% 1.52/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z))))))))),
% 1.52/1.71 inference(monotonicity,[status(thm)],[3245])).
% 1.52/1.71 tff(3247,plain,
% 1.52/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.52/1.71 inference(transitivity,[status(thm)],[3246, 3244])).
% 1.52/1.71 tff(3248,plain,
% 1.52/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.52/1.71 inference(quant_inst,[status(thm)],[])).
% 1.52/1.71 tff(3249,plain,
% 1.52/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z))))))),
% 1.52/1.71 inference(modus_ponens,[status(thm)],[3248, 3247])).
% 1.52/1.71 tff(3250,plain,
% 1.52/1.71 ($false),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[3249, 37, 114, 3195, 3243])).
% 1.52/1.71 tff(3251,plain,((~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (s(z) = s(s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (s(s(s(z))) = s(s(s(s(z))))) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.71 tff(3252,plain,
% 1.52/1.71 ((~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (s(z) = s(s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1))),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[3251, 263])).
% 1.52/1.71 tff(3253,plain,
% 1.52/1.71 (~b(s(z), s(s(s(s(z)))))),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[3252, 3195, 484, 114, 1082, 1061])).
% 1.52/1.71 tff(3254,plain,
% 1.52/1.71 ($false),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[488, 3253, 3225, 484])).
% 1.52/1.71 tff(3255,plain,((~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.71 tff(3256,plain,
% 1.52/1.71 (~r(elem!1, s(s(s(s(z)))))),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[3255, 3224, 113])).
% 1.52/1.71 tff(3257,assumption,(s(s(z)) = s(elem!1)), introduced(assumption)).
% 1.52/1.71 tff(3258,plain,
% 1.52/1.71 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 1.52/1.71 inference(monotonicity,[status(thm)],[3257])).
% 1.52/1.71 tff(3259,plain,
% 1.52/1.71 (s(z) = elem!1),
% 1.52/1.71 inference(transitivity,[status(thm)],[134, 3258, 224])).
% 1.52/1.71 tff(3260,plain,
% 1.52/1.71 ($false),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[108, 3259])).
% 1.52/1.71 tff(3261,plain,((~(s(s(z)) = s(elem!1))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.52/1.71 tff(3262,plain,
% 1.52/1.71 (~(s(s(z)) = s(elem!1))),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[3261, 108])).
% 1.52/1.71 tff(3263,plain,
% 1.52/1.71 (~r(s(s(z)), s(z))),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[123, 113, 106])).
% 1.52/1.71 tff(3264,plain,
% 1.52/1.71 (b(s(s(z)), s(z))),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[153, 3263])).
% 1.52/1.71 tff(3265,plain,
% 1.52/1.71 (~r(s(s(s(z))), s(z))),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[1075, 3224, 113])).
% 1.52/1.71 tff(3266,plain,
% 1.52/1.71 (b(s(s(s(z))), s(z))),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[1081, 3265])).
% 1.52/1.71 tff(3267,plain,
% 1.52/1.71 (s(s(s(s(z)))) = elem!1),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[3193, 266, 12, 268, 99])).
% 1.52/1.71 tff(3268,plain,
% 1.52/1.71 (s(s(s(s(s(z))))) = s(elem!1)),
% 1.52/1.71 inference(monotonicity,[status(thm)],[3267])).
% 1.52/1.71 tff(3269,plain,
% 1.52/1.71 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 1.52/1.71 inference(monotonicity,[status(thm)],[3268])).
% 1.52/1.71 tff(3270,plain,
% 1.52/1.71 (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))),
% 1.52/1.71 inference(monotonicity,[status(thm)],[3269])).
% 1.52/1.71 tff(3271,plain,
% 1.52/1.71 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 1.52/1.71 inference(symmetry,[status(thm)],[3270])).
% 1.52/1.71 tff(3272,plain,
% 1.52/1.71 ((s(s(s(elem!1))) = s(z)) <=> (s(s(s(s(s(s(s(z))))))) = s(z))),
% 1.52/1.71 inference(monotonicity,[status(thm)],[3271])).
% 1.52/1.71 tff(3273,plain,
% 1.52/1.71 ((s(s(s(s(s(s(s(z))))))) = s(z)) <=> (s(s(s(elem!1))) = s(z))),
% 1.52/1.71 inference(symmetry,[status(thm)],[3272])).
% 1.52/1.71 tff(3274,plain,
% 1.52/1.71 ((~(s(s(s(s(s(s(s(z))))))) = s(z))) <=> (~(s(s(s(elem!1))) = s(z)))),
% 1.52/1.71 inference(monotonicity,[status(thm)],[3273])).
% 1.52/1.71 tff(3275,plain,
% 1.52/1.71 (~(s(s(s(elem!1))) = s(z))),
% 1.52/1.71 inference(modus_ponens,[status(thm)],[1227, 3274])).
% 1.52/1.71 tff(3276,plain,
% 1.52/1.71 ((s(s(s(elem!1))) = elem!1) <=> (elem!1 = s(s(s(elem!1))))),
% 1.52/1.71 inference(commutativity,[status(thm)],[])).
% 1.52/1.71 tff(3277,plain,
% 1.52/1.71 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.52/1.71 inference(symmetry,[status(thm)],[3276])).
% 1.52/1.71 tff(3278,plain,
% 1.52/1.71 ((elem!1 = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.52/1.71 inference(commutativity,[status(thm)],[])).
% 1.52/1.71 tff(3279,plain,
% 1.52/1.71 ((elem!1 = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 1.52/1.71 inference(monotonicity,[status(thm)],[3271])).
% 1.52/1.71 tff(3280,plain,
% 1.52/1.71 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.52/1.71 inference(transitivity,[status(thm)],[3279, 3278])).
% 1.52/1.71 tff(3281,plain,
% 1.52/1.71 ((s(s(s(s(s(s(s(z))))))) = elem!1) <=> (elem!1 = s(s(s(elem!1))))),
% 1.52/1.71 inference(symmetry,[status(thm)],[3280])).
% 1.52/1.71 tff(3282,plain,
% 1.52/1.71 ((s(s(s(s(s(s(s(z))))))) = elem!1) <=> (s(s(s(elem!1))) = elem!1)),
% 1.52/1.71 inference(transitivity,[status(thm)],[3281, 3277])).
% 1.52/1.71 tff(3283,plain,
% 1.52/1.71 ((~(s(s(s(s(s(s(s(z))))))) = elem!1)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.52/1.71 inference(monotonicity,[status(thm)],[3282])).
% 1.52/1.71 tff(3284,assumption,(~(s(s(z)) = s(elem!1))), introduced(assumption)).
% 1.52/1.71 tff(3285,assumption,(s(s(s(s(z)))) = elem!1), introduced(assumption)).
% 1.52/1.71 tff(3286,plain,
% 1.52/1.71 (s(s(s(s(s(z))))) = s(elem!1)),
% 1.52/1.71 inference(monotonicity,[status(thm)],[3285])).
% 1.52/1.71 tff(3287,plain,
% 1.52/1.71 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 1.52/1.71 inference(monotonicity,[status(thm)],[3286])).
% 1.52/1.71 tff(3288,plain,
% 1.52/1.71 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 1.52/1.71 inference(symmetry,[status(thm)],[3287])).
% 1.52/1.71 tff(3289,plain,
% 1.52/1.71 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 1.52/1.71 inference(monotonicity,[status(thm)],[3288])).
% 1.52/1.71 tff(3290,plain,
% 1.52/1.71 (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))),
% 1.52/1.71 inference(symmetry,[status(thm)],[3289])).
% 1.52/1.71 tff(3291,plain,
% 1.52/1.71 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 1.52/1.71 inference(symmetry,[status(thm)],[709])).
% 1.52/1.71 tff(3292,plain,
% 1.52/1.71 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.52/1.71 inference(transitivity,[status(thm)],[3285, 3291, 3290])).
% 1.52/1.71 tff(3293,plain,
% 1.52/1.71 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(elem!1))))),
% 1.52/1.71 inference(monotonicity,[status(thm)],[3292])).
% 1.52/1.71 tff(3294,plain,
% 1.52/1.71 (s(s(s(z))) = s(s(elem!1))),
% 1.52/1.71 inference(transitivity,[status(thm)],[451, 3293, 11])).
% 1.52/1.71 tff(3295,plain,
% 1.52/1.71 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 1.52/1.71 inference(monotonicity,[status(thm)],[3294])).
% 1.52/1.71 tff(3296,plain,
% 1.52/1.71 (s(s(z)) = s(elem!1)),
% 1.52/1.71 inference(transitivity,[status(thm)],[254, 3295, 228])).
% 1.52/1.71 tff(3297,plain,
% 1.52/1.71 ($false),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[3284, 3296])).
% 1.52/1.71 tff(3298,plain,((~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (s(s(z)) = s(elem!1)) | (~(s(s(s(s(z)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.71 tff(3299,plain,
% 1.52/1.71 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[3298, 3267, 3284])).
% 1.52/1.71 tff(3300,plain,
% 1.52/1.71 (~(s(s(s(elem!1))) = elem!1)),
% 1.52/1.71 inference(modus_ponens,[status(thm)],[3299, 3283])).
% 1.52/1.71 tff(3301,assumption,(s(s(s(elem!1))) = s(s(s(z)))), introduced(assumption)).
% 1.52/1.71 tff(3302,plain,
% 1.52/1.71 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.52/1.71 inference(symmetry,[status(thm)],[3301])).
% 1.52/1.71 tff(3303,plain,
% 1.52/1.71 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 1.52/1.71 inference(monotonicity,[status(thm)],[3302])).
% 1.52/1.71 tff(3304,plain,
% 1.52/1.71 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 1.52/1.71 inference(symmetry,[status(thm)],[3303])).
% 1.52/1.71 tff(3305,plain,
% 1.52/1.71 (s(s(elem!1)) = s(s(z))),
% 1.52/1.71 inference(transitivity,[status(thm)],[1609, 3304, 253])).
% 1.52/1.71 tff(3306,plain,
% 1.52/1.71 ($false),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[266, 3305])).
% 1.52/1.71 tff(3307,plain,((~(s(s(s(elem!1))) = s(s(s(z))))) | (s(s(elem!1)) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.71 tff(3308,plain,
% 1.52/1.71 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[3307, 266])).
% 1.52/1.71 tff(3309,plain,
% 1.52/1.71 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(z)))),
% 1.52/1.71 inference(commutativity,[status(thm)],[])).
% 1.52/1.71 tff(3310,plain,
% 1.52/1.71 (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))),
% 1.52/1.71 inference(monotonicity,[status(thm)],[3287])).
% 1.52/1.71 tff(3311,plain,
% 1.52/1.71 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 1.52/1.71 inference(symmetry,[status(thm)],[3310])).
% 1.52/1.71 tff(3312,plain,
% 1.52/1.71 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = s(s(s(s(s(s(s(z))))))))),
% 1.52/1.71 inference(monotonicity,[status(thm)],[3311])).
% 1.52/1.71 tff(3313,plain,
% 1.52/1.71 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(z)))),
% 1.52/1.71 inference(transitivity,[status(thm)],[3312, 3309])).
% 1.52/1.71 tff(3314,plain,
% 1.52/1.71 ((s(s(s(s(s(s(s(z))))))) = s(s(z))) <=> (s(s(z)) = s(s(s(elem!1))))),
% 1.52/1.71 inference(symmetry,[status(thm)],[3313])).
% 1.52/1.71 tff(3315,plain,
% 1.52/1.71 ((~(s(s(s(s(s(s(s(z))))))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(elem!1)))))),
% 1.52/1.71 inference(monotonicity,[status(thm)],[3314])).
% 1.52/1.71 tff(3316,plain,
% 1.52/1.71 (~(s(s(z)) = s(s(s(elem!1))))),
% 1.52/1.71 inference(modus_ponens,[status(thm)],[1045, 3315])).
% 1.52/1.71 tff(3317,plain,
% 1.52/1.71 (((~![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))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.52/1.71 inference(rewrite,[status(thm)],[])).
% 1.52/1.71 tff(3318,plain,
% 1.52/1.71 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.52/1.71 inference(rewrite,[status(thm)],[])).
% 1.52/1.71 tff(3319,plain,
% 1.52/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, 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(z))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 1.52/1.71 inference(monotonicity,[status(thm)],[3318])).
% 1.52/1.71 tff(3320,plain,
% 1.52/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, 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(z))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.52/1.71 inference(transitivity,[status(thm)],[3319, 3317])).
% 1.52/1.71 tff(3321,plain,
% 1.52/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.52/1.71 inference(quant_inst,[status(thm)],[])).
% 1.52/1.71 tff(3322,plain,
% 1.52/1.71 ((~![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))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 1.52/1.71 inference(modus_ponens,[status(thm)],[3321, 3320])).
% 1.52/1.71 tff(3323,plain,
% 1.52/1.71 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[3322, 37, 1061, 624])).
% 1.52/1.71 tff(3324,assumption,(~(s(s(s(elem!1))) = s(s(s(z))))), introduced(assumption)).
% 1.52/1.71 tff(3325,plain,
% 1.52/1.71 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z)))))),
% 1.52/1.71 inference(rewrite,[status(thm)],[])).
% 1.52/1.71 tff(3326,plain,
% 1.52/1.71 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z)))))),
% 1.52/1.71 inference(quant_inst,[status(thm)],[])).
% 1.52/1.71 tff(3327,plain,
% 1.52/1.71 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z))))),
% 1.52/1.71 inference(modus_ponens,[status(thm)],[3326, 3325])).
% 1.52/1.71 tff(3328,plain,
% 1.52/1.71 (b(s(s(s(elem!1))), s(s(s(z))))),
% 1.52/1.71 inference(unit_resolution,[status(thm)],[3327, 58, 3324, 3323])).
% 1.52/1.72 tff(3329,plain,
% 1.52/1.72 ((s(s(s(elem!1))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(elem!1))))),
% 1.52/1.72 inference(commutativity,[status(thm)],[])).
% 1.52/1.72 tff(3330,plain,
% 1.52/1.72 ((~(s(s(s(elem!1))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(s(elem!1)))))),
% 1.52/1.72 inference(monotonicity,[status(thm)],[3329])).
% 1.52/1.72 tff(3331,plain,
% 1.52/1.72 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 1.52/1.72 inference(modus_ponens,[status(thm)],[3324, 3330])).
% 1.52/1.72 tff(3332,plain,
% 1.52/1.72 (((~![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))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.52/1.72 inference(rewrite,[status(thm)],[])).
% 1.52/1.72 tff(3333,plain,
% 1.52/1.72 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.52/1.72 inference(rewrite,[status(thm)],[])).
% 1.52/1.72 tff(3334,plain,
% 1.52/1.72 (((~![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))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(elem!1)))))))),
% 1.52/1.72 inference(monotonicity,[status(thm)],[3333])).
% 1.52/1.72 tff(3335,plain,
% 1.52/1.72 (((~![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))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.52/1.72 inference(transitivity,[status(thm)],[3334, 3332])).
% 1.52/1.72 tff(3336,plain,
% 1.52/1.72 ((~![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))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.52/1.72 inference(quant_inst,[status(thm)],[])).
% 1.52/1.72 tff(3337,plain,
% 1.52/1.72 ((~![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))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 1.52/1.72 inference(modus_ponens,[status(thm)],[3336, 3335])).
% 1.52/1.72 tff(3338,plain,
% 1.52/1.72 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 1.52/1.72 inference(unit_resolution,[status(thm)],[3337, 37, 1061, 624])).
% 1.52/1.72 tff(3339,plain,
% 1.52/1.72 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(elem!1)))) | b(s(s(s(z))), s(s(s(elem!1)))) | r(s(s(s(z))), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(elem!1)))) | b(s(s(s(z))), s(s(s(elem!1)))) | r(s(s(s(z))), s(s(s(elem!1)))))),
% 1.52/1.72 inference(rewrite,[status(thm)],[])).
% 1.52/1.72 tff(3340,plain,
% 1.52/1.72 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(elem!1)))) | b(s(s(s(z))), s(s(s(elem!1)))) | r(s(s(s(z))), s(s(s(elem!1)))))),
% 1.52/1.72 inference(quant_inst,[status(thm)],[])).
% 1.52/1.72 tff(3341,plain,
% 1.52/1.72 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(elem!1)))) | b(s(s(s(z))), s(s(s(elem!1)))) | r(s(s(s(z))), s(s(s(elem!1))))),
% 1.52/1.72 inference(modus_ponens,[status(thm)],[3340, 3339])).
% 1.52/1.72 tff(3342,plain,
% 1.52/1.72 ((s(s(s(z))) = s(s(s(elem!1)))) | b(s(s(s(z))), s(s(s(elem!1)))) | r(s(s(s(z))), s(s(s(elem!1))))),
% 1.52/1.72 inference(unit_resolution,[status(thm)],[3341, 58])).
% 1.52/1.72 tff(3343,plain,
% 1.52/1.72 (b(s(s(s(z))), s(s(s(elem!1))))),
% 1.52/1.72 inference(unit_resolution,[status(thm)],[3342, 3338, 3331])).
% 1.52/1.72 tff(3344,plain,
% 1.52/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.52/1.72 inference(rewrite,[status(thm)],[])).
% 1.52/1.72 tff(3345,plain,
% 1.52/1.72 (((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.52/1.72 inference(rewrite,[status(thm)],[])).
% 1.52/1.72 tff(3346,plain,
% 1.52/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 1.52/1.72 inference(monotonicity,[status(thm)],[3345])).
% 1.52/1.72 tff(3347,plain,
% 1.52/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 1.52/1.72 inference(transitivity,[status(thm)],[3346, 3344])).
% 1.52/1.72 tff(3348,plain,
% 1.52/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.52/1.72 inference(quant_inst,[status(thm)],[])).
% 1.52/1.72 tff(3349,plain,
% 1.52/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 1.52/1.72 inference(modus_ponens,[status(thm)],[3348, 3347])).
% 1.52/1.72 tff(3350,plain,
% 1.52/1.72 (~b(s(s(z)), s(s(s(elem!1))))),
% 1.52/1.72 inference(unit_resolution,[status(thm)],[3349, 75, 309, 3343, 984, 3033, 3328])).
% 1.52/1.72 tff(3351,plain,
% 1.52/1.72 (((~![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))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.52/1.72 inference(rewrite,[status(thm)],[])).
% 1.52/1.72 tff(3352,plain,
% 1.52/1.72 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.52/1.72 inference(rewrite,[status(thm)],[])).
% 1.52/1.72 tff(3353,plain,
% 1.52/1.72 (((~![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))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 1.52/1.72 inference(monotonicity,[status(thm)],[3352])).
% 1.52/1.72 tff(3354,plain,
% 1.52/1.72 (((~![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))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.52/1.72 inference(transitivity,[status(thm)],[3353, 3351])).
% 1.52/1.72 tff(3355,plain,
% 1.52/1.72 ((~![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))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.52/1.72 inference(quant_inst,[status(thm)],[])).
% 1.52/1.72 tff(3356,plain,
% 1.52/1.72 ((~![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))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 1.52/1.72 inference(modus_ponens,[status(thm)],[3355, 3354])).
% 1.52/1.72 tff(3357,plain,
% 1.52/1.72 (~r(s(s(z)), s(s(s(elem!1))))),
% 1.52/1.72 inference(unit_resolution,[status(thm)],[3356, 37, 106, 624])).
% 1.52/1.72 tff(3358,plain,
% 1.52/1.72 (((~![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)))))),
% 1.52/1.72 inference(rewrite,[status(thm)],[])).
% 1.52/1.72 tff(3359,plain,
% 1.52/1.72 ((~![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)))))),
% 1.52/1.72 inference(quant_inst,[status(thm)],[])).
% 1.52/1.72 tff(3360,plain,
% 1.52/1.72 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(elem!1)))) | b(s(s(z)), s(s(s(elem!1)))) | r(s(s(z)), s(s(s(elem!1))))),
% 1.52/1.72 inference(modus_ponens,[status(thm)],[3359, 3358])).
% 1.52/1.72 tff(3361,plain,
% 1.52/1.72 ((s(s(z)) = s(s(s(elem!1)))) | b(s(s(z)), s(s(s(elem!1))))),
% 1.52/1.72 inference(unit_resolution,[status(thm)],[3360, 58, 3357])).
% 1.52/1.72 tff(3362,plain,
% 1.52/1.72 ($false),
% 1.52/1.72 inference(unit_resolution,[status(thm)],[3361, 3350, 3316])).
% 1.52/1.72 tff(3363,plain,((~r(s(s(s(elem!1))), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~(s(s(s(s(z)))) = elem!1)) | (s(s(s(elem!1))) = s(s(s(z)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.72 tff(3364,plain,
% 1.52/1.72 (~r(s(s(s(elem!1))), elem!1)),
% 1.52/1.72 inference(unit_resolution,[status(thm)],[3363, 3267, 984, 309, 3308, 1061, 106])).
% 1.52/1.72 tff(3365,assumption,(~(s(s(s(elem!1))) = elem!1)), introduced(assumption)).
% 1.52/1.72 tff(3366,plain,
% 1.52/1.72 (((~![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))),
% 1.52/1.72 inference(rewrite,[status(thm)],[])).
% 1.52/1.72 tff(3367,plain,
% 1.52/1.72 ((~![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))),
% 1.52/1.72 inference(quant_inst,[status(thm)],[])).
% 1.52/1.72 tff(3368,plain,
% 1.52/1.72 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1)),
% 1.52/1.72 inference(modus_ponens,[status(thm)],[3367, 3366])).
% 1.52/1.72 tff(3369,plain,
% 1.52/1.72 ($false),
% 1.52/1.72 inference(unit_resolution,[status(thm)],[3368, 58, 933, 700, 3365])).
% 1.52/1.72 tff(3370,plain,(r(s(s(s(elem!1))), elem!1) | b(s(s(s(elem!1))), elem!1) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.52/1.72 tff(3371,plain,
% 1.52/1.72 (b(s(s(s(elem!1))), elem!1)),
% 1.52/1.72 inference(unit_resolution,[status(thm)],[3370, 3364, 3300])).
% 1.52/1.72 tff(3372,plain,
% 1.52/1.72 (b(elem!1, z)),
% 1.52/1.72 inference(unit_resolution,[status(thm)],[387, 305, 2614])).
% 1.52/1.72 tff(3373,plain,
% 1.52/1.72 (b(z, elem!1)),
% 1.52/1.72 inference(unit_resolution,[status(thm)],[298, 294, 13])).
% 1.52/1.72 tff(3374,plain,
% 1.52/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 1.52/1.72 inference(rewrite,[status(thm)],[])).
% 1.52/1.72 tff(3375,plain,
% 1.52/1.72 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~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))) <=> ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 1.52/1.72 inference(rewrite,[status(thm)],[])).
% 1.52/1.72 tff(3376,plain,
% 1.52/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), 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)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z))))),
% 1.52/1.72 inference(monotonicity,[status(thm)],[3375])).
% 1.52/1.72 tff(3377,plain,
% 1.52/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), 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)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 1.52/1.72 inference(transitivity,[status(thm)],[3376, 3374])).
% 1.52/1.72 tff(3378,plain,
% 1.52/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), 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)))),
% 1.52/1.72 inference(quant_inst,[status(thm)],[])).
% 1.52/1.72 tff(3379,plain,
% 1.52/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z))),
% 1.52/1.72 inference(modus_ponens,[status(thm)],[3378, 3377])).
% 1.52/1.72 tff(3380,plain,
% 1.52/1.72 (~b(s(s(s(elem!1))), z)),
% 1.52/1.72 inference(unit_resolution,[status(thm)],[3379, 75, 3373, 3372, 3371])).
% 1.52/1.72 tff(3381,plain,
% 1.52/1.72 (r(s(s(s(elem!1))), z)),
% 1.52/1.72 inference(unit_resolution,[status(thm)],[948, 58, 662, 3380])).
% 1.52/1.72 tff(3382,plain,
% 1.52/1.72 (~b(s(z), z)),
% 1.52/1.72 inference(unit_resolution,[status(thm)],[2625, 294, 13, 107, 2614])).
% 1.52/1.72 tff(3383,plain,
% 1.52/1.72 (r(s(z), z)),
% 1.52/1.72 inference(unit_resolution,[status(thm)],[169, 3382])).
% 1.52/1.72 tff(3384,plain,
% 1.52/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(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))))),
% 1.52/1.72 inference(rewrite,[status(thm)],[])).
% 1.52/1.72 tff(3385,plain,
% 1.52/1.72 (((~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))))),
% 1.52/1.72 inference(rewrite,[status(thm)],[])).
% 1.52/1.72 tff(3386,plain,
% 1.52/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(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)))))),
% 1.52/1.72 inference(monotonicity,[status(thm)],[3385])).
% 1.52/1.72 tff(3387,plain,
% 1.52/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(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))))),
% 1.52/1.72 inference(transitivity,[status(thm)],[3386, 3384])).
% 1.52/1.72 tff(3388,plain,
% 1.52/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 1.52/1.72 inference(quant_inst,[status(thm)],[])).
% 1.52/1.72 tff(3389,plain,
% 1.52/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z)))),
% 1.52/1.72 inference(modus_ponens,[status(thm)],[3388, 3387])).
% 1.52/1.72 tff(3390,plain,
% 1.52/1.72 (~r(s(s(s(elem!1))), s(z))),
% 1.52/1.72 inference(unit_resolution,[status(thm)],[3389, 37, 3383, 3381])).
% 1.52/1.72 tff(3391,plain,
% 1.52/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.52/1.72 inference(rewrite,[status(thm)],[])).
% 1.52/1.72 tff(3392,plain,
% 1.52/1.72 (((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~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(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.52/1.72 inference(rewrite,[status(thm)],[])).
% 1.52/1.72 tff(3393,plain,
% 1.52/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(elem!1))), elem!1)) | (~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(X1, 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(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.52/1.72 inference(monotonicity,[status(thm)],[3392])).
% 1.52/1.72 tff(3394,plain,
% 1.52/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(elem!1))), elem!1)) | (~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(X1, 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(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.52/1.73 inference(transitivity,[status(thm)],[3393, 3391])).
% 1.52/1.73 tff(3395,plain,
% 1.52/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(elem!1))), elem!1)) | (~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))))),
% 1.52/1.73 inference(quant_inst,[status(thm)],[])).
% 1.52/1.73 tff(3396,plain,
% 1.52/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z)))),
% 1.52/1.73 inference(modus_ponens,[status(thm)],[3395, 3394])).
% 1.52/1.73 tff(3397,plain,
% 1.52/1.73 (~b(s(s(s(elem!1))), s(z))),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[3396, 75, 3373, 3372, 107, 3371])).
% 1.52/1.73 tff(3398,plain,
% 1.52/1.73 (((~![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)))),
% 1.52/1.73 inference(rewrite,[status(thm)],[])).
% 1.52/1.73 tff(3399,plain,
% 1.52/1.73 ((~![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)))),
% 1.52/1.73 inference(quant_inst,[status(thm)],[])).
% 1.52/1.73 tff(3400,plain,
% 1.52/1.73 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z))),
% 1.52/1.73 inference(modus_ponens,[status(thm)],[3399, 3398])).
% 1.52/1.73 tff(3401,plain,
% 1.52/1.73 ((s(s(s(elem!1))) = s(z)) | r(s(s(s(elem!1))), s(z))),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[3400, 58, 3397])).
% 1.52/1.73 tff(3402,plain,
% 1.52/1.73 ($false),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[3401, 3390, 3275])).
% 1.52/1.73 tff(3403,plain,((s(s(elem!1)) = s(s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | r(elem!1, z) | (s(s(z)) = s(elem!1)) | r(z, elem!1) | r(s(s(s(s(z)))), elem!1) | r(elem!1, s(s(s(s(z))))) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.52/1.73 tff(3404,plain,
% 1.52/1.73 (s(s(elem!1)) = s(s(z))),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[3403, 3266, 107, 3264, 3224, 106, 212, 3262, 13, 12, 3256, 99])).
% 1.52/1.73 tff(3405,plain,
% 1.52/1.73 (z = elem!1),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[237, 3404])).
% 1.52/1.73 tff(3406,plain,
% 1.52/1.73 (s(z) = s(elem!1)),
% 1.52/1.73 inference(monotonicity,[status(thm)],[3405])).
% 1.52/1.73 tff(3407,plain,
% 1.52/1.73 (r(s(z), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.52/1.73 inference(monotonicity,[status(thm)],[3406])).
% 1.52/1.73 tff(3408,plain,
% 1.52/1.73 (r(s(elem!1), s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 1.52/1.73 inference(symmetry,[status(thm)],[3407])).
% 1.52/1.73 tff(3409,plain,
% 1.52/1.73 (~b(s(z), s(s(z)))),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[2743, 3224, 113, 106])).
% 1.52/1.73 tff(3410,plain,
% 1.52/1.73 (r(s(z), s(s(z)))),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[416, 3409])).
% 1.52/1.73 tff(3411,plain,
% 1.52/1.73 (r(s(z), s(s(z))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.52/1.73 inference(monotonicity,[status(thm)],[289, 290])).
% 1.52/1.73 tff(3412,plain,
% 1.52/1.73 (r(s(elem!1), s(s(elem!1)))),
% 1.52/1.73 inference(modus_ponens,[status(thm)],[1997, 3411])).
% 1.52/1.73 tff(3413,plain,
% 1.52/1.73 ($false),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[1844, 3412])).
% 1.52/1.73 tff(3414,plain,((~r(s(z), s(s(z)))) | r(s(elem!1), s(s(elem!1))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.73 tff(3415,plain,
% 1.52/1.73 (r(s(elem!1), s(s(elem!1)))),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[3414, 3405, 3410])).
% 1.52/1.73 tff(3416,plain,
% 1.52/1.73 (r(s(z), s(s(elem!1)))),
% 1.52/1.73 inference(modus_ponens,[status(thm)],[3415, 3408])).
% 1.52/1.73 tff(3417,plain,
% 1.52/1.73 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.52/1.73 inference(monotonicity,[status(thm)],[290])).
% 1.52/1.73 tff(3418,plain,
% 1.52/1.73 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.52/1.73 inference(symmetry,[status(thm)],[3417])).
% 1.52/1.73 tff(3419,plain,
% 1.52/1.73 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(z))), elem!1)),
% 1.52/1.73 inference(monotonicity,[status(thm)],[3418])).
% 1.52/1.73 tff(3420,plain,
% 1.52/1.73 (r(s(s(s(z))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 1.52/1.73 inference(symmetry,[status(thm)],[3419])).
% 1.52/1.73 tff(3421,plain,
% 1.52/1.73 (r(s(s(s(elem!1))), elem!1)),
% 1.52/1.73 inference(modus_ponens,[status(thm)],[1061, 3420])).
% 1.52/1.73 tff(3422,plain,
% 1.52/1.73 (s(elem!1) = s(z)),
% 1.52/1.73 inference(symmetry,[status(thm)],[289])).
% 1.52/1.73 tff(3423,plain,
% 1.52/1.73 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(z))), s(z))),
% 1.52/1.73 inference(monotonicity,[status(thm)],[3418, 3422])).
% 1.52/1.73 tff(3424,plain,
% 1.52/1.73 (r(s(s(s(z))), s(z)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.52/1.73 inference(symmetry,[status(thm)],[3423])).
% 1.52/1.73 tff(3425,plain,
% 1.52/1.73 ((s(s(s(z))) = elem!1) <=> (elem!1 = s(s(s(z))))),
% 1.52/1.73 inference(symmetry,[status(thm)],[1028])).
% 1.52/1.73 tff(3426,plain,
% 1.52/1.73 ((~(s(s(s(z))) = elem!1)) <=> (~(elem!1 = s(s(s(z)))))),
% 1.52/1.73 inference(monotonicity,[status(thm)],[3425])).
% 1.52/1.73 tff(3427,plain,
% 1.52/1.73 (~(elem!1 = s(s(s(z))))),
% 1.52/1.73 inference(modus_ponens,[status(thm)],[1031, 3426])).
% 1.52/1.73 tff(3428,plain,
% 1.52/1.73 ((s(s(elem!1)) = elem!1) <=> (elem!1 = s(s(elem!1)))),
% 1.52/1.73 inference(commutativity,[status(thm)],[])).
% 1.52/1.73 tff(3429,plain,
% 1.52/1.73 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 1.52/1.73 inference(monotonicity,[status(thm)],[288])).
% 1.52/1.73 tff(3430,plain,
% 1.52/1.73 ((s(s(elem!1)) = z) <=> (elem!1 = s(s(elem!1)))),
% 1.52/1.73 inference(transitivity,[status(thm)],[3429, 3428])).
% 1.52/1.73 tff(3431,plain,
% 1.52/1.73 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = s(s(elem!1))))),
% 1.52/1.73 inference(monotonicity,[status(thm)],[3430])).
% 1.52/1.73 tff(3432,plain,
% 1.52/1.73 (~(elem!1 = s(s(elem!1)))),
% 1.52/1.73 inference(modus_ponens,[status(thm)],[515, 3431])).
% 1.52/1.73 tff(3433,plain,
% 1.52/1.73 (b(elem!1, s(s(elem!1)))),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[1617, 3432, 2217])).
% 1.52/1.73 tff(3434,plain,
% 1.52/1.73 ((s(elem!1) = s(s(elem!1))) <=> (s(z) = s(s(elem!1)))),
% 1.52/1.73 inference(monotonicity,[status(thm)],[3422])).
% 1.52/1.73 tff(3435,plain,
% 1.52/1.73 ((s(elem!1) = s(s(elem!1))) <=> (s(s(elem!1)) = s(z))),
% 1.52/1.73 inference(transitivity,[status(thm)],[3434, 1882])).
% 1.52/1.73 tff(3436,plain,
% 1.52/1.73 ((s(s(elem!1)) = s(z)) <=> (s(elem!1) = s(s(elem!1)))),
% 1.52/1.73 inference(symmetry,[status(thm)],[3435])).
% 1.52/1.73 tff(3437,plain,
% 1.52/1.73 ((~(s(s(elem!1)) = s(z))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 1.52/1.73 inference(monotonicity,[status(thm)],[3436])).
% 1.52/1.73 tff(3438,plain,
% 1.52/1.73 (~(s(elem!1) = s(s(elem!1)))),
% 1.52/1.73 inference(modus_ponens,[status(thm)],[556, 3437])).
% 1.52/1.73 tff(3439,plain,
% 1.52/1.73 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(z), s(s(s(s(z)))))),
% 1.52/1.73 inference(monotonicity,[status(thm)],[3422])).
% 1.52/1.73 tff(3440,plain,
% 1.52/1.73 (r(s(z), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 1.52/1.73 inference(symmetry,[status(thm)],[3439])).
% 1.52/1.73 tff(3441,plain,
% 1.52/1.73 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 1.52/1.73 inference(monotonicity,[status(thm)],[288])).
% 1.52/1.73 tff(3442,plain,
% 1.52/1.73 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(z)))))),
% 1.52/1.73 inference(transitivity,[status(thm)],[3441, 239])).
% 1.52/1.73 tff(3443,plain,
% 1.52/1.73 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 1.52/1.73 inference(transitivity,[status(thm)],[3442, 240])).
% 1.52/1.73 tff(3444,plain,
% 1.52/1.73 ((~(s(s(s(s(z)))) = z)) <=> (~(s(s(s(s(z)))) = elem!1))),
% 1.52/1.73 inference(monotonicity,[status(thm)],[3443])).
% 1.52/1.73 tff(3445,plain,
% 1.52/1.73 (~(s(s(s(s(z)))) = elem!1)),
% 1.52/1.73 inference(modus_ponens,[status(thm)],[1143, 3444])).
% 1.52/1.73 tff(3446,plain,
% 1.52/1.73 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.52/1.73 inference(monotonicity,[status(thm)],[3418])).
% 1.52/1.73 tff(3447,plain,
% 1.52/1.73 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.52/1.73 inference(symmetry,[status(thm)],[3446])).
% 1.52/1.73 tff(3448,plain,
% 1.52/1.73 (r(s(s(s(s(z)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 1.52/1.73 inference(monotonicity,[status(thm)],[3418])).
% 1.52/1.73 tff(3449,plain,
% 1.52/1.73 ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.52/1.73 inference(monotonicity,[status(thm)],[3448])).
% 1.52/1.73 tff(3450,plain,
% 1.52/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.52/1.73 inference(rewrite,[status(thm)],[])).
% 1.52/1.73 tff(3451,plain,
% 1.52/1.73 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.52/1.73 inference(rewrite,[status(thm)],[])).
% 1.52/1.73 tff(3452,plain,
% 1.52/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 1.52/1.73 inference(monotonicity,[status(thm)],[3451])).
% 1.52/1.73 tff(3453,plain,
% 1.52/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.52/1.73 inference(transitivity,[status(thm)],[3452, 3450])).
% 1.52/1.73 tff(3454,plain,
% 1.52/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.52/1.73 inference(quant_inst,[status(thm)],[])).
% 1.52/1.73 tff(3455,plain,
% 1.52/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 1.52/1.73 inference(modus_ponens,[status(thm)],[3454, 3453])).
% 1.52/1.73 tff(3456,plain,
% 1.52/1.73 ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[3455, 37, 698])).
% 1.52/1.73 tff(3457,plain,
% 1.52/1.73 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[3456, 3421])).
% 1.52/1.73 tff(3458,plain,
% 1.52/1.73 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.52/1.73 inference(modus_ponens,[status(thm)],[3457, 3449])).
% 1.52/1.73 tff(3459,plain,
% 1.52/1.73 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[2898, 3458])).
% 1.52/1.73 tff(3460,plain,
% 1.52/1.73 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.52/1.73 inference(modus_ponens,[status(thm)],[3459, 3447])).
% 1.52/1.73 tff(3461,plain,
% 1.52/1.73 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 1.52/1.73 inference(monotonicity,[status(thm)],[3418])).
% 1.52/1.73 tff(3462,plain,
% 1.52/1.73 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.52/1.73 inference(symmetry,[status(thm)],[3461])).
% 1.52/1.73 tff(3463,plain,
% 1.52/1.73 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 1.52/1.73 inference(monotonicity,[status(thm)],[3418])).
% 1.52/1.73 tff(3464,plain,
% 1.52/1.73 ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) <=> (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.52/1.73 inference(monotonicity,[status(thm)],[3463])).
% 1.52/1.73 tff(3465,plain,
% 1.52/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.52/1.73 inference(rewrite,[status(thm)],[])).
% 1.52/1.73 tff(3466,plain,
% 1.52/1.73 (((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.52/1.73 inference(rewrite,[status(thm)],[])).
% 1.52/1.73 tff(3467,plain,
% 1.52/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), elem!1))))),
% 1.52/1.73 inference(monotonicity,[status(thm)],[3466])).
% 1.52/1.73 tff(3468,plain,
% 1.52/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.52/1.73 inference(transitivity,[status(thm)],[3467, 3465])).
% 1.52/1.73 tff(3469,plain,
% 1.52/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.52/1.73 inference(quant_inst,[status(thm)],[])).
% 1.52/1.73 tff(3470,plain,
% 1.52/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), elem!1))),
% 1.52/1.73 inference(modus_ponens,[status(thm)],[3469, 3468])).
% 1.52/1.73 tff(3471,plain,
% 1.52/1.73 ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), elem!1))),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[3470, 37, 698])).
% 1.52/1.73 tff(3472,plain,
% 1.52/1.73 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[3471, 3421])).
% 1.52/1.73 tff(3473,plain,
% 1.52/1.73 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.52/1.73 inference(modus_ponens,[status(thm)],[3472, 3464])).
% 1.52/1.73 tff(3474,plain,
% 1.52/1.73 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[575, 3473])).
% 1.52/1.73 tff(3475,plain,
% 1.52/1.73 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.52/1.73 inference(modus_ponens,[status(thm)],[3474, 3462])).
% 1.52/1.73 tff(3476,plain,
% 1.52/1.73 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(z))))),
% 1.52/1.73 inference(monotonicity,[status(thm)],[3418])).
% 1.52/1.73 tff(3477,plain,
% 1.52/1.73 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.52/1.73 inference(symmetry,[status(thm)],[3476])).
% 1.52/1.73 tff(3478,plain,
% 1.52/1.73 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(z)))))),
% 1.52/1.73 inference(symmetry,[status(thm)],[245])).
% 1.52/1.73 tff(3479,plain,
% 1.52/1.73 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(s(s(z))))))),
% 1.52/1.73 inference(monotonicity,[status(thm)],[3478])).
% 1.52/1.73 tff(3480,assumption,(~(s(s(s(s(z)))) = s(s(s(z))))), introduced(assumption)).
% 1.52/1.73 tff(3481,plain,
% 1.52/1.73 (~(s(s(s(z))) = s(s(s(s(z)))))),
% 1.52/1.73 inference(modus_ponens,[status(thm)],[3480, 3479])).
% 1.52/1.73 tff(3482,plain,
% 1.52/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.52/1.73 inference(rewrite,[status(thm)],[])).
% 1.52/1.73 tff(3483,plain,
% 1.52/1.73 (((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.52/1.73 inference(rewrite,[status(thm)],[])).
% 1.52/1.73 tff(3484,plain,
% 1.52/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.52/1.73 inference(monotonicity,[status(thm)],[3483])).
% 1.52/1.73 tff(3485,plain,
% 1.52/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.52/1.73 inference(transitivity,[status(thm)],[3484, 3482])).
% 1.52/1.73 tff(3486,plain,
% 1.52/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.52/1.73 inference(quant_inst,[status(thm)],[])).
% 1.52/1.73 tff(3487,plain,
% 1.52/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.52/1.73 inference(modus_ponens,[status(thm)],[3486, 3485])).
% 1.52/1.73 tff(3488,plain,
% 1.52/1.73 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[3487, 37, 1061, 698])).
% 1.52/1.73 tff(3489,plain,
% 1.52/1.73 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[574, 3488, 3481])).
% 1.52/1.73 tff(3490,plain,
% 1.52/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.52/1.73 inference(rewrite,[status(thm)],[])).
% 1.52/1.73 tff(3491,plain,
% 1.52/1.73 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.52/1.73 inference(rewrite,[status(thm)],[])).
% 1.52/1.73 tff(3492,plain,
% 1.52/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1))))),
% 1.52/1.73 inference(monotonicity,[status(thm)],[3491])).
% 1.52/1.73 tff(3493,plain,
% 1.52/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.52/1.73 inference(transitivity,[status(thm)],[3492, 3490])).
% 1.52/1.73 tff(3494,plain,
% 1.52/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.52/1.73 inference(quant_inst,[status(thm)],[])).
% 1.52/1.73 tff(3495,plain,
% 1.52/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1))),
% 1.52/1.73 inference(modus_ponens,[status(thm)],[3494, 3493])).
% 1.52/1.73 tff(3496,plain,
% 1.52/1.73 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[3495, 37, 1061, 698])).
% 1.52/1.73 tff(3497,plain,
% 1.52/1.73 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.52/1.73 inference(unit_resolution,[status(thm)],[2897, 3496, 3480])).
% 1.52/1.73 tff(3498,plain,
% 1.52/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.52/1.74 inference(rewrite,[status(thm)],[])).
% 1.52/1.74 tff(3499,plain,
% 1.52/1.74 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.52/1.74 inference(rewrite,[status(thm)],[])).
% 1.52/1.74 tff(3500,plain,
% 1.52/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.52/1.74 inference(monotonicity,[status(thm)],[3499])).
% 1.52/1.74 tff(3501,plain,
% 1.52/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.52/1.74 inference(transitivity,[status(thm)],[3500, 3498])).
% 1.52/1.74 tff(3502,plain,
% 1.52/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.52/1.74 inference(quant_inst,[status(thm)],[])).
% 1.52/1.74 tff(3503,plain,
% 1.52/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.52/1.74 inference(modus_ponens,[status(thm)],[3502, 3501])).
% 1.52/1.74 tff(3504,plain,
% 1.52/1.74 (~b(s(s(s(s(z)))), s(z))),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[3503, 75, 3497, 1053, 3489])).
% 1.52/1.74 tff(3505,plain,
% 1.52/1.74 ((s(s(s(s(z)))) = s(z)) | r(s(s(s(s(z)))), s(z))),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[1406, 58, 3504])).
% 1.52/1.74 tff(3506,plain,
% 1.52/1.74 (r(s(s(s(s(z)))), s(z))),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[3505, 3229])).
% 1.52/1.74 tff(3507,plain,
% 1.52/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), 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(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.52/1.74 inference(rewrite,[status(thm)],[])).
% 1.52/1.74 tff(3508,plain,
% 1.52/1.74 (((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.52/1.74 inference(rewrite,[status(thm)],[])).
% 1.52/1.74 tff(3509,plain,
% 1.52/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, 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(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z)))))),
% 1.52/1.74 inference(monotonicity,[status(thm)],[3508])).
% 1.52/1.74 tff(3510,plain,
% 1.52/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, 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(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.52/1.74 inference(transitivity,[status(thm)],[3509, 3507])).
% 1.52/1.74 tff(3511,plain,
% 1.52/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.52/1.74 inference(quant_inst,[status(thm)],[])).
% 1.52/1.74 tff(3512,plain,
% 1.52/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z)))),
% 1.52/1.74 inference(modus_ponens,[status(thm)],[3511, 3510])).
% 1.52/1.74 tff(3513,plain,
% 1.52/1.74 ($false),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[3512, 37, 114, 698, 3506])).
% 1.52/1.74 tff(3514,plain,((~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(z))) | (s(z) = s(s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (s(s(s(s(z)))) = s(s(s(z)))) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.74 tff(3515,plain,
% 1.52/1.74 ((~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(z))) | (s(z) = s(s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(z))), elem!1))),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[3514, 264])).
% 1.52/1.74 tff(3516,plain,
% 1.52/1.74 (~b(s(z), s(s(s(z))))),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[3515, 698, 484, 114, 1061])).
% 1.52/1.74 tff(3517,plain,
% 1.52/1.74 (r(s(z), s(s(s(z))))),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[1263, 3516])).
% 1.52/1.74 tff(3518,plain,
% 1.52/1.74 (~r(elem!1, s(s(s(z))))),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[1274, 3517, 114])).
% 1.52/1.74 tff(3519,plain,
% 1.52/1.74 (b(elem!1, s(s(s(z))))),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[1279, 3518, 1305])).
% 1.52/1.74 tff(3520,plain,
% 1.52/1.74 (b(elem!1, s(s(s(elem!1))))),
% 1.52/1.74 inference(modus_ponens,[status(thm)],[3519, 3477])).
% 1.52/1.74 tff(3521,plain,
% 1.52/1.74 ((~(s(s(s(s(z)))) = z)) <=> (~(elem!1 = s(s(s(s(z))))))),
% 1.52/1.74 inference(monotonicity,[status(thm)],[3442])).
% 1.52/1.74 tff(3522,plain,
% 1.52/1.74 (~(elem!1 = s(s(s(s(z)))))),
% 1.52/1.74 inference(modus_ponens,[status(thm)],[1143, 3521])).
% 1.52/1.74 tff(3523,plain,
% 1.52/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z))))) | (~b(s(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(X1, 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(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.52/1.74 inference(rewrite,[status(thm)],[])).
% 1.52/1.74 tff(3524,plain,
% 1.52/1.74 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.52/1.74 inference(rewrite,[status(thm)],[])).
% 1.52/1.74 tff(3525,plain,
% 1.52/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))))),
% 1.52/1.74 inference(monotonicity,[status(thm)],[3524])).
% 1.52/1.74 tff(3526,plain,
% 1.52/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.52/1.74 inference(transitivity,[status(thm)],[3525, 3523])).
% 1.52/1.74 tff(3527,plain,
% 1.52/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 1.52/1.74 inference(quant_inst,[status(thm)],[])).
% 1.52/1.74 tff(3528,plain,
% 1.52/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))),
% 1.52/1.74 inference(modus_ponens,[status(thm)],[3527, 3526])).
% 1.52/1.74 tff(3529,plain,
% 1.52/1.74 ($false),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[3528, 75, 3497, 984, 578, 3489])).
% 1.52/1.74 tff(3530,plain,((~r(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (s(s(s(s(z)))) = s(s(s(z)))) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.74 tff(3531,plain,
% 1.52/1.74 ((~r(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1))),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[3530, 264])).
% 1.52/1.74 tff(3532,plain,
% 1.52/1.74 (~b(s(z), s(s(s(s(z)))))),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[3531, 698, 984, 1061])).
% 1.52/1.74 tff(3533,plain,
% 1.52/1.74 (r(s(z), s(s(s(s(z)))))),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[488, 3532, 484])).
% 1.52/1.74 tff(3534,plain,
% 1.52/1.74 (~r(elem!1, s(s(s(s(z)))))),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[3203, 3533, 114])).
% 1.52/1.74 tff(3535,plain,
% 1.52/1.74 (b(elem!1, s(s(s(s(z)))))),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[278, 3534, 3522])).
% 1.52/1.74 tff(3536,plain,
% 1.52/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.52/1.74 inference(rewrite,[status(thm)],[])).
% 1.52/1.74 tff(3537,plain,
% 1.52/1.74 (((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.52/1.74 inference(rewrite,[status(thm)],[])).
% 1.52/1.74 tff(3538,plain,
% 1.52/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.52/1.74 inference(monotonicity,[status(thm)],[3537])).
% 1.52/1.74 tff(3539,plain,
% 1.52/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.52/1.74 inference(transitivity,[status(thm)],[3538, 3536])).
% 1.52/1.74 tff(3540,plain,
% 1.52/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.52/1.74 inference(quant_inst,[status(thm)],[])).
% 1.52/1.74 tff(3541,plain,
% 1.52/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.52/1.74 inference(modus_ponens,[status(thm)],[3540, 3539])).
% 1.52/1.74 tff(3542,plain,
% 1.52/1.74 ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[3541, 75, 3535, 3520])).
% 1.52/1.74 tff(3543,plain,
% 1.52/1.74 ($false),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[3542, 3475, 3460])).
% 1.52/1.74 tff(3544,plain,((~r(s(s(s(s(z)))), elem!1)) | (~(z = elem!1)) | (~r(s(s(s(z))), elem!1)) | (elem!1 = s(s(s(z)))) | (~r(elem!1, s(z))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.74 tff(3545,plain,
% 1.52/1.74 (~r(s(s(s(s(z)))), elem!1)),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[3544, 984, 1061, 1305, 114, 288])).
% 1.52/1.74 tff(3546,plain,
% 1.52/1.74 (b(s(s(s(s(z)))), elem!1)),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[283, 3545, 3445])).
% 1.52/1.74 tff(3547,plain,
% 1.52/1.74 (~b(elem!1, s(s(s(s(z)))))),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[586, 578, 107, 287])).
% 1.52/1.74 tff(3548,plain,
% 1.52/1.74 (~r(elem!1, s(s(s(s(z)))))),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[3252, 578, 484, 114, 984, 1061])).
% 1.52/1.74 tff(3549,plain,
% 1.52/1.74 ($false),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[278, 3548, 3547, 860])).
% 1.52/1.74 tff(3550,plain,((~b(s(z), s(s(s(s(z)))))) | (elem!1 = s(s(s(s(z))))) | (~r(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.74 tff(3551,plain,
% 1.52/1.74 (~b(s(z), s(s(s(s(z)))))),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[3550, 984, 114, 3522, 1061, 107, 3546])).
% 1.52/1.74 tff(3552,plain,
% 1.52/1.74 (r(s(z), s(s(s(s(z)))))),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[488, 3551, 484])).
% 1.52/1.74 tff(3553,plain,
% 1.52/1.74 (r(s(elem!1), s(s(s(s(z)))))),
% 1.52/1.74 inference(modus_ponens,[status(thm)],[3552, 3440])).
% 1.52/1.74 tff(3554,plain,
% 1.52/1.74 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 1.52/1.74 inference(monotonicity,[status(thm)],[290])).
% 1.52/1.74 tff(3555,plain,
% 1.52/1.74 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(elem!1)) = s(s(s(s(z))))))),
% 1.52/1.74 inference(monotonicity,[status(thm)],[3554])).
% 1.52/1.74 tff(3556,plain,
% 1.52/1.74 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 1.52/1.74 inference(modus_ponens,[status(thm)],[459, 3555])).
% 1.52/1.74 tff(3557,plain,
% 1.52/1.74 (~r(elem!1, s(s(s(s(z)))))),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[3203, 3552, 114])).
% 1.52/1.74 tff(3558,plain,
% 1.52/1.74 (b(elem!1, s(s(s(s(z)))))),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[278, 3557, 3522])).
% 1.52/1.74 tff(3559,plain,
% 1.52/1.74 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[1628, 3558, 1620, 3546])).
% 1.52/1.74 tff(3560,plain,
% 1.52/1.74 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[1660, 3559, 3556])).
% 1.52/1.74 tff(3561,plain,
% 1.52/1.74 (((~![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(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.52/1.74 inference(rewrite,[status(thm)],[])).
% 1.52/1.74 tff(3562,plain,
% 1.52/1.74 (((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.52/1.74 inference(rewrite,[status(thm)],[])).
% 1.52/1.74 tff(3563,plain,
% 1.52/1.74 (((~![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(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(elem!1))))))),
% 1.52/1.74 inference(monotonicity,[status(thm)],[3562])).
% 1.52/1.74 tff(3564,plain,
% 1.52/1.74 (((~![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(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.52/1.74 inference(transitivity,[status(thm)],[3563, 3561])).
% 1.52/1.74 tff(3565,plain,
% 1.52/1.74 ((~![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(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.52/1.74 inference(quant_inst,[status(thm)],[])).
% 1.52/1.74 tff(3566,plain,
% 1.52/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(elem!1))))),
% 1.52/1.74 inference(modus_ponens,[status(thm)],[3565, 3564])).
% 1.52/1.74 tff(3567,plain,
% 1.52/1.74 (~r(s(elem!1), s(s(elem!1)))),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[3566, 37, 3560, 3553])).
% 1.52/1.74 tff(3568,plain,
% 1.52/1.74 (b(s(z), elem!1) <=> b(s(elem!1), elem!1)),
% 1.52/1.74 inference(monotonicity,[status(thm)],[289])).
% 1.52/1.74 tff(3569,plain,
% 1.52/1.74 (b(s(elem!1), elem!1)),
% 1.52/1.74 inference(modus_ponens,[status(thm)],[107, 3568])).
% 1.52/1.74 tff(3570,plain,
% 1.52/1.74 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(elem!1))),
% 1.52/1.74 inference(monotonicity,[status(thm)],[290, 289])).
% 1.52/1.74 tff(3571,plain,
% 1.52/1.74 (s(s(z)) = s(s(elem!1))),
% 1.52/1.74 inference(symmetry,[status(thm)],[225])).
% 1.52/1.74 tff(3572,plain,
% 1.52/1.74 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.52/1.74 inference(monotonicity,[status(thm)],[3571])).
% 1.52/1.74 tff(3573,plain,
% 1.52/1.74 (r(s(s(elem!1)), s(s(s(s(z))))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 1.52/1.74 inference(symmetry,[status(thm)],[3572])).
% 1.52/1.74 tff(3574,plain,
% 1.52/1.74 (r(s(s(z)), s(s(s(s(z)))))),
% 1.52/1.75 inference(modus_ponens,[status(thm)],[1647, 3573])).
% 1.52/1.75 tff(3575,plain,
% 1.52/1.75 ($false),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[460, 3574])).
% 1.52/1.75 tff(3576,plain,(r(s(s(z)), s(s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~(s(s(elem!1)) = s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.75 tff(3577,plain,
% 1.52/1.75 (r(s(s(z)), s(s(s(s(z)))))),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[3576, 3560, 291])).
% 1.52/1.75 tff(3578,plain,
% 1.52/1.75 (~r(s(s(z)), s(z))),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[476, 3577, 3552])).
% 1.52/1.75 tff(3579,plain,
% 1.52/1.75 (b(s(s(z)), s(z))),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[153, 3578])).
% 1.52/1.75 tff(3580,plain,
% 1.52/1.75 (b(s(s(elem!1)), s(elem!1))),
% 1.52/1.75 inference(modus_ponens,[status(thm)],[3579, 3570])).
% 1.52/1.75 tff(3581,assumption,(b(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 1.52/1.75 tff(3582,plain,
% 1.52/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.52/1.75 inference(rewrite,[status(thm)],[])).
% 1.52/1.75 tff(3583,plain,
% 1.52/1.75 (((~b(s(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(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.52/1.75 inference(rewrite,[status(thm)],[])).
% 1.52/1.75 tff(3584,plain,
% 1.52/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1))))))),
% 1.52/1.75 inference(monotonicity,[status(thm)],[3583])).
% 1.52/1.75 tff(3585,plain,
% 1.52/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.52/1.75 inference(transitivity,[status(thm)],[3584, 3582])).
% 1.52/1.75 tff(3586,plain,
% 1.52/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 1.52/1.75 inference(quant_inst,[status(thm)],[])).
% 1.52/1.75 tff(3587,plain,
% 1.52/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1))))),
% 1.52/1.75 inference(modus_ponens,[status(thm)],[3586, 3585])).
% 1.52/1.75 tff(3588,plain,
% 1.52/1.75 ($false),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[3587, 75, 1620, 921, 3069, 3581])).
% 1.52/1.75 tff(3589,plain,((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.75 tff(3590,plain,
% 1.52/1.75 (~b(s(elem!1), s(s(elem!1)))),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[3589, 3580, 1620, 3569])).
% 1.52/1.75 tff(3591,plain,
% 1.52/1.75 ($false),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[1851, 3590, 3567, 3438])).
% 1.52/1.75 tff(3592,plain,((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~(z = elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (elem!1 = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.75 tff(3593,plain,
% 1.52/1.75 (~b(s(s(s(z))), s(z))),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[3592, 3433, 288, 114, 1061, 107, 3427])).
% 1.52/1.75 tff(3594,plain,
% 1.52/1.75 (r(s(s(s(z))), s(z))),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[1081, 3593])).
% 1.52/1.75 tff(3595,plain,
% 1.52/1.75 (r(s(s(s(elem!1))), s(elem!1))),
% 1.52/1.75 inference(modus_ponens,[status(thm)],[3594, 3424])).
% 1.52/1.75 tff(3596,plain,
% 1.52/1.75 (r(elem!1, s(z)) <=> r(elem!1, s(elem!1))),
% 1.52/1.75 inference(monotonicity,[status(thm)],[289])).
% 1.52/1.75 tff(3597,plain,
% 1.52/1.75 (r(elem!1, s(elem!1))),
% 1.52/1.75 inference(modus_ponens,[status(thm)],[114, 3596])).
% 1.52/1.75 tff(3598,plain,
% 1.52/1.75 (((~![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))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))))),
% 1.52/1.75 inference(rewrite,[status(thm)],[])).
% 1.52/1.75 tff(3599,plain,
% 1.52/1.75 (((~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(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))))),
% 1.52/1.75 inference(rewrite,[status(thm)],[])).
% 1.52/1.75 tff(3600,plain,
% 1.52/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(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(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1)))))),
% 1.52/1.75 inference(monotonicity,[status(thm)],[3599])).
% 1.52/1.75 tff(3601,plain,
% 1.52/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(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(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))))),
% 1.52/1.75 inference(transitivity,[status(thm)],[3600, 3598])).
% 1.52/1.75 tff(3602,plain,
% 1.52/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(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)))),
% 1.52/1.75 inference(quant_inst,[status(thm)],[])).
% 1.52/1.75 tff(3603,plain,
% 1.52/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1)))),
% 1.52/1.75 inference(modus_ponens,[status(thm)],[3602, 3601])).
% 1.52/1.75 tff(3604,plain,
% 1.52/1.75 ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[3603, 37, 3597])).
% 1.52/1.75 tff(3605,plain,
% 1.52/1.75 ($false),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[3604, 3595, 3421])).
% 1.52/1.75 tff(3606,plain,((~(z = elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(z))) | (~b(s(z), elem!1)) | (s(s(s(z))) = elem!1) | r(elem!1, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.75 tff(3607,plain,
% 1.52/1.75 (r(elem!1, s(s(elem!1)))),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[3606, 3405, 107, 113, 3223, 3224])).
% 1.52/1.75 tff(3608,plain,
% 1.52/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(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(elem!1, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 1.52/1.75 inference(rewrite,[status(thm)],[])).
% 1.52/1.75 tff(3609,plain,
% 1.52/1.75 (((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 1.52/1.75 inference(rewrite,[status(thm)],[])).
% 1.52/1.75 tff(3610,plain,
% 1.52/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))))),
% 1.52/1.75 inference(monotonicity,[status(thm)],[3609])).
% 1.52/1.75 tff(3611,plain,
% 1.52/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 1.52/1.75 inference(transitivity,[status(thm)],[3610, 3608])).
% 1.52/1.75 tff(3612,plain,
% 1.52/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))))),
% 1.52/1.75 inference(quant_inst,[status(thm)],[])).
% 1.52/1.75 tff(3613,plain,
% 1.52/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))),
% 1.52/1.75 inference(modus_ponens,[status(thm)],[3612, 3611])).
% 1.52/1.75 tff(3614,plain,
% 1.52/1.75 ($false),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[3613, 37, 1490, 114, 1871])).
% 1.52/1.75 tff(3615,plain,((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.75 tff(3616,plain,
% 1.52/1.75 (~r(s(z), s(s(elem!1)))),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[3615, 3607, 113])).
% 1.52/1.75 tff(3617,plain,
% 1.52/1.75 ($false),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[3616, 3416])).
% 1.52/1.75 tff(3618,plain,((s(z) = elem!1) | (~b(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | r(z, elem!1) | r(s(s(s(s(z)))), elem!1) | b(s(s(z)), elem!1) | b(s(s(s(z))), elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.75 tff(3619,plain,
% 1.52/1.75 (s(z) = elem!1),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[3618, 107, 106, 13, 12, 99, 100, 14])).
% 1.52/1.75 tff(3620,plain,
% 1.52/1.75 (b(s(z), elem!1) <=> b(elem!1, elem!1)),
% 1.52/1.75 inference(monotonicity,[status(thm)],[3619])).
% 1.52/1.75 tff(3621,plain,
% 1.52/1.75 (b(elem!1, elem!1) <=> b(s(z), elem!1)),
% 1.52/1.75 inference(symmetry,[status(thm)],[3620])).
% 1.52/1.75 tff(3622,plain,
% 1.52/1.75 ((~b(elem!1, elem!1)) <=> (~b(s(z), elem!1))),
% 1.52/1.75 inference(monotonicity,[status(thm)],[3621])).
% 1.52/1.75 tff(3623,plain,
% 1.52/1.75 (~b(s(z), elem!1)),
% 1.52/1.75 inference(modus_ponens,[status(thm)],[1389, 3622])).
% 1.52/1.75 tff(3624,plain,
% 1.52/1.75 ($false),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[107, 3623])).
% 1.52/1.75 tff(3625,plain,((~b(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | r(z, elem!1) | r(s(s(s(s(z)))), elem!1) | b(s(s(z)), elem!1) | b(s(s(s(z))), elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.75 tff(3626,plain,
% 1.52/1.75 (~b(s(z), elem!1)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[3625, 105, 13, 12, 99, 100, 14])).
% 1.52/1.75 tff(3627,assumption,(~b(s(z), elem!1)), introduced(assumption)).
% 1.52/1.75 tff(3628,assumption,(b(s(s(s(z))), s(s(elem!1)))), introduced(assumption)).
% 1.52/1.75 tff(3629,plain,
% 1.52/1.75 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), elem!1)),
% 1.52/1.75 inference(symmetry,[status(thm)],[2266])).
% 1.52/1.75 tff(3630,plain,
% 1.52/1.75 (b(s(s(s(z))), elem!1)),
% 1.52/1.75 inference(modus_ponens,[status(thm)],[3628, 3629])).
% 1.52/1.75 tff(3631,plain,
% 1.52/1.75 ($false),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[100, 3630])).
% 1.52/1.75 tff(3632,plain,((~(elem!1 = s(s(elem!1)))) | b(s(s(s(z))), elem!1) | (~b(s(s(s(z))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.75 tff(3633,plain,
% 1.52/1.75 (~(elem!1 = s(s(elem!1)))),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[3632, 3628, 100])).
% 1.52/1.75 tff(3634,plain,
% 1.52/1.75 (~(s(s(elem!1)) = elem!1)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[2555, 3633])).
% 1.52/1.75 tff(3635,plain,
% 1.52/1.75 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(z))), s(z))),
% 1.52/1.75 inference(monotonicity,[status(thm)],[19])).
% 1.52/1.75 tff(3636,plain,
% 1.52/1.75 (b(s(s(s(z))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.52/1.75 inference(symmetry,[status(thm)],[3635])).
% 1.52/1.75 tff(3637,plain,
% 1.52/1.75 ((~b(s(s(s(z))), s(z))) <=> (~b(s(s(elem!1)), s(z)))),
% 1.52/1.75 inference(monotonicity,[status(thm)],[3636])).
% 1.52/1.75 tff(3638,plain,
% 1.52/1.75 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(z))),
% 1.52/1.75 inference(monotonicity,[status(thm)],[17])).
% 1.52/1.75 tff(3639,plain,
% 1.52/1.75 ((~b(s(s(s(z))), elem!1)) <=> (~b(s(s(s(z))), s(z)))),
% 1.52/1.75 inference(monotonicity,[status(thm)],[3638])).
% 1.52/1.75 tff(3640,plain,
% 1.52/1.75 (~b(s(s(s(z))), s(z))),
% 1.52/1.75 inference(modus_ponens,[status(thm)],[100, 3639])).
% 1.52/1.75 tff(3641,plain,
% 1.52/1.75 (~b(s(s(elem!1)), s(z))),
% 1.52/1.75 inference(modus_ponens,[status(thm)],[3640, 3637])).
% 1.52/1.75 tff(3642,plain,
% 1.52/1.75 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(z))),
% 1.52/1.75 inference(monotonicity,[status(thm)],[17])).
% 1.52/1.75 tff(3643,plain,
% 1.52/1.75 (b(s(s(elem!1)), s(z))),
% 1.52/1.75 inference(modus_ponens,[status(thm)],[707, 3642])).
% 1.52/1.75 tff(3644,plain,
% 1.52/1.75 ($false),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[3643, 3641])).
% 1.52/1.75 tff(3645,plain,((~(elem!1 = s(z))) | (~b(s(s(elem!1)), elem!1)) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.52/1.75 tff(3646,plain,
% 1.52/1.75 (~(elem!1 = s(z))),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[3645, 707, 100])).
% 1.52/1.75 tff(3647,plain,
% 1.52/1.75 (r(elem!1, s(z))),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[89, 3646, 14])).
% 1.52/1.75 tff(3648,plain,
% 1.52/1.75 (b(s(s(z)), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.52/1.75 inference(monotonicity,[status(thm)],[290])).
% 1.52/1.75 tff(3649,plain,
% 1.52/1.75 (b(s(s(elem!1)), elem!1) <=> b(s(s(z)), elem!1)),
% 1.52/1.75 inference(symmetry,[status(thm)],[3648])).
% 1.52/1.75 tff(3650,plain,
% 1.52/1.75 (b(s(s(z)), elem!1)),
% 1.52/1.75 inference(modus_ponens,[status(thm)],[707, 3649])).
% 1.52/1.75 tff(3651,plain,
% 1.52/1.75 ($false),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[99, 3650])).
% 1.52/1.75 tff(3652,plain,((~(z = elem!1)) | b(s(s(z)), elem!1) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.75 tff(3653,plain,
% 1.52/1.75 (~(z = elem!1)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[3652, 707, 99])).
% 1.52/1.75 tff(3654,plain,
% 1.52/1.75 (~(s(s(elem!1)) = s(s(z)))),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[237, 3653])).
% 1.52/1.75 tff(3655,plain,
% 1.52/1.75 (b(z, elem!1)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[298, 3653, 13])).
% 1.52/1.75 tff(3656,assumption,(~r(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 1.52/1.75 tff(3657,plain,
% 1.52/1.75 (b(s(z), s(s(s(s(z)))))),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[489, 3656])).
% 1.52/1.75 tff(3658,plain,
% 1.52/1.75 ((s(z) = s(s(s(s(z))))) <=> (s(z) = elem!1)),
% 1.52/1.75 inference(monotonicity,[status(thm)],[3285])).
% 1.52/1.75 tff(3659,plain,
% 1.52/1.75 ((s(z) = elem!1) <=> (s(z) = s(s(s(s(z)))))),
% 1.52/1.75 inference(symmetry,[status(thm)],[3658])).
% 1.52/1.75 tff(3660,plain,
% 1.52/1.75 (r(s(z), s(s(s(s(z))))) <=> r(s(z), elem!1)),
% 1.52/1.75 inference(monotonicity,[status(thm)],[3285])).
% 1.52/1.75 tff(3661,plain,
% 1.52/1.75 (r(s(z), elem!1) <=> r(s(z), s(s(s(s(z)))))),
% 1.52/1.75 inference(symmetry,[status(thm)],[3660])).
% 1.52/1.75 tff(3662,plain,
% 1.52/1.75 (r(s(z), s(s(s(s(z)))))),
% 1.52/1.75 inference(modus_ponens,[status(thm)],[588, 3661])).
% 1.52/1.75 tff(3663,plain,
% 1.52/1.75 ($false),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[3656, 3662])).
% 1.52/1.75 tff(3664,plain,((~(s(s(s(s(z)))) = elem!1)) | r(s(z), s(s(s(s(z))))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.75 tff(3665,plain,
% 1.52/1.75 (~r(s(z), elem!1)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[3664, 3285, 3656])).
% 1.52/1.75 tff(3666,plain,
% 1.52/1.75 (s(z) = elem!1),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[601, 3665, 3627])).
% 1.52/1.75 tff(3667,plain,
% 1.52/1.75 (s(z) = s(s(s(s(z))))),
% 1.52/1.75 inference(modus_ponens,[status(thm)],[3666, 3659])).
% 1.52/1.75 tff(3668,plain,
% 1.52/1.75 ($false),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[484, 3667])).
% 1.52/1.75 tff(3669,plain,((~(s(s(s(s(z)))) = elem!1)) | b(s(z), elem!1) | r(s(z), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.75 tff(3670,plain,
% 1.52/1.75 (~(s(s(s(s(z)))) = elem!1)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[3669, 3656, 3627])).
% 1.52/1.75 tff(3671,plain,
% 1.52/1.75 (r(elem!1, s(s(s(s(z)))))),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[3193, 267, 12, 266, 99])).
% 1.52/1.75 tff(3672,plain,
% 1.52/1.75 (~r(elem!1, s(z))),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[3255, 3671, 1061])).
% 1.52/1.75 tff(3673,plain,
% 1.52/1.75 (elem!1 = s(z)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[89, 3672, 14])).
% 1.52/1.75 tff(3674,plain,
% 1.52/1.75 (b(elem!1, s(s(s(s(z))))) <=> b(s(z), s(s(s(s(z)))))),
% 1.52/1.75 inference(monotonicity,[status(thm)],[3673])).
% 1.52/1.75 tff(3675,plain,
% 1.52/1.75 (b(s(z), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.52/1.75 inference(symmetry,[status(thm)],[3674])).
% 1.52/1.75 tff(3676,plain,
% 1.52/1.75 (b(elem!1, s(s(s(s(z)))))),
% 1.52/1.75 inference(modus_ponens,[status(thm)],[578, 3675])).
% 1.52/1.75 tff(3677,plain,
% 1.52/1.75 (s(z) = elem!1),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[111, 3673])).
% 1.52/1.75 tff(3678,plain,
% 1.52/1.75 (~b(elem!1, s(s(s(s(z)))))),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[3103, 3677, 106, 1518, 2949, 1061, 2561])).
% 1.52/1.75 tff(3679,plain,
% 1.52/1.75 ($false),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[3678, 3676])).
% 1.52/1.75 tff(3680,plain,((s(s(s(s(z)))) = elem!1) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | b(elem!1, s(z)) | r(s(s(s(s(z)))), elem!1) | (s(s(elem!1)) = s(s(z))) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.52/1.75 tff(3681,plain,
% 1.52/1.75 (~r(s(s(s(z))), elem!1)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[3680, 3670, 106, 1518, 3657, 14, 12, 3654, 99])).
% 1.52/1.75 tff(3682,plain,
% 1.52/1.75 (s(s(s(z))) = elem!1),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[1115, 3681, 100])).
% 1.52/1.75 tff(3683,plain,
% 1.52/1.75 (b(s(s(s(z))), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 1.52/1.75 inference(monotonicity,[status(thm)],[213])).
% 1.52/1.75 tff(3684,plain,
% 1.52/1.75 (b(elem!1, s(s(elem!1)))),
% 1.52/1.75 inference(modus_ponens,[status(thm)],[3628, 3683])).
% 1.52/1.75 tff(3685,assumption,(~b(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.52/1.75 tff(3686,plain,
% 1.52/1.75 ($false),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[3685, 3684])).
% 1.52/1.75 tff(3687,plain,((~b(s(s(s(z))), s(s(elem!1)))) | b(elem!1, s(s(elem!1))) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.75 tff(3688,plain,
% 1.52/1.75 (b(elem!1, s(s(elem!1)))),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[3687, 3682, 3628])).
% 1.52/1.75 tff(3689,plain,
% 1.52/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)))),
% 1.52/1.75 inference(rewrite,[status(thm)],[])).
% 1.52/1.75 tff(3690,plain,
% 1.52/1.75 (((~b(s(s(elem!1)), elem!1)) | (~b(z, 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(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)))),
% 1.52/1.75 inference(rewrite,[status(thm)],[])).
% 1.52/1.75 tff(3691,plain,
% 1.52/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1))))),
% 1.52/1.75 inference(monotonicity,[status(thm)],[3690])).
% 1.52/1.75 tff(3692,plain,
% 1.52/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)))),
% 1.52/1.76 inference(transitivity,[status(thm)],[3691, 3689])).
% 1.52/1.76 tff(3693,plain,
% 1.52/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))),
% 1.52/1.76 inference(quant_inst,[status(thm)],[])).
% 1.52/1.76 tff(3694,plain,
% 1.52/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1))),
% 1.52/1.76 inference(modus_ponens,[status(thm)],[3693, 3692])).
% 1.52/1.76 tff(3695,plain,
% 1.52/1.76 (~b(s(s(elem!1)), z)),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[3694, 75, 1518, 3688, 707])).
% 1.52/1.76 tff(3696,plain,
% 1.52/1.76 (r(s(s(elem!1)), z)),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[2696, 3695])).
% 1.52/1.76 tff(3697,plain,
% 1.52/1.76 (b(s(s(s(s(z)))), elem!1)),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[283, 3670, 12])).
% 1.52/1.76 tff(3698,plain,
% 1.52/1.76 (b(s(elem!1), elem!1)),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[1983, 3682, 3697])).
% 1.52/1.76 tff(3699,plain,
% 1.52/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), 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(X1, 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)), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 1.52/1.76 inference(rewrite,[status(thm)],[])).
% 1.52/1.76 tff(3700,plain,
% 1.52/1.76 (((~b(s(s(elem!1)), elem!1)) | (~b(z, 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(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 1.52/1.76 inference(rewrite,[status(thm)],[])).
% 1.52/1.76 tff(3701,plain,
% 1.52/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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)), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))))),
% 1.52/1.76 inference(monotonicity,[status(thm)],[3700])).
% 1.52/1.76 tff(3702,plain,
% 1.52/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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)), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 1.52/1.76 inference(transitivity,[status(thm)],[3701, 3699])).
% 1.52/1.76 tff(3703,plain,
% 1.52/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))),
% 1.52/1.76 inference(quant_inst,[status(thm)],[])).
% 1.52/1.76 tff(3704,plain,
% 1.52/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))),
% 1.52/1.76 inference(modus_ponens,[status(thm)],[3703, 3702])).
% 1.52/1.76 tff(3705,plain,
% 1.52/1.76 (~b(s(elem!1), z)),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[3704, 75, 1518, 3688, 3698, 707])).
% 1.52/1.76 tff(3706,plain,
% 1.52/1.76 (r(s(elem!1), z)),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[766, 3705])).
% 1.52/1.76 tff(3707,plain,
% 1.52/1.76 (~(s(elem!1) = s(s(elem!1)))),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[1771, 3682, 1011])).
% 1.52/1.76 tff(3708,plain,
% 1.52/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), 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(X1, 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)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.52/1.76 inference(rewrite,[status(thm)],[])).
% 1.52/1.76 tff(3709,plain,
% 1.52/1.76 (((~b(s(s(elem!1)), 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)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.52/1.76 inference(rewrite,[status(thm)],[])).
% 1.52/1.76 tff(3710,plain,
% 1.52/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1))))))),
% 1.52/1.76 inference(monotonicity,[status(thm)],[3709])).
% 1.52/1.76 tff(3711,plain,
% 1.52/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.52/1.76 inference(transitivity,[status(thm)],[3710, 3708])).
% 1.52/1.76 tff(3712,plain,
% 1.52/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))))),
% 1.52/1.76 inference(quant_inst,[status(thm)],[])).
% 1.52/1.76 tff(3713,plain,
% 1.52/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1))))),
% 1.52/1.76 inference(modus_ponens,[status(thm)],[3712, 3711])).
% 1.52/1.76 tff(3714,plain,
% 1.52/1.76 (~b(s(elem!1), s(s(elem!1)))),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[3713, 75, 3688, 3698, 707])).
% 1.52/1.76 tff(3715,plain,
% 1.52/1.76 (r(s(elem!1), s(s(elem!1)))),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[1851, 3714, 3707])).
% 1.52/1.76 tff(3716,plain,
% 1.52/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.52/1.76 inference(rewrite,[status(thm)],[])).
% 1.52/1.76 tff(3717,plain,
% 1.52/1.76 (((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.52/1.76 inference(rewrite,[status(thm)],[])).
% 1.52/1.76 tff(3718,plain,
% 1.52/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1))))))),
% 1.52/1.76 inference(monotonicity,[status(thm)],[3717])).
% 1.52/1.76 tff(3719,plain,
% 1.52/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.52/1.76 inference(transitivity,[status(thm)],[3718, 3716])).
% 1.52/1.76 tff(3720,plain,
% 1.52/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.52/1.76 inference(quant_inst,[status(thm)],[])).
% 1.52/1.76 tff(3721,plain,
% 1.52/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1))))),
% 1.52/1.76 inference(modus_ponens,[status(thm)],[3720, 3719])).
% 1.52/1.76 tff(3722,plain,
% 1.52/1.76 ($false),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[3721, 37, 3715, 3706, 3696])).
% 1.52/1.76 tff(3723,plain,(r(s(z), s(s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(s(z))))) | b(s(s(s(z))), elem!1) | (~r(s(s(z)), elem!1)) | b(elem!1, s(z)) | r(s(s(s(s(z)))), elem!1) | b(s(s(z)), elem!1) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.52/1.76 tff(3724,plain,
% 1.52/1.76 (r(s(z), s(s(s(s(z)))))),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[3723, 3655, 707, 3628, 1011, 100, 106, 14, 12, 99, 3627])).
% 1.52/1.76 tff(3725,plain,
% 1.52/1.76 (~r(elem!1, s(s(s(s(z)))))),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[3203, 3647, 3724])).
% 1.52/1.76 tff(3726,plain,
% 1.52/1.76 (s(s(s(s(z)))) = elem!1),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[3193, 3725, 12, 3654, 99])).
% 1.52/1.76 tff(3727,plain,
% 1.52/1.76 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 1.52/1.76 inference(monotonicity,[status(thm)],[3726])).
% 1.52/1.76 tff(3728,plain,
% 1.52/1.76 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 1.52/1.76 inference(transitivity,[status(thm)],[3727, 1028])).
% 1.52/1.76 tff(3729,plain,
% 1.52/1.76 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(z))) = elem!1))),
% 1.52/1.76 inference(monotonicity,[status(thm)],[3728])).
% 1.52/1.76 tff(3730,plain,
% 1.52/1.76 (~(s(s(s(z))) = elem!1)),
% 1.52/1.76 inference(modus_ponens,[status(thm)],[264, 3729])).
% 1.52/1.76 tff(3731,plain,
% 1.52/1.76 (r(s(s(s(z))), elem!1)),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[1115, 3730, 100])).
% 1.52/1.76 tff(3732,plain,
% 1.52/1.76 (~(s(z) = elem!1)),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[97, 3646])).
% 1.52/1.76 tff(3733,plain,
% 1.52/1.76 (r(s(z), elem!1)),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[601, 3732, 3627])).
% 1.52/1.76 tff(3734,plain,
% 1.52/1.76 (~r(s(z), s(s(z)))),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[2081, 37, 3733, 106])).
% 1.52/1.76 tff(3735,plain,
% 1.52/1.76 (b(s(z), s(s(z)))),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[416, 3734])).
% 1.52/1.76 tff(3736,plain,
% 1.52/1.76 ($false),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[2743, 3735, 3731, 3647, 106])).
% 1.52/1.76 tff(3737,plain,((~b(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | b(s(s(s(z))), elem!1) | r(s(s(s(s(z)))), elem!1) | b(s(s(z)), elem!1) | b(s(z), elem!1) | b(elem!1, s(z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(s(z))))) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.52/1.76 tff(3738,plain,
% 1.52/1.76 (~b(s(s(elem!1)), elem!1)),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[3737, 3627, 100, 12, 99, 106, 14, 3628, 1011, 13])).
% 1.52/1.76 tff(3739,plain,
% 1.52/1.76 (r(s(s(elem!1)), elem!1)),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[2673, 3738, 3634])).
% 1.52/1.76 tff(3740,plain,
% 1.52/1.76 (r(s(z), elem!1)),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[601, 2560, 3627])).
% 1.52/1.76 tff(3741,plain,
% 1.52/1.76 ($false),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[2665, 3740, 238, 2647, 106])).
% 1.52/1.76 tff(3742,plain,((~(s(s(s(z))) = elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.52/1.76 tff(3743,plain,
% 1.52/1.76 (~(s(s(s(z))) = elem!1)),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[3742, 3739, 106, 3627])).
% 1.52/1.76 tff(3744,plain,
% 1.52/1.76 (r(s(s(s(z))), elem!1)),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[1115, 3743, 100])).
% 1.52/1.76 tff(3745,plain,
% 1.52/1.76 (r(s(z), elem!1)),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[601, 108, 3627])).
% 1.52/1.76 tff(3746,plain,
% 1.52/1.76 (s(s(elem!1)) = s(s(z))),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[2665, 3745, 2647, 106])).
% 1.52/1.76 tff(3747,plain,
% 1.52/1.76 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(z)))),
% 1.52/1.76 inference(monotonicity,[status(thm)],[3746])).
% 1.52/1.76 tff(3748,plain,
% 1.52/1.76 (b(s(z), s(s(z))) <=> b(s(z), s(s(elem!1)))),
% 1.52/1.76 inference(symmetry,[status(thm)],[3747])).
% 1.52/1.76 tff(3749,plain,
% 1.52/1.76 ((~b(s(z), s(s(z)))) <=> (~b(s(z), s(s(elem!1))))),
% 1.52/1.76 inference(monotonicity,[status(thm)],[3748])).
% 1.52/1.76 tff(3750,plain,
% 1.52/1.76 (~b(s(z), s(s(z)))),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[2743, 113, 1061, 106])).
% 1.52/1.76 tff(3751,plain,
% 1.52/1.76 (~b(s(z), s(s(elem!1)))),
% 1.52/1.76 inference(modus_ponens,[status(thm)],[3750, 3749])).
% 1.52/1.76 tff(3752,plain,
% 1.52/1.76 ($false),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[2653, 37, 588, 1871, 2647])).
% 1.52/1.76 tff(3753,plain,((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.76 tff(3754,plain,
% 1.52/1.76 (~r(s(z), s(s(elem!1)))),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[3753, 3745, 2647])).
% 1.52/1.76 tff(3755,plain,
% 1.52/1.76 (b(s(z), s(s(elem!1)))),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[1890, 3754])).
% 1.52/1.76 tff(3756,plain,
% 1.52/1.76 ($false),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[3755, 3751])).
% 1.52/1.76 tff(3757,plain,((s(z) = elem!1) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), elem!1)) | b(elem!1, s(z)) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.52/1.76 tff(3758,plain,
% 1.52/1.76 (s(z) = elem!1),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[3757, 3744, 106, 3739, 14, 3627])).
% 1.52/1.76 tff(3759,plain,
% 1.52/1.76 (s(s(z)) = s(elem!1)),
% 1.52/1.76 inference(monotonicity,[status(thm)],[3758])).
% 1.52/1.76 tff(3760,plain,
% 1.52/1.76 (s(s(s(z))) = s(s(elem!1))),
% 1.52/1.76 inference(monotonicity,[status(thm)],[3759])).
% 1.52/1.76 tff(3761,plain,
% 1.52/1.76 (b(s(s(s(z))), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.52/1.76 inference(monotonicity,[status(thm)],[3760])).
% 1.52/1.76 tff(3762,plain,
% 1.52/1.76 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(s(z))), s(s(s(z))))),
% 1.52/1.76 inference(symmetry,[status(thm)],[3761])).
% 1.52/1.76 tff(3763,plain,
% 1.52/1.76 (s(s(elem!1)) = s(s(s(z)))),
% 1.52/1.76 inference(symmetry,[status(thm)],[3760])).
% 1.52/1.76 tff(3764,plain,
% 1.52/1.76 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.52/1.76 inference(monotonicity,[status(thm)],[3760, 3763])).
% 1.52/1.76 tff(3765,plain,
% 1.52/1.76 (b(s(s(elem!1)), s(s(s(z))))),
% 1.52/1.76 inference(modus_ponens,[status(thm)],[3628, 3764])).
% 1.52/1.76 tff(3766,plain,
% 1.52/1.76 (b(s(s(s(z))), s(s(s(z))))),
% 1.52/1.76 inference(modus_ponens,[status(thm)],[3765, 3762])).
% 1.52/1.76 tff(3767,plain,
% 1.52/1.76 (~r(s(s(s(z))), s(s(z)))),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[3030, 37, 106, 3744])).
% 1.52/1.76 tff(3768,plain,
% 1.52/1.76 ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z)))),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[2173, 58, 3767])).
% 1.52/1.76 tff(3769,plain,
% 1.52/1.76 (b(s(s(s(z))), s(s(z)))),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[3768, 2150])).
% 1.52/1.76 tff(3770,plain,
% 1.52/1.76 (~r(s(s(z)), s(s(s(z))))),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[2718, 37, 106, 3744])).
% 1.52/1.76 tff(3771,plain,
% 1.52/1.76 (b(s(s(z)), s(s(s(z))))),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[1559, 58, 1556, 3770])).
% 1.52/1.76 tff(3772,plain,
% 1.52/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.52/1.76 inference(rewrite,[status(thm)],[])).
% 1.52/1.76 tff(3773,plain,
% 1.52/1.76 (((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.52/1.76 inference(rewrite,[status(thm)],[])).
% 1.52/1.76 tff(3774,plain,
% 1.52/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 1.52/1.76 inference(monotonicity,[status(thm)],[3773])).
% 1.52/1.76 tff(3775,plain,
% 1.52/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.52/1.76 inference(transitivity,[status(thm)],[3774, 3772])).
% 1.52/1.76 tff(3776,plain,
% 1.52/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(z))))))),
% 1.52/1.76 inference(quant_inst,[status(thm)],[])).
% 1.52/1.76 tff(3777,plain,
% 1.52/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 1.52/1.76 inference(modus_ponens,[status(thm)],[3776, 3775])).
% 1.52/1.76 tff(3778,plain,
% 1.52/1.76 ((~b(s(s(s(z))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[3777, 75, 3628, 3771])).
% 1.52/1.76 tff(3779,plain,
% 1.52/1.76 (~b(s(s(s(z))), s(s(s(z))))),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[3778, 3769])).
% 1.52/1.76 tff(3780,plain,
% 1.52/1.76 ($false),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[3779, 3766])).
% 1.52/1.76 tff(3781,plain,(b(s(z), elem!1) | (~b(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), elem!1)) | b(elem!1, s(z)) | b(s(s(s(z))), elem!1) | r(s(s(s(s(z)))), elem!1) | b(s(s(z)), elem!1) | (s(s(elem!1)) = s(s(s(s(z))))) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.52/1.76 tff(3782,plain,
% 1.52/1.76 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[3781, 3626, 105, 14, 100, 12, 99, 1426, 13])).
% 1.52/1.76 tff(3783,plain,
% 1.52/1.76 (r(s(s(s(z))), s(s(elem!1)))),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[62, 3782, 16])).
% 1.52/1.76 tff(3784,plain,
% 1.52/1.76 (~(elem!1 = s(z))),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[47, 3783])).
% 1.52/1.76 tff(3785,plain,
% 1.52/1.76 (r(elem!1, s(z))),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[89, 3784, 14])).
% 1.52/1.76 tff(3786,plain,
% 1.52/1.76 (~(s(z) = elem!1)),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[97, 3784])).
% 1.52/1.76 tff(3787,plain,
% 1.52/1.76 (r(s(z), elem!1)),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[601, 3786, 3626])).
% 1.52/1.76 tff(3788,plain,
% 1.52/1.76 (~r(s(z), s(s(z)))),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[2081, 37, 3787, 105])).
% 1.52/1.76 tff(3789,plain,
% 1.52/1.76 (b(s(z), s(s(z)))),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[416, 3788])).
% 1.52/1.76 tff(3790,plain,
% 1.52/1.76 (~r(s(s(s(z))), elem!1)),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[2743, 3789, 3785, 105])).
% 1.52/1.76 tff(3791,plain,
% 1.52/1.76 (s(s(s(z))) = elem!1),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[1115, 3790, 100])).
% 1.52/1.76 tff(3792,plain,
% 1.52/1.76 (~r(s(s(elem!1)), elem!1)),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[3742, 3791, 105, 3626])).
% 1.52/1.76 tff(3793,plain,
% 1.52/1.76 (~(elem!1 = s(s(elem!1)))),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[1612, 3791])).
% 1.52/1.76 tff(3794,plain,
% 1.52/1.76 (~(s(s(elem!1)) = elem!1)),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[2555, 3793])).
% 1.52/1.76 tff(3795,plain,
% 1.52/1.76 (b(s(s(elem!1)), elem!1)),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[2673, 3794, 3792])).
% 1.52/1.76 tff(3796,plain,
% 1.52/1.76 (~(z = elem!1)),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[3652, 3795, 99])).
% 1.52/1.76 tff(3797,plain,
% 1.52/1.76 (~(s(s(elem!1)) = s(s(z)))),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[237, 3796])).
% 1.52/1.76 tff(3798,plain,
% 1.52/1.76 (b(z, elem!1)),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[298, 3796, 13])).
% 1.52/1.76 tff(3799,plain,
% 1.52/1.76 (~r(s(s(elem!1)), elem!1)),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[3742, 213, 106, 3627])).
% 1.52/1.76 tff(3800,plain,
% 1.52/1.76 (b(s(s(elem!1)), elem!1)),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[2673, 3799, 2556])).
% 1.52/1.76 tff(3801,plain,
% 1.52/1.76 (r(s(s(s(z))), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 1.52/1.76 inference(monotonicity,[status(thm)],[213])).
% 1.52/1.76 tff(3802,plain,
% 1.52/1.76 (r(elem!1, s(s(elem!1)))),
% 1.52/1.76 inference(modus_ponens,[status(thm)],[27, 3801])).
% 1.52/1.76 tff(3803,plain,
% 1.52/1.76 (r(elem!1, s(s(s(s(z)))))),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[3193, 265, 12, 266, 99])).
% 1.52/1.76 tff(3804,plain,
% 1.52/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(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(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(elem!1)))))),
% 1.52/1.76 inference(rewrite,[status(thm)],[])).
% 1.52/1.76 tff(3805,plain,
% 1.52/1.76 (((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(elem!1)))))),
% 1.52/1.76 inference(rewrite,[status(thm)],[])).
% 1.52/1.76 tff(3806,plain,
% 1.52/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(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(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(elem!1))))))),
% 1.52/1.76 inference(monotonicity,[status(thm)],[3805])).
% 1.52/1.77 tff(3807,plain,
% 1.52/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(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(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(elem!1)))))),
% 1.52/1.77 inference(transitivity,[status(thm)],[3806, 3804])).
% 1.52/1.77 tff(3808,plain,
% 1.52/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, s(s(elem!1)))))),
% 1.52/1.77 inference(quant_inst,[status(thm)],[])).
% 1.52/1.77 tff(3809,plain,
% 1.52/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(elem!1))))),
% 1.52/1.77 inference(modus_ponens,[status(thm)],[3808, 3807])).
% 1.52/1.77 tff(3810,plain,
% 1.52/1.77 ($false),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[3809, 37, 1490, 3195, 1647])).
% 1.52/1.77 tff(3811,plain,((~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.77 tff(3812,plain,
% 1.52/1.77 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[3811, 3803, 3802])).
% 1.52/1.77 tff(3813,plain,
% 1.52/1.77 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[1660, 3812, 1011])).
% 1.52/1.77 tff(3814,plain,
% 1.52/1.77 (b(s(s(elem!1)), s(elem!1))),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[1865, 3813, 213])).
% 1.52/1.77 tff(3815,plain,
% 1.52/1.77 (~(elem!1 = s(z))),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[3645, 3800, 100])).
% 1.52/1.77 tff(3816,plain,
% 1.52/1.77 (r(elem!1, s(z))),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[89, 3815, 14])).
% 1.52/1.77 tff(3817,plain,
% 1.52/1.77 (~r(elem!1, z)),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[211, 3816, 106])).
% 1.52/1.77 tff(3818,plain,
% 1.52/1.77 (b(elem!1, z)),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[387, 3817, 305])).
% 1.52/1.77 tff(3819,plain,
% 1.52/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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, z)) | (~b(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(X1, 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, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.52/1.77 inference(rewrite,[status(thm)],[])).
% 1.52/1.77 tff(3820,plain,
% 1.52/1.77 (((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.52/1.77 inference(rewrite,[status(thm)],[])).
% 1.52/1.77 tff(3821,plain,
% 1.52/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))))),
% 1.52/1.77 inference(monotonicity,[status(thm)],[3820])).
% 1.52/1.77 tff(3822,plain,
% 1.52/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.52/1.77 inference(transitivity,[status(thm)],[3821, 3819])).
% 1.52/1.77 tff(3823,plain,
% 1.52/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.52/1.77 inference(quant_inst,[status(thm)],[])).
% 1.52/1.77 tff(3824,plain,
% 1.52/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.52/1.77 inference(modus_ponens,[status(thm)],[3823, 3822])).
% 1.52/1.77 tff(3825,plain,
% 1.52/1.77 ($false),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[3824, 75, 1518, 3818, 3210, 3814, 3800])).
% 1.52/1.77 tff(3826,plain,((~(s(s(s(z))) = elem!1)) | (~b(z, elem!1)) | (s(s(elem!1)) = s(s(s(s(z))))) | r(s(s(s(s(z)))), elem!1) | (s(s(elem!1)) = s(s(z))) | b(s(s(z)), elem!1) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), elem!1)) | b(elem!1, s(z)) | b(s(s(s(z))), elem!1) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.52/1.77 tff(3827,plain,
% 1.52/1.77 ($false),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[3826, 3798, 3797, 1426, 12, 3791, 99, 3783, 105, 14, 100, 3626])).
% 1.52/1.77 tff(3828,plain,(b(s(s(z)), elem!1) | r(s(s(s(s(z)))), elem!1) | b(elem!1, s(z)) | b(s(s(s(z))), elem!1) | r(z, elem!1) | (s(s(s(z))) = s(s(elem!1))) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.52/1.77 tff(3829,plain,
% 1.52/1.77 (b(s(s(s(z))), elem!1)),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[3828, 99, 14, 12, 13, 16, 15])).
% 1.52/1.77 tff(3830,plain,
% 1.52/1.77 (~r(elem!1, z)),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[211, 105, 90])).
% 1.52/1.77 tff(3831,plain,
% 1.52/1.77 (b(s(z), s(s(s(z)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.52/1.77 inference(monotonicity,[status(thm)],[289, 3417])).
% 1.52/1.77 tff(3832,plain,
% 1.52/1.77 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.52/1.77 inference(monotonicity,[status(thm)],[3417])).
% 1.52/1.77 tff(3833,plain,
% 1.52/1.77 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 1.52/1.77 inference(symmetry,[status(thm)],[3832])).
% 1.52/1.77 tff(3834,plain,
% 1.52/1.77 ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) <=> (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.52/1.77 inference(monotonicity,[status(thm)],[3833])).
% 1.52/1.77 tff(3835,plain,
% 1.52/1.77 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), elem!1)),
% 1.52/1.77 inference(monotonicity,[status(thm)],[3418])).
% 1.52/1.77 tff(3836,plain,
% 1.52/1.77 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 1.52/1.77 inference(symmetry,[status(thm)],[3835])).
% 1.52/1.77 tff(3837,plain,
% 1.52/1.77 (b(s(s(s(elem!1))), elem!1)),
% 1.52/1.77 inference(modus_ponens,[status(thm)],[1119, 3836])).
% 1.52/1.77 tff(3838,plain,
% 1.52/1.77 (b(s(s(s(s(z)))), elem!1)),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[283, 3445, 12])).
% 1.52/1.77 tff(3839,plain,
% 1.52/1.77 (s(s(elem!1)) = s(s(z))),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[293, 288])).
% 1.52/1.77 tff(3840,plain,
% 1.52/1.77 (r(s(s(z)), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 1.52/1.77 inference(monotonicity,[status(thm)],[290])).
% 1.52/1.77 tff(3841,plain,
% 1.52/1.77 (r(s(s(elem!1)), elem!1)),
% 1.52/1.77 inference(modus_ponens,[status(thm)],[106, 3840])).
% 1.52/1.77 tff(3842,plain,
% 1.52/1.77 (b(s(z), s(s(s(s(z)))))),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[489, 3225])).
% 1.52/1.77 tff(3843,plain,
% 1.52/1.77 (z = elem!1),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[237, 225])).
% 1.52/1.77 tff(3844,plain,
% 1.52/1.77 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 1.52/1.77 inference(monotonicity,[status(thm)],[3843])).
% 1.52/1.77 tff(3845,plain,
% 1.52/1.77 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(z)))))),
% 1.52/1.77 inference(transitivity,[status(thm)],[3844, 239])).
% 1.52/1.77 tff(3846,plain,
% 1.52/1.77 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 1.52/1.77 inference(transitivity,[status(thm)],[3845, 240])).
% 1.52/1.77 tff(3847,plain,
% 1.52/1.77 ((~(s(s(s(s(z)))) = z)) <=> (~(s(s(s(s(z)))) = elem!1))),
% 1.52/1.77 inference(monotonicity,[status(thm)],[3846])).
% 1.52/1.77 tff(3848,plain,
% 1.52/1.77 (~(s(s(s(s(z)))) = elem!1)),
% 1.52/1.77 inference(modus_ponens,[status(thm)],[1143, 3847])).
% 1.52/1.77 tff(3849,plain,
% 1.52/1.77 (r(s(s(elem!1)), elem!1) <=> r(s(s(z)), elem!1)),
% 1.52/1.77 inference(monotonicity,[status(thm)],[225])).
% 1.52/1.77 tff(3850,plain,
% 1.52/1.77 (r(s(s(z)), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 1.52/1.77 inference(symmetry,[status(thm)],[3849])).
% 1.52/1.77 tff(3851,plain,
% 1.52/1.77 (r(s(s(elem!1)), elem!1)),
% 1.52/1.77 inference(modus_ponens,[status(thm)],[106, 3850])).
% 1.52/1.77 tff(3852,plain,
% 1.52/1.77 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(z), s(s(s(s(z)))))),
% 1.52/1.77 inference(monotonicity,[status(thm)],[3422])).
% 1.52/1.77 tff(3853,plain,
% 1.52/1.77 (b(s(z), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 1.52/1.77 inference(symmetry,[status(thm)],[3852])).
% 1.52/1.77 tff(3854,plain,
% 1.52/1.77 (b(s(elem!1), s(s(s(s(z)))))),
% 1.52/1.77 inference(modus_ponens,[status(thm)],[578, 3853])).
% 1.52/1.77 tff(3855,assumption,(~b(s(elem!1), s(s(s(s(z)))))), introduced(assumption)).
% 1.52/1.77 tff(3856,plain,
% 1.52/1.77 ($false),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[3855, 3854])).
% 1.52/1.77 tff(3857,plain,(b(s(elem!1), s(s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.77 tff(3858,plain,
% 1.52/1.77 (b(s(elem!1), s(s(s(s(z)))))),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[3857, 3843, 578])).
% 1.52/1.77 tff(3859,plain,
% 1.52/1.77 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(z)), s(z))),
% 1.52/1.77 inference(monotonicity,[status(thm)],[225, 230])).
% 1.52/1.77 tff(3860,plain,
% 1.52/1.77 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(elem!1))),
% 1.52/1.77 inference(symmetry,[status(thm)],[3859])).
% 1.52/1.77 tff(3861,plain,
% 1.52/1.77 (b(s(s(elem!1)), s(elem!1))),
% 1.52/1.77 inference(modus_ponens,[status(thm)],[154, 3860])).
% 1.52/1.77 tff(3862,assumption,(b(s(elem!1), s(s(s(s(z)))))), introduced(assumption)).
% 1.52/1.77 tff(3863,plain,
% 1.52/1.77 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 1.52/1.77 inference(commutativity,[status(thm)],[])).
% 1.52/1.77 tff(3864,plain,
% 1.52/1.77 ((s(s(elem!1)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 1.52/1.77 inference(symmetry,[status(thm)],[3863])).
% 1.52/1.77 tff(3865,plain,
% 1.52/1.77 ((~(s(s(elem!1)) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(elem!1))))),
% 1.52/1.77 inference(monotonicity,[status(thm)],[3864])).
% 1.52/1.77 tff(3866,plain,
% 1.52/1.77 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 1.52/1.77 inference(modus_ponens,[status(thm)],[1011, 3865])).
% 1.52/1.77 tff(3867,plain,
% 1.52/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(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(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 1.52/1.77 inference(rewrite,[status(thm)],[])).
% 1.52/1.77 tff(3868,plain,
% 1.52/1.77 (((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 1.52/1.77 inference(rewrite,[status(thm)],[])).
% 1.52/1.77 tff(3869,plain,
% 1.52/1.77 (((~![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)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))))),
% 1.52/1.77 inference(monotonicity,[status(thm)],[3868])).
% 1.52/1.77 tff(3870,plain,
% 1.52/1.77 (((~![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)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 1.52/1.77 inference(transitivity,[status(thm)],[3869, 3867])).
% 1.52/1.77 tff(3871,plain,
% 1.52/1.77 ((~![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)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.52/1.77 inference(quant_inst,[status(thm)],[])).
% 1.52/1.77 tff(3872,plain,
% 1.52/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))),
% 1.52/1.77 inference(modus_ponens,[status(thm)],[3871, 3870])).
% 1.52/1.77 tff(3873,plain,
% 1.52/1.77 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[3872, 37, 698, 2647])).
% 1.52/1.77 tff(3874,plain,
% 1.52/1.77 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(elem!1))) | b(s(s(s(s(z)))), s(s(elem!1))) | r(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(elem!1))) | b(s(s(s(s(z)))), s(s(elem!1))) | r(s(s(s(s(z)))), s(s(elem!1))))),
% 1.52/1.77 inference(rewrite,[status(thm)],[])).
% 1.52/1.77 tff(3875,plain,
% 1.52/1.77 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(elem!1))) | b(s(s(s(s(z)))), s(s(elem!1))) | r(s(s(s(s(z)))), s(s(elem!1))))),
% 1.52/1.77 inference(quant_inst,[status(thm)],[])).
% 1.52/1.77 tff(3876,plain,
% 1.52/1.77 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(elem!1))) | b(s(s(s(s(z)))), s(s(elem!1))) | r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.52/1.77 inference(modus_ponens,[status(thm)],[3875, 3874])).
% 1.52/1.77 tff(3877,plain,
% 1.52/1.77 ((s(s(s(s(z)))) = s(s(elem!1))) | b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[3876, 58, 3873])).
% 1.52/1.77 tff(3878,plain,
% 1.52/1.77 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[3877, 3866])).
% 1.52/1.77 tff(3879,plain,
% 1.52/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), 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)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 1.52/1.77 inference(rewrite,[status(thm)],[])).
% 1.52/1.77 tff(3880,plain,
% 1.52/1.77 (((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 1.52/1.77 inference(rewrite,[status(thm)],[])).
% 1.52/1.77 tff(3881,plain,
% 1.52/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), elem!1))))),
% 1.52/1.77 inference(monotonicity,[status(thm)],[3880])).
% 1.52/1.77 tff(3882,plain,
% 1.52/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 1.52/1.77 inference(transitivity,[status(thm)],[3881, 3879])).
% 1.52/1.77 tff(3883,plain,
% 1.52/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.52/1.77 inference(quant_inst,[status(thm)],[])).
% 1.52/1.77 tff(3884,plain,
% 1.52/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), elem!1))),
% 1.52/1.77 inference(modus_ponens,[status(thm)],[3883, 3882])).
% 1.52/1.77 tff(3885,plain,
% 1.52/1.77 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[3884, 37, 698, 2647])).
% 1.52/1.77 tff(3886,plain,
% 1.52/1.77 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[1660, 3885, 1011])).
% 1.52/1.77 tff(3887,plain,
% 1.52/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.52/1.77 inference(rewrite,[status(thm)],[])).
% 1.52/1.77 tff(3888,plain,
% 1.52/1.77 (((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.52/1.77 inference(rewrite,[status(thm)],[])).
% 1.52/1.77 tff(3889,plain,
% 1.52/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))))),
% 1.52/1.77 inference(monotonicity,[status(thm)],[3888])).
% 1.52/1.77 tff(3890,plain,
% 1.52/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.52/1.77 inference(transitivity,[status(thm)],[3889, 3887])).
% 1.52/1.77 tff(3891,plain,
% 1.52/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.52/1.77 inference(quant_inst,[status(thm)],[])).
% 1.52/1.77 tff(3892,plain,
% 1.52/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 1.52/1.77 inference(modus_ponens,[status(thm)],[3891, 3890])).
% 1.52/1.77 tff(3893,plain,
% 1.52/1.77 ($false),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[3892, 75, 3886, 3069, 3878, 3862])).
% 1.52/1.77 tff(3894,plain,((~r(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (s(s(elem!1)) = s(s(s(s(z))))) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.77 tff(3895,plain,
% 1.52/1.77 (~r(s(s(s(s(z)))), elem!1)),
% 1.52/1.78 inference(unit_resolution,[status(thm)],[3894, 3861, 3858, 1011, 3851])).
% 1.52/1.78 tff(3896,plain,
% 1.52/1.78 (b(s(s(s(s(z)))), elem!1)),
% 1.52/1.78 inference(unit_resolution,[status(thm)],[283, 3895, 3848])).
% 1.52/1.78 tff(3897,plain,
% 1.52/1.78 ((~(s(s(s(s(z)))) = z)) <=> (~(elem!1 = s(s(s(s(z))))))),
% 1.52/1.78 inference(monotonicity,[status(thm)],[3845])).
% 1.52/1.78 tff(3898,plain,
% 1.52/1.78 (~(elem!1 = s(s(s(s(z)))))),
% 1.52/1.78 inference(modus_ponens,[status(thm)],[1143, 3897])).
% 1.52/1.78 tff(3899,plain,
% 1.52/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.52/1.78 inference(rewrite,[status(thm)],[])).
% 1.52/1.78 tff(3900,plain,
% 1.52/1.78 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.52/1.78 inference(rewrite,[status(thm)],[])).
% 1.52/1.78 tff(3901,plain,
% 1.52/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))))),
% 1.52/1.78 inference(monotonicity,[status(thm)],[3900])).
% 1.52/1.78 tff(3902,plain,
% 1.52/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.52/1.78 inference(transitivity,[status(thm)],[3901, 3899])).
% 1.52/1.78 tff(3903,plain,
% 1.52/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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))))),
% 1.52/1.78 inference(quant_inst,[status(thm)],[])).
% 1.52/1.78 tff(3904,plain,
% 1.52/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))),
% 1.52/1.78 inference(modus_ponens,[status(thm)],[3903, 3902])).
% 1.52/1.78 tff(3905,plain,
% 1.52/1.78 ($false),
% 1.52/1.78 inference(unit_resolution,[status(thm)],[3904, 75, 309, 578, 895, 982])).
% 1.52/1.78 tff(3906,plain,((~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(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.78 tff(3907,plain,
% 1.52/1.78 (~b(s(s(s(s(z)))), s(z))),
% 1.52/1.78 inference(unit_resolution,[status(thm)],[3906, 154, 578, 895])).
% 1.52/1.78 tff(3908,plain,
% 1.52/1.78 (r(s(s(s(s(z)))), s(z))),
% 1.52/1.78 inference(unit_resolution,[status(thm)],[1406, 58, 3907, 483])).
% 1.52/1.78 tff(3909,plain,
% 1.52/1.78 ($false),
% 1.52/1.78 inference(unit_resolution,[status(thm)],[3249, 37, 114, 3195, 1409])).
% 1.52/1.78 tff(3910,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.78 tff(3911,plain,
% 1.52/1.78 (~r(elem!1, s(s(s(s(z)))))),
% 1.52/1.78 inference(unit_resolution,[status(thm)],[3910, 3908, 114])).
% 1.52/1.78 tff(3912,plain,
% 1.52/1.78 (b(elem!1, s(s(s(s(z)))))),
% 1.52/1.78 inference(unit_resolution,[status(thm)],[278, 3911, 3898])).
% 1.52/1.78 tff(3913,plain,
% 1.52/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(s(s(z)), s(s(s(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(X1, 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(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.52/1.78 inference(rewrite,[status(thm)],[])).
% 1.52/1.78 tff(3914,plain,
% 1.52/1.78 (((~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))) <=> ((~b(elem!1, 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)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.52/1.78 inference(rewrite,[status(thm)],[])).
% 1.52/1.78 tff(3915,plain,
% 1.52/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~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(X1, 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(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z))))))))),
% 1.52/1.78 inference(monotonicity,[status(thm)],[3914])).
% 1.52/1.78 tff(3916,plain,
% 1.52/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~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(X1, 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(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.52/1.78 inference(transitivity,[status(thm)],[3915, 3913])).
% 1.52/1.78 tff(3917,plain,
% 1.52/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 1.52/1.78 inference(quant_inst,[status(thm)],[])).
% 1.52/1.78 tff(3918,plain,
% 1.52/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z))))))),
% 1.52/1.78 inference(modus_ponens,[status(thm)],[3917, 3916])).
% 1.52/1.78 tff(3919,plain,
% 1.52/1.78 ($false),
% 1.52/1.78 inference(unit_resolution,[status(thm)],[3918, 75, 154, 578, 3912, 3896, 895])).
% 1.52/1.78 tff(3920,plain,((~r(elem!1, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (s(s(elem!1)) = s(s(s(s(z))))) | (~(s(s(elem!1)) = s(s(z)))) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.78 tff(3921,plain,
% 1.52/1.78 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.52/1.78 inference(unit_resolution,[status(thm)],[3920, 3842, 106, 1011, 225, 114])).
% 1.52/1.78 tff(3922,plain,
% 1.52/1.78 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.52/1.78 inference(monotonicity,[status(thm)],[3571])).
% 1.52/1.78 tff(3923,plain,
% 1.52/1.78 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 1.52/1.78 inference(symmetry,[status(thm)],[3922])).
% 1.52/1.78 tff(3924,plain,
% 1.52/1.78 (b(s(s(z)), s(s(s(s(z)))))),
% 1.52/1.78 inference(modus_ponens,[status(thm)],[1619, 3923])).
% 1.52/1.78 tff(3925,plain,
% 1.52/1.78 ($false),
% 1.52/1.78 inference(unit_resolution,[status(thm)],[428, 3924])).
% 1.52/1.78 tff(3926,plain,(b(s(s(z)), s(s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~(s(s(elem!1)) = s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.78 tff(3927,plain,
% 1.52/1.78 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.52/1.78 inference(unit_resolution,[status(thm)],[3926, 3921, 225])).
% 1.52/1.78 tff(3928,plain,
% 1.52/1.78 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.52/1.78 inference(unit_resolution,[status(thm)],[1660, 3927, 1011])).
% 1.52/1.78 tff(3929,plain,
% 1.52/1.78 (((~![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(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), elem!1)))),
% 1.52/1.78 inference(rewrite,[status(thm)],[])).
% 1.52/1.78 tff(3930,plain,
% 1.52/1.78 (((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), elem!1)))),
% 1.52/1.78 inference(rewrite,[status(thm)],[])).
% 1.52/1.78 tff(3931,plain,
% 1.52/1.78 (((~![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(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), elem!1))))),
% 1.52/1.78 inference(monotonicity,[status(thm)],[3930])).
% 1.52/1.78 tff(3932,plain,
% 1.52/1.78 (((~![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(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), elem!1)))),
% 1.52/1.78 inference(transitivity,[status(thm)],[3931, 3929])).
% 1.52/1.78 tff(3933,plain,
% 1.52/1.78 ((~![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(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), elem!1)))),
% 1.52/1.78 inference(quant_inst,[status(thm)],[])).
% 1.52/1.78 tff(3934,plain,
% 1.52/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), elem!1))),
% 1.52/1.78 inference(modus_ponens,[status(thm)],[3933, 3932])).
% 1.52/1.78 tff(3935,plain,
% 1.52/1.78 ($false),
% 1.52/1.78 inference(unit_resolution,[status(thm)],[3934, 37, 3195, 3928, 2647])).
% 1.52/1.78 tff(3936,plain,((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), elem!1)) | (s(s(elem!1)) = s(s(s(s(z))))) | (~(s(s(elem!1)) = s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.78 tff(3937,plain,
% 1.52/1.78 (~r(elem!1, s(s(s(s(z)))))),
% 1.52/1.78 inference(unit_resolution,[status(thm)],[3936, 3841, 1011, 3839, 106, 114])).
% 1.52/1.78 tff(3938,plain,
% 1.52/1.78 (b(elem!1, s(s(s(s(z)))))),
% 1.52/1.78 inference(unit_resolution,[status(thm)],[278, 3937, 3522])).
% 1.52/1.78 tff(3939,plain,
% 1.52/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.52/1.78 inference(rewrite,[status(thm)],[])).
% 1.52/1.78 tff(3940,plain,
% 1.52/1.78 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.52/1.78 inference(rewrite,[status(thm)],[])).
% 1.52/1.78 tff(3941,plain,
% 1.52/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~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(X1, 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(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), elem!1))))),
% 1.52/1.78 inference(monotonicity,[status(thm)],[3940])).
% 1.52/1.78 tff(3942,plain,
% 1.52/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~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(X1, 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(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.52/1.78 inference(transitivity,[status(thm)],[3941, 3939])).
% 1.52/1.78 tff(3943,plain,
% 1.52/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.52/1.78 inference(quant_inst,[status(thm)],[])).
% 1.52/1.78 tff(3944,plain,
% 1.52/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), elem!1))),
% 1.52/1.78 inference(modus_ponens,[status(thm)],[3943, 3942])).
% 1.52/1.78 tff(3945,plain,
% 1.52/1.78 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.52/1.78 inference(unit_resolution,[status(thm)],[3944, 75, 3938, 3838, 3837])).
% 1.52/1.78 tff(3946,plain,
% 1.52/1.78 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.52/1.78 inference(modus_ponens,[status(thm)],[3945, 3834])).
% 1.52/1.78 tff(3947,plain,
% 1.52/1.78 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.52/1.78 inference(unit_resolution,[status(thm)],[575, 3946])).
% 1.52/1.78 tff(3948,plain,
% 1.52/1.78 (b(s(s(elem!1)), s(elem!1))),
% 1.52/1.78 inference(modus_ponens,[status(thm)],[2734, 3570])).
% 1.52/1.78 tff(3949,plain,
% 1.52/1.78 ((s(elem!1) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.52/1.78 inference(symmetry,[status(thm)],[269])).
% 1.52/1.78 tff(3950,plain,
% 1.52/1.78 ((s(s(s(s(s(s(s(z))))))) = s(z)) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.52/1.78 inference(monotonicity,[status(thm)],[289])).
% 1.52/1.78 tff(3951,plain,
% 1.52/1.78 ((s(s(s(s(s(s(s(z))))))) = s(z)) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.52/1.78 inference(transitivity,[status(thm)],[3950, 269])).
% 1.52/1.78 tff(3952,plain,
% 1.52/1.78 ((s(s(s(s(s(s(s(z))))))) = s(z)) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.52/1.78 inference(transitivity,[status(thm)],[3951, 3949])).
% 1.52/1.78 tff(3953,plain,
% 1.52/1.78 ((~(s(s(s(s(s(s(s(z))))))) = s(z))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(elem!1)))),
% 1.52/1.78 inference(monotonicity,[status(thm)],[3952])).
% 1.52/1.78 tff(3954,plain,
% 1.52/1.78 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.52/1.78 inference(modus_ponens,[status(thm)],[1227, 3953])).
% 1.52/1.78 tff(3955,plain,
% 1.52/1.78 ((s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 1.52/1.78 inference(commutativity,[status(thm)],[])).
% 1.52/1.78 tff(3956,plain,
% 1.52/1.78 ((s(s(s(s(s(s(s(z))))))) = s(s(z))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 1.52/1.78 inference(monotonicity,[status(thm)],[290])).
% 1.52/1.78 tff(3957,plain,
% 1.52/1.78 ((s(s(s(s(s(s(s(z))))))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 1.52/1.78 inference(transitivity,[status(thm)],[3956, 3955])).
% 1.52/1.78 tff(3958,plain,
% 1.52/1.78 ((~(s(s(s(s(s(s(s(z))))))) = s(s(z)))) <=> (~(s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))))),
% 1.52/1.78 inference(monotonicity,[status(thm)],[3957])).
% 1.52/1.78 tff(3959,plain,
% 1.52/1.78 (~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 1.52/1.78 inference(modus_ponens,[status(thm)],[1045, 3958])).
% 1.52/1.78 tff(3960,plain,
% 1.52/1.78 ((~(s(s(s(s(s(s(s(z))))))) = s(z))) <=> (~(s(elem!1) = s(s(s(s(s(s(s(z)))))))))),
% 1.52/1.78 inference(monotonicity,[status(thm)],[3951])).
% 1.52/1.78 tff(3961,plain,
% 1.52/1.78 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.52/1.78 inference(modus_ponens,[status(thm)],[1227, 3960])).
% 1.52/1.78 tff(3962,plain,
% 1.52/1.78 (elem!1 = z),
% 1.52/1.78 inference(symmetry,[status(thm)],[288])).
% 1.52/1.78 tff(3963,plain,
% 1.52/1.78 ((s(s(s(s(s(s(s(z))))))) = elem!1) <=> (s(s(s(s(s(s(s(z))))))) = z)),
% 1.52/1.78 inference(monotonicity,[status(thm)],[3962])).
% 1.52/1.78 tff(3964,plain,
% 1.52/1.78 ((s(s(s(s(s(s(s(z))))))) = z) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.52/1.78 inference(symmetry,[status(thm)],[3963])).
% 1.52/1.78 tff(3965,plain,
% 1.52/1.78 ((~(s(s(s(s(s(s(s(z))))))) = z)) <=> (~(s(s(s(s(s(s(s(z))))))) = elem!1))),
% 1.52/1.78 inference(monotonicity,[status(thm)],[3964])).
% 1.52/1.78 tff(3966,plain,
% 1.52/1.78 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.52/1.78 inference(modus_ponens,[status(thm)],[747, 3965])).
% 1.52/1.78 tff(3967,plain,
% 1.52/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 1.52/1.78 inference(rewrite,[status(thm)],[])).
% 1.52/1.78 tff(3968,plain,
% 1.52/1.78 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 1.52/1.79 inference(rewrite,[status(thm)],[])).
% 1.52/1.79 tff(3969,plain,
% 1.52/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))))),
% 1.52/1.79 inference(monotonicity,[status(thm)],[3968])).
% 1.52/1.79 tff(3970,plain,
% 1.52/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 1.52/1.79 inference(transitivity,[status(thm)],[3969, 3967])).
% 1.52/1.79 tff(3971,plain,
% 1.52/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 1.52/1.79 inference(quant_inst,[status(thm)],[])).
% 1.52/1.79 tff(3972,plain,
% 1.52/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))),
% 1.52/1.79 inference(modus_ponens,[status(thm)],[3971, 3970])).
% 1.52/1.79 tff(3973,plain,
% 1.52/1.79 (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[3972, 75, 286, 287, 1168, 922])).
% 1.52/1.79 tff(3974,plain,
% 1.52/1.79 (~(s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[862, 3522])).
% 1.52/1.79 tff(3975,plain,
% 1.52/1.79 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[3083, 58, 3974, 3973])).
% 1.52/1.79 tff(3976,plain,
% 1.52/1.79 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.52/1.79 inference(symmetry,[status(thm)],[3463])).
% 1.52/1.79 tff(3977,plain,
% 1.52/1.79 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[3944, 75, 286, 287, 922])).
% 1.52/1.79 tff(3978,plain,
% 1.52/1.79 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.52/1.79 inference(modus_ponens,[status(thm)],[3977, 3834])).
% 1.52/1.79 tff(3979,plain,
% 1.52/1.79 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[575, 3978])).
% 1.52/1.79 tff(3980,plain,
% 1.52/1.79 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.52/1.79 inference(modus_ponens,[status(thm)],[3979, 3976])).
% 1.52/1.79 tff(3981,plain,
% 1.52/1.79 (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))),
% 1.52/1.79 inference(transitivity,[status(thm)],[714, 1125, 250, 3417])).
% 1.52/1.79 tff(3982,plain,
% 1.52/1.79 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(s(elem!1))))),
% 1.52/1.79 inference(monotonicity,[status(thm)],[3981])).
% 1.52/1.79 tff(3983,plain,
% 1.52/1.79 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.52/1.79 inference(symmetry,[status(thm)],[3982])).
% 1.52/1.79 tff(3984,plain,
% 1.52/1.79 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 1.52/1.79 inference(transitivity,[status(thm)],[1609, 3983, 730])).
% 1.52/1.79 tff(3985,plain,
% 1.52/1.79 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(z))))))),
% 1.52/1.79 inference(monotonicity,[status(thm)],[3984])).
% 1.52/1.79 tff(3986,plain,
% 1.52/1.79 (s(z) = s(s(s(s(z))))),
% 1.52/1.79 inference(transitivity,[status(thm)],[289, 229, 3985, 832])).
% 1.52/1.79 tff(3987,plain,
% 1.52/1.79 ($false),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[484, 3986])).
% 1.52/1.79 tff(3988,plain,((~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(z)))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.79 tff(3989,plain,
% 1.52/1.79 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(z)))))),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[3988, 288])).
% 1.52/1.79 tff(3990,plain,
% 1.52/1.79 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[1179, 58, 3989, 1175])).
% 1.52/1.79 tff(3991,plain,
% 1.52/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.52/1.79 inference(rewrite,[status(thm)],[])).
% 1.52/1.79 tff(3992,plain,
% 1.52/1.79 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.52/1.79 inference(rewrite,[status(thm)],[])).
% 1.52/1.79 tff(3993,plain,
% 1.52/1.79 (((~![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(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 1.52/1.79 inference(monotonicity,[status(thm)],[3992])).
% 1.52/1.79 tff(3994,plain,
% 1.52/1.79 (((~![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(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.52/1.79 inference(transitivity,[status(thm)],[3993, 3991])).
% 1.52/1.79 tff(3995,plain,
% 1.52/1.79 ((~![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(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 1.52/1.79 inference(quant_inst,[status(thm)],[])).
% 1.52/1.79 tff(3996,plain,
% 1.52/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 1.52/1.79 inference(modus_ponens,[status(thm)],[3995, 3994])).
% 1.52/1.79 tff(3997,plain,
% 1.52/1.79 ($false),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[3996, 37, 3990, 3980, 3975])).
% 1.52/1.79 tff(3998,plain,((~b(elem!1, s(s(s(s(z)))))) | (~(z = elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.79 tff(3999,plain,
% 1.52/1.79 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[3998, 3938, 3838, 288, 3837])).
% 1.52/1.79 tff(4000,plain,
% 1.52/1.79 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[813, 3999, 3966])).
% 1.52/1.79 tff(4001,plain,
% 1.52/1.79 (~r(s(elem!1), elem!1)),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[3071, 4000, 3961, 3959, 3841, 3954, 3948])).
% 1.52/1.79 tff(4002,plain,
% 1.52/1.79 (r(s(z), elem!1) <=> r(s(elem!1), elem!1)),
% 1.52/1.79 inference(monotonicity,[status(thm)],[289])).
% 1.52/1.79 tff(4003,plain,
% 1.52/1.79 (r(s(elem!1), elem!1)),
% 1.52/1.79 inference(modus_ponens,[status(thm)],[588, 4002])).
% 1.52/1.79 tff(4004,plain,
% 1.52/1.79 ($false),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[1974, 4003])).
% 1.52/1.79 tff(4005,plain,((~r(s(z), elem!1)) | r(s(elem!1), elem!1) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.79 tff(4006,plain,
% 1.52/1.79 (~r(s(z), elem!1)),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[4005, 4001, 288])).
% 1.52/1.79 tff(4007,plain,
% 1.52/1.79 (b(s(z), elem!1)),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[601, 4006, 108])).
% 1.52/1.79 tff(4008,plain,
% 1.52/1.79 (~b(s(z), s(s(s(s(z)))))),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[586, 4007, 3938, 3838])).
% 1.52/1.79 tff(4009,plain,
% 1.52/1.79 (r(s(z), s(s(s(s(z)))))),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[489, 4008])).
% 1.52/1.79 tff(4010,plain,
% 1.52/1.79 (~r(s(z), s(s(s(z))))),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[1316, 4009, 3947])).
% 1.52/1.79 tff(4011,plain,
% 1.52/1.79 (b(s(z), s(s(s(z))))),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[1263, 4010])).
% 1.52/1.79 tff(4012,plain,
% 1.52/1.79 (b(s(elem!1), s(s(s(elem!1))))),
% 1.52/1.79 inference(modus_ponens,[status(thm)],[4011, 3831])).
% 1.52/1.79 tff(4013,plain,
% 1.52/1.79 (b(s(elem!1), elem!1)),
% 1.52/1.79 inference(modus_ponens,[status(thm)],[4007, 3568])).
% 1.52/1.79 tff(4014,plain,
% 1.52/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.52/1.79 inference(rewrite,[status(thm)],[])).
% 1.52/1.79 tff(4015,plain,
% 1.52/1.79 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.52/1.79 inference(rewrite,[status(thm)],[])).
% 1.52/1.79 tff(4016,plain,
% 1.52/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~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(X1, 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(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1))))),
% 1.52/1.79 inference(monotonicity,[status(thm)],[4015])).
% 1.52/1.79 tff(4017,plain,
% 1.52/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~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(X1, 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(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.52/1.79 inference(transitivity,[status(thm)],[4016, 4014])).
% 1.52/1.79 tff(4018,plain,
% 1.52/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.52/1.79 inference(quant_inst,[status(thm)],[])).
% 1.52/1.79 tff(4019,plain,
% 1.52/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1))),
% 1.52/1.79 inference(modus_ponens,[status(thm)],[4018, 4017])).
% 1.52/1.79 tff(4020,plain,
% 1.52/1.79 ($false),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[4019, 75, 3938, 3838, 4013, 3837, 4012])).
% 1.52/1.79 tff(4021,plain,((~(z = elem!1)) | (s(z) = elem!1) | (s(s(elem!1)) = s(s(s(s(z))))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(z))) | r(s(s(s(s(z)))), elem!1) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.79 tff(4022,plain,
% 1.52/1.79 (~(z = elem!1)),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[4021, 105, 1426, 98, 90, 12, 3829])).
% 1.52/1.79 tff(4023,plain,
% 1.52/1.79 (~(elem!1 = z)),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[304, 4022])).
% 1.52/1.79 tff(4024,plain,
% 1.52/1.79 (b(elem!1, z)),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[387, 4023, 3830])).
% 1.52/1.79 tff(4025,plain,
% 1.52/1.79 (b(z, elem!1)),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[298, 4022, 13])).
% 1.52/1.79 tff(4026,plain,
% 1.52/1.79 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)))),
% 1.52/1.79 inference(rewrite,[status(thm)],[])).
% 1.52/1.79 tff(4027,plain,
% 1.52/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z))))),
% 1.52/1.79 inference(monotonicity,[status(thm)],[4026])).
% 1.52/1.79 tff(4028,plain,
% 1.52/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)))),
% 1.52/1.79 inference(transitivity,[status(thm)],[4027, 2756])).
% 1.52/1.79 tff(4029,plain,
% 1.52/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))),
% 1.52/1.79 inference(quant_inst,[status(thm)],[])).
% 1.52/1.79 tff(4030,plain,
% 1.52/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z))),
% 1.52/1.79 inference(modus_ponens,[status(thm)],[4029, 4028])).
% 1.52/1.79 tff(4031,plain,
% 1.52/1.79 (~b(s(s(s(z))), z)),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[4030, 75, 4025, 4024, 3829])).
% 1.52/1.79 tff(4032,plain,
% 1.52/1.79 (r(s(s(s(z))), z)),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[1334, 58, 221, 4031])).
% 1.52/1.79 tff(4033,plain,
% 1.52/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.52/1.79 inference(rewrite,[status(thm)],[])).
% 1.52/1.79 tff(4034,plain,
% 1.52/1.79 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.52/1.79 inference(rewrite,[status(thm)],[])).
% 1.52/1.79 tff(4035,plain,
% 1.52/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))))),
% 1.52/1.79 inference(monotonicity,[status(thm)],[4034])).
% 1.52/1.79 tff(4036,plain,
% 1.52/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.52/1.79 inference(transitivity,[status(thm)],[4035, 4033])).
% 1.52/1.79 tff(4037,plain,
% 1.52/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.52/1.79 inference(quant_inst,[status(thm)],[])).
% 1.52/1.79 tff(4038,plain,
% 1.52/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))),
% 1.52/1.79 inference(modus_ponens,[status(thm)],[4037, 4036])).
% 1.52/1.79 tff(4039,plain,
% 1.52/1.79 ($false),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[4038, 37, 2899, 2870, 2886])).
% 1.52/1.79 tff(4040,plain,((~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.79 tff(4041,plain,
% 1.52/1.79 (~b(s(s(s(s(z)))), elem!1)),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[4040, 4025, 4024, 3829])).
% 1.52/1.79 tff(4042,plain,
% 1.52/1.79 (s(s(s(s(z)))) = elem!1),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[283, 4041, 12])).
% 1.52/1.79 tff(4043,plain,
% 1.52/1.79 (~(s(s(elem!1)) = s(s(z)))),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[237, 4022])).
% 1.52/1.79 tff(4044,plain,
% 1.52/1.79 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[3307, 4043])).
% 1.52/1.79 tff(4045,plain,
% 1.52/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.52/1.80 inference(rewrite,[status(thm)],[])).
% 1.52/1.80 tff(4046,plain,
% 1.52/1.80 (((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.52/1.80 inference(rewrite,[status(thm)],[])).
% 1.52/1.80 tff(4047,plain,
% 1.52/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 1.52/1.80 inference(monotonicity,[status(thm)],[4046])).
% 1.52/1.80 tff(4048,plain,
% 1.52/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.62/1.80 inference(transitivity,[status(thm)],[4047, 4045])).
% 1.62/1.80 tff(4049,plain,
% 1.62/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.62/1.80 inference(quant_inst,[status(thm)],[])).
% 1.62/1.80 tff(4050,plain,
% 1.62/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 1.62/1.80 inference(modus_ponens,[status(thm)],[4049, 4048])).
% 1.62/1.80 tff(4051,plain,
% 1.62/1.80 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[4050, 75, 1518, 1958, 1119, 922])).
% 1.62/1.80 tff(4052,plain,
% 1.62/1.80 (r(s(s(s(elem!1))), s(s(s(z))))),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[3327, 58, 3324, 4051])).
% 1.62/1.80 tff(4053,plain,
% 1.62/1.80 (~b(s(s(s(elem!1))), z)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[3379, 75, 1518, 1958, 922])).
% 1.62/1.80 tff(4054,plain,
% 1.62/1.80 (r(s(s(s(elem!1))), z)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[948, 58, 662, 4053])).
% 1.62/1.80 tff(4055,plain,
% 1.62/1.80 (~b(s(s(s(z))), z)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[4030, 75, 1518, 1958, 1119])).
% 1.62/1.80 tff(4056,plain,
% 1.62/1.80 (r(s(s(s(z))), z)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[1334, 58, 221, 4055])).
% 1.62/1.80 tff(4057,plain,
% 1.62/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.62/1.80 inference(rewrite,[status(thm)],[])).
% 1.62/1.80 tff(4058,plain,
% 1.62/1.80 (((~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.62/1.80 inference(rewrite,[status(thm)],[])).
% 1.62/1.80 tff(4059,plain,
% 1.62/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 1.62/1.80 inference(monotonicity,[status(thm)],[4058])).
% 1.62/1.80 tff(4060,plain,
% 1.62/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.62/1.80 inference(transitivity,[status(thm)],[4059, 4057])).
% 1.62/1.80 tff(4061,plain,
% 1.62/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.62/1.80 inference(quant_inst,[status(thm)],[])).
% 1.62/1.80 tff(4062,plain,
% 1.62/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 1.62/1.80 inference(modus_ponens,[status(thm)],[4061, 4060])).
% 1.62/1.80 tff(4063,plain,
% 1.62/1.80 ($false),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[4062, 37, 4056, 4054, 4052])).
% 1.62/1.80 tff(4064,plain,((~b(s(s(s(elem!1))), elem!1)) | (s(s(s(elem!1))) = s(s(s(z)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.80 tff(4065,plain,
% 1.62/1.80 (~b(s(s(s(elem!1))), elem!1)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[4064, 4044, 4025, 4024, 3829])).
% 1.62/1.80 tff(4066,plain,
% 1.62/1.80 (s(s(s(s(s(z))))) = s(elem!1)),
% 1.62/1.80 inference(monotonicity,[status(thm)],[4042])).
% 1.62/1.80 tff(4067,plain,
% 1.62/1.80 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 1.62/1.80 inference(monotonicity,[status(thm)],[4066])).
% 1.62/1.80 tff(4068,plain,
% 1.62/1.80 (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))),
% 1.62/1.80 inference(monotonicity,[status(thm)],[4067])).
% 1.62/1.80 tff(4069,plain,
% 1.62/1.80 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 1.62/1.80 inference(symmetry,[status(thm)],[4068])).
% 1.62/1.80 tff(4070,plain,
% 1.62/1.80 ((elem!1 = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 1.62/1.80 inference(monotonicity,[status(thm)],[4069])).
% 1.62/1.80 tff(4071,plain,
% 1.62/1.80 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.62/1.80 inference(transitivity,[status(thm)],[4070, 3278])).
% 1.62/1.80 tff(4072,plain,
% 1.62/1.80 ((s(s(s(s(s(s(s(z))))))) = elem!1) <=> (elem!1 = s(s(s(elem!1))))),
% 1.62/1.80 inference(symmetry,[status(thm)],[4071])).
% 1.62/1.80 tff(4073,plain,
% 1.62/1.80 ((s(s(s(s(s(s(s(z))))))) = elem!1) <=> (s(s(s(elem!1))) = elem!1)),
% 1.62/1.80 inference(transitivity,[status(thm)],[4072, 3277])).
% 1.62/1.80 tff(4074,plain,
% 1.62/1.80 ((~(s(s(s(s(s(s(s(z))))))) = elem!1)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.62/1.80 inference(monotonicity,[status(thm)],[4073])).
% 1.62/1.80 tff(4075,plain,
% 1.62/1.80 (~(s(s(z)) = s(elem!1))),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[3261, 98])).
% 1.62/1.80 tff(4076,plain,
% 1.62/1.80 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[3298, 4042, 4075])).
% 1.62/1.80 tff(4077,plain,
% 1.62/1.80 (~(s(s(s(elem!1))) = elem!1)),
% 1.62/1.80 inference(modus_ponens,[status(thm)],[4076, 4074])).
% 1.62/1.80 tff(4078,plain,
% 1.62/1.80 (r(s(s(s(elem!1))), elem!1)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[3370, 4077, 4065])).
% 1.62/1.80 tff(4079,plain,
% 1.62/1.80 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(z)))),
% 1.62/1.80 inference(monotonicity,[status(thm)],[3311])).
% 1.62/1.80 tff(4080,plain,
% 1.62/1.80 ((s(s(s(s(s(s(s(z))))))) = s(s(z))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 1.62/1.80 inference(symmetry,[status(thm)],[4079])).
% 1.62/1.80 tff(4081,plain,
% 1.62/1.80 ((~(s(s(s(s(s(s(s(z))))))) = s(s(z)))) <=> (~(s(s(s(elem!1))) = s(s(z))))),
% 1.62/1.80 inference(monotonicity,[status(thm)],[4080])).
% 1.62/1.80 tff(4082,plain,
% 1.62/1.80 (~(s(s(s(elem!1))) = s(s(z)))),
% 1.62/1.80 inference(modus_ponens,[status(thm)],[1045, 4081])).
% 1.62/1.80 tff(4083,plain,
% 1.62/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.62/1.80 inference(rewrite,[status(thm)],[])).
% 1.62/1.80 tff(4084,plain,
% 1.62/1.80 (((~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), s(s(z))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.62/1.80 inference(rewrite,[status(thm)],[])).
% 1.62/1.80 tff(4085,plain,
% 1.62/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 1.62/1.80 inference(monotonicity,[status(thm)],[4084])).
% 1.62/1.80 tff(4086,plain,
% 1.62/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.62/1.80 inference(transitivity,[status(thm)],[4085, 4083])).
% 1.62/1.80 tff(4087,plain,
% 1.62/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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)))))),
% 1.62/1.80 inference(quant_inst,[status(thm)],[])).
% 1.62/1.80 tff(4088,plain,
% 1.62/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), s(s(z))))),
% 1.62/1.80 inference(modus_ponens,[status(thm)],[4087, 4086])).
% 1.62/1.80 tff(4089,plain,
% 1.62/1.80 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[4088, 37, 106, 624])).
% 1.62/1.80 tff(4090,plain,
% 1.62/1.80 (((~![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))))),
% 1.62/1.80 inference(rewrite,[status(thm)],[])).
% 1.62/1.80 tff(4091,plain,
% 1.62/1.80 ((~![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))))),
% 1.62/1.80 inference(quant_inst,[status(thm)],[])).
% 1.62/1.80 tff(4092,plain,
% 1.62/1.80 ((~![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)))),
% 1.62/1.80 inference(modus_ponens,[status(thm)],[4091, 4090])).
% 1.62/1.80 tff(4093,plain,
% 1.62/1.80 ((s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z)))),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[4092, 58, 4089])).
% 1.62/1.80 tff(4094,plain,
% 1.62/1.80 (b(s(s(s(elem!1))), s(s(z)))),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[4093, 4082])).
% 1.62/1.80 tff(4095,plain,
% 1.62/1.80 ((s(s(s(elem!1))) = s(z)) <=> (s(s(s(s(s(s(s(z))))))) = s(z))),
% 1.62/1.80 inference(monotonicity,[status(thm)],[3311])).
% 1.62/1.80 tff(4096,plain,
% 1.62/1.80 ((s(s(s(s(s(s(s(z))))))) = s(z)) <=> (s(s(s(elem!1))) = s(z))),
% 1.62/1.80 inference(symmetry,[status(thm)],[4095])).
% 1.62/1.80 tff(4097,plain,
% 1.62/1.80 ((~(s(s(s(s(s(s(s(z))))))) = s(z))) <=> (~(s(s(s(elem!1))) = s(z)))),
% 1.62/1.80 inference(monotonicity,[status(thm)],[4096])).
% 1.62/1.80 tff(4098,plain,
% 1.62/1.80 (~(s(s(s(elem!1))) = s(z))),
% 1.62/1.80 inference(modus_ponens,[status(thm)],[1227, 4097])).
% 1.62/1.80 tff(4099,plain,
% 1.62/1.80 (((~![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(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(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))))),
% 1.62/1.80 inference(rewrite,[status(thm)],[])).
% 1.62/1.80 tff(4100,plain,
% 1.62/1.80 (((~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))))),
% 1.62/1.80 inference(rewrite,[status(thm)],[])).
% 1.62/1.80 tff(4101,plain,
% 1.62/1.80 (((~![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(elem!1))), elem!1)) | (~r(s(z), 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), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z)))))),
% 1.62/1.80 inference(monotonicity,[status(thm)],[4100])).
% 1.62/1.80 tff(4102,plain,
% 1.62/1.80 (((~![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(elem!1))), elem!1)) | (~r(s(z), 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), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))))),
% 1.62/1.80 inference(transitivity,[status(thm)],[4101, 4099])).
% 1.62/1.80 tff(4103,plain,
% 1.62/1.80 ((~![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(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))))),
% 1.62/1.80 inference(quant_inst,[status(thm)],[])).
% 1.62/1.80 tff(4104,plain,
% 1.62/1.80 ((~![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(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z)))),
% 1.62/1.80 inference(modus_ponens,[status(thm)],[4103, 4102])).
% 1.62/1.80 tff(4105,plain,
% 1.62/1.80 (~r(s(s(s(elem!1))), s(z))),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[4104, 37, 588, 624])).
% 1.62/1.80 tff(4106,plain,
% 1.62/1.80 ((s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z))),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[3400, 58, 4105])).
% 1.62/1.80 tff(4107,plain,
% 1.62/1.80 (b(s(s(s(elem!1))), s(z))),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[4106, 4098])).
% 1.62/1.80 tff(4108,assumption,(~r(s(s(z)), s(s(s(elem!1))))), introduced(assumption)).
% 1.62/1.80 tff(4109,plain,
% 1.62/1.80 ((s(s(z)) = s(s(s(elem!1)))) | b(s(s(z)), s(s(s(elem!1))))),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[3360, 58, 4108])).
% 1.62/1.80 tff(4110,plain,
% 1.62/1.80 (b(s(s(z)), s(s(s(elem!1))))),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[4109, 3316])).
% 1.62/1.80 tff(4111,plain,
% 1.62/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), 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(X1, 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(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.62/1.80 inference(rewrite,[status(thm)],[])).
% 1.62/1.80 tff(4112,plain,
% 1.62/1.80 (((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.62/1.80 inference(rewrite,[status(thm)],[])).
% 1.62/1.80 tff(4113,plain,
% 1.62/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 1.62/1.80 inference(monotonicity,[status(thm)],[4112])).
% 1.62/1.80 tff(4114,plain,
% 1.62/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.62/1.80 inference(transitivity,[status(thm)],[4113, 4111])).
% 1.62/1.80 tff(4115,plain,
% 1.62/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.62/1.80 inference(quant_inst,[status(thm)],[])).
% 1.62/1.80 tff(4116,plain,
% 1.62/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 1.62/1.80 inference(modus_ponens,[status(thm)],[4115, 4114])).
% 1.62/1.80 tff(4117,plain,
% 1.62/1.80 ($false),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[4116, 75, 2644, 4110, 4107, 4094])).
% 1.62/1.80 tff(4118,plain,(r(s(s(z)), s(s(s(elem!1)))) | (~(s(s(s(s(z)))) = elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.80 tff(4119,plain,
% 1.62/1.80 (r(s(s(z)), s(s(s(elem!1))))),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[4118, 624, 106, 3285, 588])).
% 1.62/1.80 tff(4120,plain,
% 1.62/1.80 ($false),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[3356, 37, 106, 624, 4119])).
% 1.62/1.80 tff(4121,plain,((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~(s(s(s(s(z)))) = elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.80 tff(4122,plain,
% 1.62/1.80 (~r(s(z), elem!1)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[4121, 4078, 4042, 105])).
% 1.62/1.80 tff(4123,plain,
% 1.62/1.80 (b(s(z), elem!1)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[601, 4122, 98])).
% 1.62/1.80 tff(4124,plain,
% 1.62/1.80 (~b(s(z), z)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[2625, 4123, 13, 3830, 4022])).
% 1.62/1.81 tff(4125,plain,
% 1.62/1.81 (r(s(z), z)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[169, 4124])).
% 1.62/1.81 tff(4126,plain,
% 1.62/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(4127,plain,
% 1.62/1.81 (((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(4128,plain,
% 1.62/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z))))),
% 1.62/1.81 inference(monotonicity,[status(thm)],[4127])).
% 1.62/1.81 tff(4129,plain,
% 1.62/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 1.62/1.81 inference(transitivity,[status(thm)],[4128, 4126])).
% 1.62/1.81 tff(4130,plain,
% 1.62/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))),
% 1.62/1.81 inference(quant_inst,[status(thm)],[])).
% 1.62/1.81 tff(4131,plain,
% 1.62/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z))),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[4130, 4129])).
% 1.62/1.81 tff(4132,plain,
% 1.62/1.81 (~r(s(s(s(z))), s(z))),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[4131, 37, 4125, 4032])).
% 1.62/1.81 tff(4133,plain,
% 1.62/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(z))))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(4134,plain,
% 1.62/1.81 (((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(z))))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(4135,plain,
% 1.62/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))), elem!1)) | (~b(elem!1, 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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(z)))))),
% 1.62/1.81 inference(monotonicity,[status(thm)],[4134])).
% 1.62/1.81 tff(4136,plain,
% 1.62/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))), elem!1)) | (~b(elem!1, 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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(z))))),
% 1.62/1.81 inference(transitivity,[status(thm)],[4135, 4133])).
% 1.62/1.81 tff(4137,plain,
% 1.62/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 1.62/1.81 inference(quant_inst,[status(thm)],[])).
% 1.62/1.81 tff(4138,plain,
% 1.62/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), s(z)))),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[4137, 4136])).
% 1.62/1.81 tff(4139,plain,
% 1.62/1.81 (~b(s(s(s(z))), s(z))),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[4138, 75, 4025, 4024, 4123, 3829])).
% 1.62/1.81 tff(4140,plain,
% 1.62/1.81 ($false),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[1081, 4139, 4132])).
% 1.62/1.81 tff(4141,plain,(b(s(s(z)), elem!1) | r(z, elem!1) | r(s(s(s(s(z)))), elem!1) | b(elem!1, s(z)) | (s(s(s(z))) = s(s(elem!1))) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.62/1.81 tff(4142,plain,
% 1.62/1.81 (b(s(s(z)), elem!1)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[4141, 16, 12, 14, 13, 15])).
% 1.62/1.81 tff(4143,plain,
% 1.62/1.81 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 1.62/1.81 inference(monotonicity,[status(thm)],[288])).
% 1.62/1.81 tff(4144,plain,
% 1.62/1.81 ((~(s(s(s(z))) = z)) <=> (~(s(s(s(z))) = elem!1))),
% 1.62/1.81 inference(monotonicity,[status(thm)],[4143])).
% 1.62/1.81 tff(4145,plain,
% 1.62/1.81 (~(s(s(s(z))) = elem!1)),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[221, 4144])).
% 1.62/1.81 tff(4146,plain,
% 1.62/1.81 (b(s(s(elem!1)), elem!1)),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[964, 3648])).
% 1.62/1.81 tff(4147,plain,
% 1.62/1.81 (b(s(z), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.62/1.81 inference(monotonicity,[status(thm)],[289])).
% 1.62/1.81 tff(4148,plain,
% 1.62/1.81 (~r(elem!1, s(s(s(s(z)))))),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[3255, 1061, 114])).
% 1.62/1.81 tff(4149,plain,
% 1.62/1.81 (b(elem!1, s(s(s(s(z)))))),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[278, 4148, 3522])).
% 1.62/1.81 tff(4150,plain,
% 1.62/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(4151,plain,
% 1.62/1.81 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(4152,plain,
% 1.62/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.62/1.81 inference(monotonicity,[status(thm)],[4151])).
% 1.62/1.81 tff(4153,plain,
% 1.62/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.62/1.81 inference(transitivity,[status(thm)],[4152, 4150])).
% 1.62/1.81 tff(4154,plain,
% 1.62/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.62/1.81 inference(quant_inst,[status(thm)],[])).
% 1.62/1.81 tff(4155,plain,
% 1.62/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[4154, 4153])).
% 1.62/1.81 tff(4156,plain,
% 1.62/1.81 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[4155, 75, 4149, 287, 707])).
% 1.62/1.81 tff(4157,plain,
% 1.62/1.81 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[1660, 4156, 1011])).
% 1.62/1.81 tff(4158,plain,
% 1.62/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(4159,plain,
% 1.62/1.81 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(4160,plain,
% 1.62/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 1.62/1.81 inference(monotonicity,[status(thm)],[4159])).
% 1.62/1.81 tff(4161,plain,
% 1.62/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.62/1.81 inference(transitivity,[status(thm)],[4160, 4158])).
% 1.62/1.81 tff(4162,plain,
% 1.62/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.81 inference(quant_inst,[status(thm)],[])).
% 1.62/1.81 tff(4163,plain,
% 1.62/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[4162, 4161])).
% 1.62/1.81 tff(4164,plain,
% 1.62/1.81 (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[4163, 75, 286, 287, 1168, 707])).
% 1.62/1.81 tff(4165,plain,
% 1.62/1.81 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[840, 58, 3067, 4164])).
% 1.62/1.81 tff(4166,plain,
% 1.62/1.81 (((~![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)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(4167,plain,
% 1.62/1.81 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(4168,plain,
% 1.62/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(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(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 1.62/1.81 inference(monotonicity,[status(thm)],[4167])).
% 1.62/1.81 tff(4169,plain,
% 1.62/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(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(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.62/1.81 inference(transitivity,[status(thm)],[4168, 4166])).
% 1.62/1.81 tff(4170,plain,
% 1.62/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.81 inference(quant_inst,[status(thm)],[])).
% 1.62/1.81 tff(4171,plain,
% 1.62/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[4170, 4169])).
% 1.62/1.81 tff(4172,plain,
% 1.62/1.81 ($false),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[4171, 37, 1647, 1180, 4165])).
% 1.62/1.81 tff(4173,plain,((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.81 tff(4174,plain,
% 1.62/1.81 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[4173, 4157, 3959, 3989, 4149, 287, 707])).
% 1.62/1.81 tff(4175,plain,
% 1.62/1.81 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[813, 4174, 3966])).
% 1.62/1.81 tff(4176,plain,
% 1.62/1.81 (r(s(s(s(z))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 1.62/1.81 inference(monotonicity,[status(thm)],[3417])).
% 1.62/1.81 tff(4177,plain,
% 1.62/1.81 (r(s(s(s(elem!1))), elem!1)),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[1061, 4176])).
% 1.62/1.81 tff(4178,plain,
% 1.62/1.81 (((~![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(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(s(z))))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(4179,plain,
% 1.62/1.81 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(4180,plain,
% 1.62/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(s(z))))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))))),
% 1.62/1.81 inference(monotonicity,[status(thm)],[4179])).
% 1.62/1.81 tff(4181,plain,
% 1.62/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(s(z))))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.82 inference(transitivity,[status(thm)],[4180, 4178])).
% 1.62/1.82 tff(4182,plain,
% 1.62/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 1.62/1.82 inference(quant_inst,[status(thm)],[])).
% 1.62/1.82 tff(4183,plain,
% 1.62/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))),
% 1.62/1.82 inference(modus_ponens,[status(thm)],[4182, 4181])).
% 1.62/1.82 tff(4184,plain,
% 1.62/1.82 (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[4183, 37, 4175, 4177])).
% 1.62/1.82 tff(4185,plain,
% 1.62/1.82 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[3083, 58, 3974, 4184])).
% 1.62/1.82 tff(4186,plain,
% 1.62/1.82 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(z))), s(z))),
% 1.62/1.82 inference(monotonicity,[status(thm)],[3418, 3422])).
% 1.62/1.82 tff(4187,plain,
% 1.62/1.82 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.62/1.82 inference(symmetry,[status(thm)],[4186])).
% 1.62/1.82 tff(4188,plain,
% 1.62/1.82 (b(s(s(s(elem!1))), s(elem!1))),
% 1.62/1.82 inference(modus_ponens,[status(thm)],[1082, 4187])).
% 1.62/1.82 tff(4189,assumption,(b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.62/1.82 tff(4190,assumption,(b(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 1.62/1.82 tff(4191,plain,
% 1.62/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.62/1.82 inference(rewrite,[status(thm)],[])).
% 1.62/1.82 tff(4192,plain,
% 1.62/1.82 (((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.62/1.82 inference(rewrite,[status(thm)],[])).
% 1.62/1.82 tff(4193,plain,
% 1.62/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 1.62/1.82 inference(monotonicity,[status(thm)],[4192])).
% 1.62/1.82 tff(4194,plain,
% 1.62/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.62/1.82 inference(transitivity,[status(thm)],[4193, 4191])).
% 1.62/1.82 tff(4195,plain,
% 1.62/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.62/1.82 inference(quant_inst,[status(thm)],[])).
% 1.62/1.82 tff(4196,plain,
% 1.62/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 1.62/1.82 inference(modus_ponens,[status(thm)],[4195, 4194])).
% 1.62/1.82 tff(4197,plain,
% 1.62/1.82 ($false),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[4196, 75, 794, 4190, 4189, 3065])).
% 1.62/1.82 tff(4198,plain,((~r(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.82 tff(4199,plain,
% 1.62/1.82 (~r(s(elem!1), elem!1)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[4198, 4188, 4185, 3961, 3954, 4175])).
% 1.62/1.82 tff(4200,plain,
% 1.62/1.82 (~r(s(z), elem!1)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[4005, 4199, 288])).
% 1.62/1.82 tff(4201,plain,
% 1.62/1.82 (b(s(z), elem!1)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[601, 4200, 108])).
% 1.62/1.82 tff(4202,plain,
% 1.62/1.82 (r(elem!1, s(s(elem!1)))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[3606, 4201, 288, 114, 4145, 1061])).
% 1.62/1.82 tff(4203,plain,
% 1.62/1.82 (~r(s(z), s(s(elem!1)))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[3615, 4202, 114])).
% 1.62/1.82 tff(4204,plain,
% 1.62/1.82 (b(s(z), s(s(elem!1)))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[1890, 4203])).
% 1.62/1.82 tff(4205,plain,
% 1.62/1.82 (b(s(elem!1), s(s(elem!1)))),
% 1.62/1.82 inference(modus_ponens,[status(thm)],[4204, 4147])).
% 1.62/1.82 tff(4206,plain,
% 1.62/1.82 (b(s(elem!1), elem!1)),
% 1.62/1.82 inference(modus_ponens,[status(thm)],[4201, 3568])).
% 1.62/1.82 tff(4207,plain,
% 1.62/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), 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(X1, 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(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.62/1.82 inference(rewrite,[status(thm)],[])).
% 1.62/1.82 tff(4208,plain,
% 1.62/1.82 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.62/1.82 inference(rewrite,[status(thm)],[])).
% 1.62/1.82 tff(4209,plain,
% 1.62/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1))))))),
% 1.62/1.82 inference(monotonicity,[status(thm)],[4208])).
% 1.62/1.82 tff(4210,plain,
% 1.62/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.62/1.82 inference(transitivity,[status(thm)],[4209, 4207])).
% 1.62/1.82 tff(4211,plain,
% 1.62/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.62/1.82 inference(quant_inst,[status(thm)],[])).
% 1.62/1.82 tff(4212,plain,
% 1.62/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1))))),
% 1.62/1.82 inference(modus_ponens,[status(thm)],[4211, 4210])).
% 1.62/1.82 tff(4213,plain,
% 1.62/1.82 ($false),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[4212, 75, 4149, 287, 4206, 4205, 707])).
% 1.62/1.82 tff(4214,plain,((~r(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~(z = elem!1)) | (~r(elem!1, s(z))) | (s(z) = elem!1) | (s(s(elem!1)) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.82 tff(4215,plain,
% 1.62/1.82 (~r(s(s(s(z))), elem!1)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[4214, 3838, 4146, 288, 114, 108, 1011])).
% 1.62/1.82 tff(4216,plain,
% 1.62/1.82 (b(s(s(s(z))), elem!1)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[1115, 4215, 4145])).
% 1.62/1.82 tff(4217,plain,
% 1.62/1.82 (b(s(s(s(elem!1))), elem!1)),
% 1.62/1.82 inference(modus_ponens,[status(thm)],[4216, 3836])).
% 1.62/1.82 tff(4218,plain,
% 1.62/1.82 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[4155, 75, 286, 287, 707])).
% 1.62/1.82 tff(4219,plain,
% 1.62/1.82 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[1660, 4218, 1011])).
% 1.62/1.82 tff(4220,plain,
% 1.62/1.82 ((s(s(z)) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 1.62/1.82 inference(monotonicity,[status(thm)],[290])).
% 1.62/1.82 tff(4221,plain,
% 1.62/1.82 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(z)))))),
% 1.62/1.82 inference(monotonicity,[status(thm)],[4220])).
% 1.62/1.82 tff(4222,plain,
% 1.62/1.82 (~(s(s(elem!1)) = s(s(s(z))))),
% 1.62/1.82 inference(modus_ponens,[status(thm)],[1556, 4221])).
% 1.62/1.82 tff(4223,plain,
% 1.62/1.82 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.62/1.82 inference(monotonicity,[status(thm)],[3418])).
% 1.62/1.82 tff(4224,plain,
% 1.62/1.82 ((~b(s(s(elem!1)), s(s(s(elem!1))))) <=> (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.62/1.82 inference(monotonicity,[status(thm)],[4223])).
% 1.62/1.82 tff(4225,plain,
% 1.62/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(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(X1, 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(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.62/1.82 inference(rewrite,[status(thm)],[])).
% 1.62/1.82 tff(4226,plain,
% 1.62/1.82 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~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(elem!1, s(s(s(s(z)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.62/1.82 inference(rewrite,[status(thm)],[])).
% 1.62/1.82 tff(4227,plain,
% 1.62/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~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(X1, 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(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.62/1.82 inference(monotonicity,[status(thm)],[4226])).
% 1.62/1.82 tff(4228,plain,
% 1.62/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~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(X1, 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(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.62/1.82 inference(transitivity,[status(thm)],[4227, 4225])).
% 1.62/1.82 tff(4229,plain,
% 1.62/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~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))))))),
% 1.62/1.82 inference(quant_inst,[status(thm)],[])).
% 1.62/1.82 tff(4230,plain,
% 1.62/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.62/1.82 inference(modus_ponens,[status(thm)],[4229, 4228])).
% 1.62/1.82 tff(4231,plain,
% 1.62/1.82 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[4230, 75, 286, 287, 707, 922])).
% 1.62/1.82 tff(4232,plain,
% 1.62/1.82 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.62/1.82 inference(modus_ponens,[status(thm)],[4231, 4224])).
% 1.62/1.82 tff(4233,plain,
% 1.62/1.82 (r(s(s(elem!1)), s(s(s(z))))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[1936, 4232, 4222])).
% 1.62/1.82 tff(4234,plain,
% 1.62/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.62/1.82 inference(rewrite,[status(thm)],[])).
% 1.62/1.82 tff(4235,plain,
% 1.62/1.82 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(z)))))) <=> ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.62/1.82 inference(rewrite,[status(thm)],[])).
% 1.62/1.82 tff(4236,plain,
% 1.62/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 1.62/1.82 inference(monotonicity,[status(thm)],[4235])).
% 1.62/1.82 tff(4237,plain,
% 1.62/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.62/1.82 inference(transitivity,[status(thm)],[4236, 4234])).
% 1.62/1.82 tff(4238,plain,
% 1.62/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.62/1.82 inference(quant_inst,[status(thm)],[])).
% 1.62/1.82 tff(4239,plain,
% 1.62/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.62/1.82 inference(modus_ponens,[status(thm)],[4238, 4237])).
% 1.62/1.82 tff(4240,plain,
% 1.62/1.82 ($false),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[4239, 37, 1921, 1647, 1308])).
% 1.62/1.82 tff(4241,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.82 tff(4242,plain,
% 1.62/1.82 ($false),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[4241, 4233, 3979, 4219])).
% 1.62/1.82 tff(4243,plain,((~b(elem!1, s(s(s(s(z)))))) | (~(z = elem!1)) | (s(s(elem!1)) = s(s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.82 tff(4244,plain,
% 1.62/1.82 (~b(elem!1, s(s(s(s(z)))))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[4243, 288, 1011, 3838, 4146, 4217])).
% 1.62/1.82 tff(4245,plain,
% 1.62/1.82 (r(elem!1, s(s(s(s(z)))))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[278, 4244, 3522])).
% 1.62/1.82 tff(4246,plain,
% 1.62/1.82 (~r(s(s(s(s(z)))), s(z))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[3910, 4245, 114])).
% 1.62/1.82 tff(4247,plain,
% 1.62/1.82 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(s(z)))), s(elem!1))),
% 1.62/1.82 inference(monotonicity,[status(thm)],[289])).
% 1.62/1.82 tff(4248,plain,
% 1.62/1.82 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(z))),
% 1.62/1.82 inference(symmetry,[status(thm)],[4247])).
% 1.62/1.82 tff(4249,assumption,(r(s(s(s(s(z)))), s(elem!1))), introduced(assumption)).
% 1.62/1.82 tff(4250,plain,
% 1.62/1.82 (r(s(s(s(s(z)))), s(z))),
% 1.62/1.82 inference(modus_ponens,[status(thm)],[4249, 4248])).
% 1.62/1.82 tff(4251,assumption,(~r(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.62/1.82 tff(4252,plain,
% 1.62/1.82 ($false),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[4251, 4250])).
% 1.62/1.82 tff(4253,plain,((~r(s(s(s(s(z)))), s(elem!1))) | r(s(s(s(s(z)))), s(z)) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.82 tff(4254,plain,
% 1.62/1.82 (~r(s(s(s(s(z)))), s(elem!1))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[4253, 4246, 288])).
% 1.62/1.82 tff(4255,assumption,(s(s(s(s(z)))) = s(elem!1)), introduced(assumption)).
% 1.62/1.82 tff(4256,plain,
% 1.62/1.82 (s(elem!1) = s(s(s(s(z))))),
% 1.62/1.82 inference(symmetry,[status(thm)],[4255])).
% 1.62/1.82 tff(4257,plain,
% 1.62/1.82 (s(z) = s(s(s(s(z))))),
% 1.62/1.82 inference(transitivity,[status(thm)],[289, 4256])).
% 1.62/1.82 tff(4258,plain,
% 1.62/1.82 ($false),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[484, 4257])).
% 1.62/1.82 tff(4259,plain,((~(s(s(s(s(z)))) = s(elem!1))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.82 tff(4260,plain,
% 1.62/1.82 (~(s(s(s(s(z)))) = s(elem!1))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[4259, 288])).
% 1.62/1.82 tff(4261,plain,
% 1.62/1.82 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1)) | r(s(s(s(s(z)))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1)) | r(s(s(s(s(z)))), s(elem!1)))),
% 1.62/1.83 inference(rewrite,[status(thm)],[])).
% 1.62/1.83 tff(4262,plain,
% 1.62/1.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1)) | r(s(s(s(s(z)))), s(elem!1)))),
% 1.62/1.83 inference(quant_inst,[status(thm)],[])).
% 1.62/1.83 tff(4263,plain,
% 1.62/1.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1)) | r(s(s(s(s(z)))), s(elem!1))),
% 1.62/1.83 inference(modus_ponens,[status(thm)],[4262, 4261])).
% 1.62/1.83 tff(4264,plain,
% 1.62/1.83 (b(s(s(s(s(z)))), s(elem!1))),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[4263, 58, 4260, 4254])).
% 1.62/1.83 tff(4265,plain,
% 1.62/1.83 (~r(s(z), s(s(s(s(z)))))),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[3203, 4245, 114])).
% 1.62/1.83 tff(4266,plain,
% 1.62/1.83 (b(s(z), s(s(s(s(z)))))),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[489, 4265])).
% 1.62/1.83 tff(4267,plain,
% 1.62/1.83 (b(s(elem!1), s(s(s(s(z)))))),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[3857, 4266, 288])).
% 1.62/1.83 tff(4268,plain,
% 1.62/1.83 (b(elem!1, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 1.62/1.83 inference(monotonicity,[status(thm)],[290])).
% 1.62/1.83 tff(4269,plain,
% 1.62/1.83 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(z)))),
% 1.62/1.83 inference(symmetry,[status(thm)],[4268])).
% 1.62/1.83 tff(4270,plain,
% 1.62/1.83 (b(s(elem!1), s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 1.62/1.83 inference(symmetry,[status(thm)],[4147])).
% 1.62/1.83 tff(4271,plain,
% 1.62/1.83 ((~b(s(elem!1), s(s(elem!1)))) <=> (~b(s(z), s(s(elem!1))))),
% 1.62/1.83 inference(monotonicity,[status(thm)],[4270])).
% 1.62/1.83 tff(4272,assumption,(b(s(s(s(s(z)))), s(elem!1))), introduced(assumption)).
% 1.62/1.83 tff(4273,plain,
% 1.62/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(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(X1, 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(z)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.62/1.83 inference(rewrite,[status(thm)],[])).
% 1.62/1.83 tff(4274,plain,
% 1.62/1.83 (((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.62/1.83 inference(rewrite,[status(thm)],[])).
% 1.62/1.83 tff(4275,plain,
% 1.62/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 1.62/1.83 inference(monotonicity,[status(thm)],[4274])).
% 1.62/1.83 tff(4276,plain,
% 1.62/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.62/1.83 inference(transitivity,[status(thm)],[4275, 4273])).
% 1.62/1.83 tff(4277,plain,
% 1.62/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.62/1.83 inference(quant_inst,[status(thm)],[])).
% 1.62/1.83 tff(4278,plain,
% 1.62/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 1.62/1.83 inference(modus_ponens,[status(thm)],[4277, 4276])).
% 1.62/1.83 tff(4279,plain,
% 1.62/1.83 ($false),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[4278, 75, 1619, 3581, 3862, 4272])).
% 1.62/1.83 tff(4280,plain,((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.83 tff(4281,plain,
% 1.62/1.83 (~b(s(elem!1), s(s(elem!1)))),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[4280, 1619, 3862, 4272])).
% 1.62/1.83 tff(4282,plain,
% 1.62/1.83 (~b(s(z), s(s(elem!1)))),
% 1.62/1.83 inference(modus_ponens,[status(thm)],[4281, 4271])).
% 1.62/1.83 tff(4283,plain,
% 1.62/1.83 (r(s(z), s(s(elem!1)))),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[1890, 4282])).
% 1.62/1.83 tff(4284,plain,
% 1.62/1.83 (~r(elem!1, s(s(elem!1)))),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[3615, 4283, 114])).
% 1.62/1.83 tff(4285,plain,
% 1.62/1.83 (b(elem!1, s(s(elem!1)))),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[1617, 4284, 3432])).
% 1.62/1.83 tff(4286,plain,
% 1.62/1.83 (b(elem!1, s(s(z)))),
% 1.62/1.83 inference(modus_ponens,[status(thm)],[4285, 4269])).
% 1.62/1.83 tff(4287,plain,
% 1.62/1.83 (b(s(s(z)), s(s(s(s(z)))))),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[3926, 1619, 3839])).
% 1.62/1.83 tff(4288,plain,
% 1.62/1.83 (~b(elem!1, s(s(z)))),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[2255, 4287, 964, 287])).
% 1.62/1.83 tff(4289,plain,
% 1.62/1.83 ($false),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[4288, 4286])).
% 1.62/1.83 tff(4290,plain,((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~(z = elem!1)) | (~r(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.83 tff(4291,plain,
% 1.62/1.83 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[4290, 288, 114, 964, 3838, 4267, 4264])).
% 1.62/1.83 tff(4292,plain,
% 1.62/1.83 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[1660, 4291, 1011])).
% 1.62/1.83 tff(4293,plain,
% 1.62/1.83 (~r(elem!1, s(s(elem!1)))),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[3811, 4292, 4245])).
% 1.62/1.83 tff(4294,plain,
% 1.62/1.83 (b(elem!1, s(s(elem!1)))),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[1617, 4293, 3432])).
% 1.62/1.83 tff(4295,plain,
% 1.62/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.62/1.83 inference(rewrite,[status(thm)],[])).
% 1.62/1.83 tff(4296,plain,
% 1.62/1.83 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.62/1.83 inference(rewrite,[status(thm)],[])).
% 1.62/1.83 tff(4297,plain,
% 1.62/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~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(X1, 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)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), elem!1))))),
% 1.62/1.83 inference(monotonicity,[status(thm)],[4296])).
% 1.62/1.83 tff(4298,plain,
% 1.62/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~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(X1, 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)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.62/1.83 inference(transitivity,[status(thm)],[4297, 4295])).
% 1.62/1.83 tff(4299,plain,
% 1.62/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.62/1.83 inference(quant_inst,[status(thm)],[])).
% 1.62/1.83 tff(4300,plain,
% 1.62/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), elem!1))),
% 1.62/1.83 inference(modus_ponens,[status(thm)],[4299, 4298])).
% 1.62/1.83 tff(4301,plain,
% 1.62/1.83 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[4300, 75, 4294, 3838, 4146, 4217])).
% 1.62/1.83 tff(4302,plain,
% 1.62/1.83 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.62/1.83 inference(modus_ponens,[status(thm)],[4301, 3834])).
% 1.62/1.83 tff(4303,plain,
% 1.62/1.83 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[575, 4302])).
% 1.62/1.83 tff(4304,plain,
% 1.62/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(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(X1, 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)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.62/1.83 inference(rewrite,[status(thm)],[])).
% 1.62/1.83 tff(4305,plain,
% 1.62/1.83 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(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(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.62/1.83 inference(rewrite,[status(thm)],[])).
% 1.62/1.83 tff(4306,plain,
% 1.62/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.62/1.83 inference(monotonicity,[status(thm)],[4305])).
% 1.62/1.83 tff(4307,plain,
% 1.62/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.62/1.83 inference(transitivity,[status(thm)],[4306, 4304])).
% 1.62/1.83 tff(4308,plain,
% 1.62/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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))))))),
% 1.62/1.83 inference(quant_inst,[status(thm)],[])).
% 1.62/1.83 tff(4309,plain,
% 1.62/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.62/1.83 inference(modus_ponens,[status(thm)],[4308, 4307])).
% 1.62/1.83 tff(4310,plain,
% 1.62/1.83 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[4309, 75, 4294, 4146, 4217])).
% 1.62/1.83 tff(4311,plain,
% 1.62/1.83 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.62/1.83 inference(modus_ponens,[status(thm)],[4310, 4224])).
% 1.62/1.83 tff(4312,plain,
% 1.62/1.83 (r(s(s(elem!1)), s(s(s(z))))),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[1936, 4311, 4222])).
% 1.62/1.83 tff(4313,plain,
% 1.62/1.83 ($false),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[4241, 4312, 4303, 4292])).
% 1.62/1.83 tff(4314,plain,((~(z = elem!1)) | (s(s(elem!1)) = s(s(s(s(z))))) | (~r(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (s(z) = elem!1) | r(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.62/1.83 tff(4315,plain,
% 1.62/1.83 (~(z = elem!1)),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[4314, 90, 1426, 4142, 98, 12])).
% 1.62/1.83 tff(4316,plain,
% 1.62/1.83 (~(elem!1 = z)),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[304, 4315])).
% 1.62/1.83 tff(4317,plain,
% 1.62/1.83 (b(z, elem!1)),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[298, 4315, 13])).
% 1.62/1.83 tff(4318,plain,
% 1.62/1.83 ((s(s(z)) = s(elem!1)) <=> (s(s(z)) = s(s(s(s(z)))))),
% 1.62/1.83 inference(monotonicity,[status(thm)],[1019])).
% 1.62/1.83 tff(4319,plain,
% 1.62/1.83 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(z)) = s(elem!1))),
% 1.62/1.83 inference(symmetry,[status(thm)],[4318])).
% 1.62/1.83 tff(4320,plain,
% 1.62/1.83 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(z)) = s(elem!1)))),
% 1.62/1.83 inference(monotonicity,[status(thm)],[4319])).
% 1.62/1.83 tff(4321,plain,
% 1.62/1.83 (~(s(s(z)) = s(elem!1))),
% 1.62/1.83 inference(modus_ponens,[status(thm)],[459, 4320])).
% 1.62/1.83 tff(4322,plain,
% 1.62/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))))),
% 1.62/1.83 inference(rewrite,[status(thm)],[])).
% 1.62/1.83 tff(4323,plain,
% 1.62/1.83 (((~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1)))) <=> ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))))),
% 1.62/1.83 inference(rewrite,[status(thm)],[])).
% 1.62/1.83 tff(4324,plain,
% 1.62/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1)))))),
% 1.62/1.83 inference(monotonicity,[status(thm)],[4323])).
% 1.62/1.83 tff(4325,plain,
% 1.62/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))))),
% 1.62/1.83 inference(transitivity,[status(thm)],[4324, 4322])).
% 1.62/1.83 tff(4326,plain,
% 1.62/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))))),
% 1.62/1.83 inference(quant_inst,[status(thm)],[])).
% 1.62/1.83 tff(4327,plain,
% 1.62/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1)))),
% 1.62/1.83 inference(modus_ponens,[status(thm)],[4326, 4325])).
% 1.62/1.83 tff(4328,plain,
% 1.62/1.83 (~b(s(s(z)), s(elem!1))),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[4327, 75, 964, 2247, 921])).
% 1.62/1.83 tff(4329,plain,
% 1.62/1.83 (((~![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)))),
% 1.62/1.83 inference(rewrite,[status(thm)],[])).
% 1.62/1.83 tff(4330,plain,
% 1.62/1.83 ((~![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)))),
% 1.62/1.83 inference(quant_inst,[status(thm)],[])).
% 1.62/1.83 tff(4331,plain,
% 1.62/1.83 ((~![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))),
% 1.62/1.83 inference(modus_ponens,[status(thm)],[4330, 4329])).
% 1.62/1.83 tff(4332,plain,
% 1.62/1.83 (r(s(s(z)), s(elem!1))),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[4331, 58, 3284, 4328])).
% 1.62/1.83 tff(4333,plain,
% 1.62/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1), elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 1.62/1.83 inference(rewrite,[status(thm)],[])).
% 1.62/1.83 tff(4334,plain,
% 1.62/1.83 (((~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))) <=> ((~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 1.62/1.84 inference(rewrite,[status(thm)],[])).
% 1.62/1.84 tff(4335,plain,
% 1.62/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1), elem!1)) | (~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(X1, 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(elem!1), elem!1)) | (~b(s(elem!1), z))))),
% 1.62/1.84 inference(monotonicity,[status(thm)],[4334])).
% 1.62/1.84 tff(4336,plain,
% 1.62/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1), elem!1)) | (~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(X1, 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(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 1.62/1.84 inference(transitivity,[status(thm)],[4335, 4333])).
% 1.62/1.84 tff(4337,plain,
% 1.62/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 1.62/1.84 inference(quant_inst,[status(thm)],[])).
% 1.62/1.84 tff(4338,plain,
% 1.62/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1), elem!1)) | (~b(s(elem!1), z))),
% 1.62/1.84 inference(modus_ponens,[status(thm)],[4337, 4336])).
% 1.62/1.84 tff(4339,plain,
% 1.62/1.84 (~b(s(elem!1), z)),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[4338, 75, 1518, 964, 2247, 921])).
% 1.62/1.84 tff(4340,plain,
% 1.62/1.84 (r(s(elem!1), z)),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[766, 4339])).
% 1.62/1.84 tff(4341,plain,
% 1.62/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))))),
% 1.62/1.84 inference(rewrite,[status(thm)],[])).
% 1.62/1.84 tff(4342,plain,
% 1.62/1.84 (((~b(s(s(z)), elem!1)) | (~b(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(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))))),
% 1.62/1.84 inference(rewrite,[status(thm)],[])).
% 1.62/1.84 tff(4343,plain,
% 1.62/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(z))))))),
% 1.62/1.84 inference(monotonicity,[status(thm)],[4342])).
% 1.62/1.84 tff(4344,plain,
% 1.62/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))))),
% 1.62/1.84 inference(transitivity,[status(thm)],[4343, 4341])).
% 1.62/1.84 tff(4345,plain,
% 1.62/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))),
% 1.62/1.84 inference(quant_inst,[status(thm)],[])).
% 1.62/1.84 tff(4346,plain,
% 1.62/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(z))))),
% 1.62/1.84 inference(modus_ponens,[status(thm)],[4345, 4344])).
% 1.62/1.84 tff(4347,plain,
% 1.62/1.84 (~b(s(s(z)), z)),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[4346, 75, 1518, 964, 2247])).
% 1.62/1.84 tff(4348,plain,
% 1.62/1.84 (r(s(s(z)), z)),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[202, 4347])).
% 1.62/1.84 tff(4349,plain,
% 1.62/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), 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(z)), z)) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), z)))),
% 1.62/1.84 inference(rewrite,[status(thm)],[])).
% 1.62/1.84 tff(4350,plain,
% 1.62/1.84 (((~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(elem!1), z)) | (~r(s(s(z)), s(elem!1)))) <=> ((~r(s(s(z)), z)) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), z)))),
% 1.62/1.84 inference(rewrite,[status(thm)],[])).
% 1.62/1.84 tff(4351,plain,
% 1.62/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), 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(s(z)), z)) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), z))))),
% 1.62/1.84 inference(monotonicity,[status(thm)],[4350])).
% 1.62/1.84 tff(4352,plain,
% 1.62/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), 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(s(z)), z)) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), z)))),
% 1.62/1.84 inference(transitivity,[status(thm)],[4351, 4349])).
% 1.62/1.84 tff(4353,plain,
% 1.62/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(z)), z)) | (~r(s(elem!1), z)) | (~r(s(s(z)), s(elem!1))))),
% 1.62/1.84 inference(quant_inst,[status(thm)],[])).
% 1.62/1.84 tff(4354,plain,
% 1.62/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), z))),
% 1.62/1.84 inference(modus_ponens,[status(thm)],[4353, 4352])).
% 1.62/1.84 tff(4355,plain,
% 1.62/1.84 ($false),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[4354, 37, 4348, 4340, 4332])).
% 1.62/1.84 tff(4356,plain,((~b(elem!1, s(s(z)))) | (s(s(z)) = s(elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.84 tff(4357,plain,
% 1.62/1.84 (~b(elem!1, s(s(z)))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[4356, 4321, 964, 3210, 1518])).
% 1.62/1.84 tff(4358,plain,
% 1.62/1.84 ((elem!1 = s(s(z))) | r(elem!1, s(s(z)))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[398, 58, 4357])).
% 1.62/1.84 tff(4359,plain,
% 1.62/1.84 (r(elem!1, s(s(z)))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[4358, 1478])).
% 1.62/1.84 tff(4360,plain,
% 1.62/1.84 ((s(s(s(z))) = s(z)) <=> (elem!1 = s(z))),
% 1.62/1.84 inference(transitivity,[status(thm)],[2558, 92])).
% 1.62/1.84 tff(4361,plain,
% 1.62/1.84 ((~(s(s(s(z))) = s(z))) <=> (~(elem!1 = s(z)))),
% 1.62/1.84 inference(monotonicity,[status(thm)],[4360])).
% 1.62/1.84 tff(4362,plain,
% 1.62/1.84 (~(elem!1 = s(z))),
% 1.62/1.84 inference(modus_ponens,[status(thm)],[457, 4361])).
% 1.62/1.84 tff(4363,plain,
% 1.62/1.84 (r(elem!1, s(z))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[89, 4362, 14])).
% 1.62/1.84 tff(4364,plain,
% 1.62/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))))),
% 1.62/1.84 inference(rewrite,[status(thm)],[])).
% 1.62/1.84 tff(4365,plain,
% 1.62/1.84 (((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1)))) <=> ((~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))))),
% 1.62/1.84 inference(rewrite,[status(thm)],[])).
% 1.62/1.84 tff(4366,plain,
% 1.62/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1)))))),
% 1.62/1.84 inference(monotonicity,[status(thm)],[4365])).
% 1.62/1.84 tff(4367,plain,
% 1.62/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))))),
% 1.62/1.84 inference(transitivity,[status(thm)],[4366, 4364])).
% 1.62/1.84 tff(4368,plain,
% 1.62/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)), elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))))),
% 1.62/1.84 inference(quant_inst,[status(thm)],[])).
% 1.62/1.84 tff(4369,plain,
% 1.62/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1)))),
% 1.62/1.84 inference(modus_ponens,[status(thm)],[4368, 4367])).
% 1.62/1.84 tff(4370,plain,
% 1.62/1.84 (~b(s(s(z)), s(elem!1))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[4369, 75, 1518, 1958, 964, 921])).
% 1.62/1.84 tff(4371,plain,
% 1.62/1.84 (r(s(s(z)), s(elem!1))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[4331, 58, 3284, 4370])).
% 1.62/1.84 tff(4372,plain,
% 1.62/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 1.62/1.84 inference(rewrite,[status(thm)],[])).
% 1.62/1.84 tff(4373,plain,
% 1.62/1.84 (((~b(z, elem!1)) | (~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(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 1.62/1.84 inference(rewrite,[status(thm)],[])).
% 1.62/1.84 tff(4374,plain,
% 1.62/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))))),
% 1.62/1.84 inference(monotonicity,[status(thm)],[4373])).
% 1.62/1.84 tff(4375,plain,
% 1.62/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 1.62/1.84 inference(transitivity,[status(thm)],[4374, 4372])).
% 1.62/1.84 tff(4376,plain,
% 1.62/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 1.62/1.84 inference(quant_inst,[status(thm)],[])).
% 1.62/1.84 tff(4377,plain,
% 1.62/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))),
% 1.62/1.84 inference(modus_ponens,[status(thm)],[4376, 4375])).
% 1.62/1.84 tff(4378,plain,
% 1.62/1.84 (~b(s(elem!1), z)),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[4377, 75, 1518, 1958, 921])).
% 1.62/1.84 tff(4379,plain,
% 1.62/1.84 (r(s(elem!1), z)),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[766, 4378])).
% 1.62/1.84 tff(4380,plain,
% 1.62/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)))),
% 1.62/1.84 inference(rewrite,[status(thm)],[])).
% 1.62/1.84 tff(4381,plain,
% 1.62/1.84 (((~b(z, elem!1)) | (~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(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)))),
% 1.62/1.84 inference(rewrite,[status(thm)],[])).
% 1.62/1.84 tff(4382,plain,
% 1.62/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), 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(X1, 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)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z))))),
% 1.62/1.84 inference(monotonicity,[status(thm)],[4381])).
% 1.62/1.84 tff(4383,plain,
% 1.62/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), 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(X1, 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)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)))),
% 1.62/1.84 inference(transitivity,[status(thm)],[4382, 4380])).
% 1.62/1.84 tff(4384,plain,
% 1.62/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 1.62/1.84 inference(quant_inst,[status(thm)],[])).
% 1.62/1.84 tff(4385,plain,
% 1.62/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z))),
% 1.62/1.84 inference(modus_ponens,[status(thm)],[4384, 4383])).
% 1.62/1.84 tff(4386,plain,
% 1.62/1.84 (~b(s(s(z)), z)),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[4385, 75, 1518, 1958, 964])).
% 1.62/1.84 tff(4387,plain,
% 1.62/1.84 (r(s(s(z)), z)),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[202, 4386])).
% 1.62/1.84 tff(4388,plain,
% 1.62/1.84 ($false),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[4354, 37, 4387, 4379, 4371])).
% 1.62/1.84 tff(4389,plain,((~b(elem!1, z)) | (s(s(z)) = s(elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.84 tff(4390,plain,
% 1.62/1.84 (~b(elem!1, z)),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[4389, 4321, 1518, 964, 3210])).
% 1.62/1.84 tff(4391,plain,
% 1.62/1.84 (r(elem!1, z)),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[387, 4390, 353])).
% 1.62/1.84 tff(4392,plain,
% 1.62/1.84 (~r(z, s(z))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[177, 4391, 4363])).
% 1.62/1.84 tff(4393,plain,
% 1.62/1.84 (b(z, s(z))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[187, 4392])).
% 1.62/1.84 tff(4394,plain,
% 1.62/1.84 (((~![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, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))))),
% 1.62/1.84 inference(rewrite,[status(thm)],[])).
% 1.62/1.84 tff(4395,plain,
% 1.62/1.84 (((~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z))))) <=> ((~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))))),
% 1.62/1.84 inference(rewrite,[status(thm)],[])).
% 1.62/1.84 tff(4396,plain,
% 1.62/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z))))))),
% 1.62/1.84 inference(monotonicity,[status(thm)],[4395])).
% 1.62/1.84 tff(4397,plain,
% 1.62/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))))),
% 1.62/1.84 inference(transitivity,[status(thm)],[4396, 4394])).
% 1.62/1.84 tff(4398,plain,
% 1.62/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))))),
% 1.62/1.84 inference(quant_inst,[status(thm)],[])).
% 1.62/1.84 tff(4399,plain,
% 1.62/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z))))),
% 1.62/1.84 inference(modus_ponens,[status(thm)],[4398, 4397])).
% 1.62/1.84 tff(4400,plain,
% 1.62/1.84 ($false),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[4399, 37, 155, 320, 1489])).
% 1.62/1.85 tff(4401,plain,((~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.85 tff(4402,plain,
% 1.62/1.85 (~r(s(s(z)), z)),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[4401, 4391, 4359])).
% 1.62/1.85 tff(4403,plain,
% 1.62/1.85 (b(s(s(z)), z)),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[202, 4402])).
% 1.62/1.85 tff(4404,plain,
% 1.62/1.85 (b(s(s(z)), s(elem!1)) <=> b(s(s(z)), s(s(s(s(z)))))),
% 1.62/1.85 inference(monotonicity,[status(thm)],[1019])).
% 1.62/1.85 tff(4405,plain,
% 1.62/1.85 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(z)), s(elem!1))),
% 1.62/1.85 inference(symmetry,[status(thm)],[4404])).
% 1.62/1.85 tff(4406,plain,
% 1.62/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)))),
% 1.62/1.85 inference(rewrite,[status(thm)],[])).
% 1.62/1.85 tff(4407,plain,
% 1.62/1.85 (((~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)))),
% 1.62/1.85 inference(rewrite,[status(thm)],[])).
% 1.62/1.85 tff(4408,plain,
% 1.62/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1))))),
% 1.62/1.85 inference(monotonicity,[status(thm)],[4407])).
% 1.62/1.85 tff(4409,plain,
% 1.62/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)))),
% 1.62/1.85 inference(transitivity,[status(thm)],[4408, 4406])).
% 1.62/1.85 tff(4410,plain,
% 1.62/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 1.62/1.85 inference(quant_inst,[status(thm)],[])).
% 1.62/1.85 tff(4411,plain,
% 1.62/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1))),
% 1.62/1.85 inference(modus_ponens,[status(thm)],[4410, 4409])).
% 1.62/1.85 tff(4412,plain,
% 1.62/1.85 (~b(s(s(z)), z)),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[4411, 75, 1518, 964, 2562, 2561])).
% 1.62/1.85 tff(4413,plain,
% 1.62/1.85 (r(s(s(z)), z)),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[202, 4412])).
% 1.62/1.85 tff(4414,plain,
% 1.62/1.85 (((~![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(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)))),
% 1.62/1.85 inference(rewrite,[status(thm)],[])).
% 1.62/1.85 tff(4415,plain,
% 1.62/1.85 (((~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)), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)))),
% 1.62/1.85 inference(rewrite,[status(thm)],[])).
% 1.62/1.85 tff(4416,plain,
% 1.62/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(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)), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z))))),
% 1.62/1.85 inference(monotonicity,[status(thm)],[4415])).
% 1.62/1.85 tff(4417,plain,
% 1.62/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(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)), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)))),
% 1.62/1.85 inference(transitivity,[status(thm)],[4416, 4414])).
% 1.62/1.85 tff(4418,plain,
% 1.62/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.62/1.85 inference(quant_inst,[status(thm)],[])).
% 1.62/1.85 tff(4419,plain,
% 1.62/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z))),
% 1.62/1.85 inference(modus_ponens,[status(thm)],[4418, 4417])).
% 1.62/1.85 tff(4420,plain,
% 1.62/1.85 ($false),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[4419, 37, 4413, 467, 2578])).
% 1.62/1.85 tff(4421,plain,((s(s(s(s(z)))) = elem!1) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | r(elem!1, s(s(s(s(z))))) | r(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.62/1.85 tff(4422,plain,
% 1.62/1.85 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[4421, 268, 12, 964, 1518, 265])).
% 1.62/1.85 tff(4423,plain,
% 1.62/1.85 (b(s(s(z)), s(s(s(s(z)))))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[465, 4422])).
% 1.62/1.85 tff(4424,plain,
% 1.62/1.85 (b(s(s(z)), s(elem!1))),
% 1.62/1.85 inference(modus_ponens,[status(thm)],[4423, 4405])).
% 1.62/1.85 tff(4425,plain,
% 1.62/1.85 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(s(z))))))),
% 1.62/1.85 inference(monotonicity,[status(thm)],[242])).
% 1.62/1.85 tff(4426,plain,
% 1.62/1.85 (~(elem!1 = s(s(s(s(z)))))),
% 1.62/1.85 inference(modus_ponens,[status(thm)],[264, 4425])).
% 1.62/1.85 tff(4427,plain,
% 1.62/1.85 (b(elem!1, s(s(s(s(z)))))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[278, 268, 4426])).
% 1.62/1.85 tff(4428,plain,
% 1.62/1.85 (b(elem!1, s(elem!1))),
% 1.62/1.85 inference(modus_ponens,[status(thm)],[4427, 2550])).
% 1.62/1.85 tff(4429,plain,
% 1.62/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.62/1.85 inference(rewrite,[status(thm)],[])).
% 1.62/1.85 tff(4430,plain,
% 1.62/1.85 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1)))) <=> ((~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.62/1.85 inference(rewrite,[status(thm)],[])).
% 1.62/1.85 tff(4431,plain,
% 1.62/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1)))))),
% 1.62/1.85 inference(monotonicity,[status(thm)],[4430])).
% 1.62/1.85 tff(4432,plain,
% 1.62/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))))),
% 1.62/1.85 inference(transitivity,[status(thm)],[4431, 4429])).
% 1.62/1.85 tff(4433,plain,
% 1.62/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))))),
% 1.62/1.85 inference(quant_inst,[status(thm)],[])).
% 1.62/1.85 tff(4434,plain,
% 1.62/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1)))),
% 1.62/1.85 inference(modus_ponens,[status(thm)],[4433, 4432])).
% 1.62/1.85 tff(4435,plain,
% 1.62/1.85 (~b(s(s(z)), s(elem!1))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[4434, 75, 964, 3210, 4428])).
% 1.62/1.85 tff(4436,plain,
% 1.62/1.85 ($false),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[4435, 4424])).
% 1.62/1.85 tff(4437,plain,(r(elem!1, s(s(s(s(z))))) | (~(s(s(s(z))) = elem!1)) | (~b(s(s(z)), elem!1)) | r(s(s(s(s(z)))), elem!1) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.85 tff(4438,plain,
% 1.62/1.85 (r(elem!1, s(s(s(s(z)))))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[4437, 213, 964, 12, 1518])).
% 1.62/1.85 tff(4439,plain,
% 1.62/1.85 (~r(s(z), s(s(s(s(z)))))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[3203, 4438, 4363])).
% 1.62/1.85 tff(4440,plain,
% 1.62/1.85 (b(s(z), s(s(s(s(z)))))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[489, 4439])).
% 1.62/1.85 tff(4441,plain,
% 1.62/1.85 (b(s(z), s(elem!1))),
% 1.62/1.85 inference(modus_ponens,[status(thm)],[4440, 215])).
% 1.62/1.85 tff(4442,plain,
% 1.62/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)))),
% 1.62/1.85 inference(rewrite,[status(thm)],[])).
% 1.62/1.85 tff(4443,plain,
% 1.62/1.85 (((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))) <=> ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)))),
% 1.62/1.85 inference(rewrite,[status(thm)],[])).
% 1.62/1.85 tff(4444,plain,
% 1.62/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)), elem!1)) | (~b(s(z), s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1))))),
% 1.62/1.85 inference(monotonicity,[status(thm)],[4443])).
% 1.62/1.85 tff(4445,plain,
% 1.62/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)), elem!1)) | (~b(s(z), s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)))),
% 1.62/1.85 inference(transitivity,[status(thm)],[4444, 4442])).
% 1.62/1.85 tff(4446,plain,
% 1.62/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)), elem!1)) | (~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.62/1.85 inference(quant_inst,[status(thm)],[])).
% 1.62/1.85 tff(4447,plain,
% 1.62/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1))),
% 1.62/1.85 inference(modus_ponens,[status(thm)],[4446, 4445])).
% 1.62/1.85 tff(4448,plain,
% 1.62/1.85 ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[4447, 75, 1518, 964, 3210, 4441])).
% 1.62/1.85 tff(4449,plain,
% 1.62/1.85 (~b(s(s(z)), s(z))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[4448, 4403, 4393])).
% 1.62/1.85 tff(4450,plain,
% 1.62/1.85 (r(s(s(z)), s(z))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[153, 4449])).
% 1.62/1.85 tff(4451,plain,
% 1.62/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(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)))))),
% 1.62/1.85 inference(rewrite,[status(thm)],[])).
% 1.62/1.85 tff(4452,plain,
% 1.62/1.85 (((~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)))))),
% 1.62/1.85 inference(rewrite,[status(thm)],[])).
% 1.62/1.85 tff(4453,plain,
% 1.62/1.85 (((~![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(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))))))),
% 1.62/1.85 inference(monotonicity,[status(thm)],[4452])).
% 1.62/1.85 tff(4454,plain,
% 1.62/1.85 (((~![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(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)))))),
% 1.62/1.85 inference(transitivity,[status(thm)],[4453, 4451])).
% 1.62/1.85 tff(4455,plain,
% 1.62/1.85 ((~![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(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))))),
% 1.62/1.85 inference(quant_inst,[status(thm)],[])).
% 1.62/1.85 tff(4456,plain,
% 1.62/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z))))),
% 1.62/1.85 inference(modus_ponens,[status(thm)],[4455, 4454])).
% 1.62/1.85 tff(4457,plain,
% 1.62/1.85 ($false),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[4456, 37, 4363, 4450, 4359])).
% 1.62/1.85 tff(4458,plain,((~(s(s(s(z))) = elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (s(s(z)) = elem!1) | (elem!1 = z) | r(s(s(s(s(z)))), elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.85 tff(4459,plain,
% 1.62/1.85 (~(s(s(s(z))) = elem!1)),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[4458, 4317, 4142, 15, 4316, 12, 14])).
% 1.62/1.85 tff(4460,plain,
% 1.62/1.85 (~(s(s(elem!1)) = s(s(z)))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[237, 4315])).
% 1.62/1.85 tff(4461,plain,
% 1.62/1.85 (elem!1 = s(s(s(s(z))))),
% 1.62/1.85 inference(modus_ponens,[status(thm)],[3285, 239])).
% 1.62/1.85 tff(4462,plain,
% 1.62/1.85 ($false),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[860, 4461])).
% 1.62/1.85 tff(4463,plain,((~(s(s(s(s(z)))) = elem!1)) | (elem!1 = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.85 tff(4464,plain,
% 1.62/1.85 (elem!1 = s(s(s(s(z))))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[4463, 3285])).
% 1.62/1.85 tff(4465,plain,
% 1.62/1.85 (s(elem!1) = s(s(s(s(s(z)))))),
% 1.62/1.85 inference(monotonicity,[status(thm)],[270])).
% 1.62/1.85 tff(4466,plain,
% 1.62/1.85 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 1.62/1.85 inference(monotonicity,[status(thm)],[4465])).
% 1.62/1.85 tff(4467,plain,
% 1.62/1.85 (s(s(s(s(z)))) = elem!1),
% 1.62/1.85 inference(symmetry,[status(thm)],[270])).
% 1.62/1.85 tff(4468,plain,
% 1.62/1.85 (s(s(s(s(z)))) = s(s(s(s(s(s(z))))))),
% 1.62/1.85 inference(transitivity,[status(thm)],[4467, 1602, 4466])).
% 1.62/1.85 tff(4469,plain,
% 1.62/1.85 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.62/1.85 inference(monotonicity,[status(thm)],[4468])).
% 1.62/1.85 tff(4470,plain,
% 1.62/1.85 (s(s(s(z))) = s(s(s(s(s(z)))))),
% 1.62/1.85 inference(transitivity,[status(thm)],[451, 4469, 730])).
% 1.62/1.85 tff(4471,plain,
% 1.62/1.85 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(z))))))),
% 1.62/1.85 inference(monotonicity,[status(thm)],[4470])).
% 1.62/1.85 tff(4472,plain,
% 1.62/1.85 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(z))))),
% 1.62/1.85 inference(symmetry,[status(thm)],[4471])).
% 1.62/1.85 tff(4473,plain,
% 1.62/1.85 (s(s(elem!1)) = s(s(z))),
% 1.62/1.85 inference(transitivity,[status(thm)],[2323, 270, 833, 4472, 253])).
% 1.62/1.85 tff(4474,plain,
% 1.62/1.85 ($false),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[266, 4473])).
% 1.62/1.85 tff(4475,plain,((~(elem!1 = s(s(elem!1)))) | (s(s(elem!1)) = s(s(z))) | (~(elem!1 = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.85 tff(4476,plain,
% 1.62/1.85 (~(elem!1 = s(s(elem!1)))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[4475, 4464, 266])).
% 1.62/1.85 tff(4477,plain,
% 1.62/1.85 (~(s(s(elem!1)) = elem!1)),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[2555, 4476])).
% 1.62/1.85 tff(4478,plain,
% 1.62/1.85 (r(s(z), elem!1)),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[601, 3627, 98])).
% 1.62/1.85 tff(4479,plain,
% 1.62/1.85 (~r(s(z), s(s(elem!1)))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[3753, 4478, 2647])).
% 1.62/1.85 tff(4480,plain,
% 1.62/1.85 (b(s(z), s(s(elem!1)))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[1890, 4479])).
% 1.62/1.85 tff(4481,plain,
% 1.62/1.85 (r(s(s(elem!1)), s(s(s(s(z))))) <=> r(s(s(elem!1)), elem!1)),
% 1.62/1.85 inference(monotonicity,[status(thm)],[3285])).
% 1.62/1.85 tff(4482,plain,
% 1.62/1.85 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.62/1.85 inference(symmetry,[status(thm)],[4481])).
% 1.62/1.85 tff(4483,plain,
% 1.62/1.85 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.62/1.85 inference(modus_ponens,[status(thm)],[2647, 4482])).
% 1.62/1.85 tff(4484,assumption,(~r(s(s(elem!1)), s(s(s(s(z)))))), introduced(assumption)).
% 1.62/1.85 tff(4485,plain,
% 1.62/1.85 ($false),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[4484, 4483])).
% 1.62/1.85 tff(4486,plain,(r(s(s(elem!1)), s(s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)) | (~(s(s(s(s(z)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.85 tff(4487,plain,
% 1.62/1.85 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[4486, 2647, 3285])).
% 1.62/1.85 tff(4488,plain,
% 1.62/1.85 (r(s(z), s(s(s(s(z)))))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[3669, 3627, 3285])).
% 1.62/1.85 tff(4489,plain,
% 1.62/1.85 (~r(s(s(elem!1)), s(z))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[1655, 4488, 4487])).
% 1.62/1.85 tff(4490,plain,
% 1.62/1.85 (b(s(s(elem!1)), s(z))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[561, 4489])).
% 1.62/1.85 tff(4491,plain,
% 1.62/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(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(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 1.62/1.86 inference(rewrite,[status(thm)],[])).
% 1.62/1.86 tff(4492,plain,
% 1.62/1.86 (((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), s(s(elem!1))))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 1.62/1.86 inference(rewrite,[status(thm)],[])).
% 1.62/1.86 tff(4493,plain,
% 1.62/1.86 (((~![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(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))))),
% 1.62/1.86 inference(monotonicity,[status(thm)],[4492])).
% 1.62/1.86 tff(4494,plain,
% 1.62/1.86 (((~![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(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 1.62/1.86 inference(transitivity,[status(thm)],[4493, 4491])).
% 1.62/1.86 tff(4495,plain,
% 1.62/1.86 ((~![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(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.62/1.86 inference(quant_inst,[status(thm)],[])).
% 1.62/1.86 tff(4496,plain,
% 1.62/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))),
% 1.62/1.86 inference(modus_ponens,[status(thm)],[4495, 4494])).
% 1.62/1.86 tff(4497,plain,
% 1.62/1.86 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[4496, 37, 1061, 2647])).
% 1.62/1.86 tff(4498,plain,
% 1.62/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.62/1.86 inference(rewrite,[status(thm)],[])).
% 1.62/1.86 tff(4499,plain,
% 1.62/1.86 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.62/1.86 inference(rewrite,[status(thm)],[])).
% 1.62/1.86 tff(4500,plain,
% 1.62/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 1.62/1.86 inference(monotonicity,[status(thm)],[4499])).
% 1.62/1.86 tff(4501,plain,
% 1.62/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.62/1.86 inference(transitivity,[status(thm)],[4500, 4498])).
% 1.62/1.86 tff(4502,plain,
% 1.62/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.62/1.86 inference(quant_inst,[status(thm)],[])).
% 1.62/1.86 tff(4503,plain,
% 1.62/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 1.62/1.86 inference(modus_ponens,[status(thm)],[4502, 4501])).
% 1.62/1.86 tff(4504,plain,
% 1.62/1.86 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[4503, 75, 1457, 1894, 984])).
% 1.62/1.86 tff(4505,plain,
% 1.62/1.86 ($false),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[62, 4504, 4497, 16])).
% 1.62/1.86 tff(4506,plain,((~b(s(s(elem!1)), s(z))) | (s(s(s(z))) = s(s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.86 tff(4507,plain,
% 1.62/1.86 ($false),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[4506, 4490, 4480, 16, 984, 1061, 2647])).
% 1.62/1.86 tff(4508,plain,(b(s(z), elem!1) | (s(s(s(z))) = s(s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~(s(s(s(s(z)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.86 tff(4509,plain,
% 1.62/1.86 (b(s(z), elem!1)),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[4508, 2647, 1082, 1061, 16, 3285])).
% 1.62/1.86 tff(4510,plain,
% 1.62/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.62/1.86 inference(rewrite,[status(thm)],[])).
% 1.62/1.86 tff(4511,plain,
% 1.62/1.86 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.62/1.86 inference(rewrite,[status(thm)],[])).
% 1.62/1.86 tff(4512,plain,
% 1.62/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), z)) | (~b(s(s(s(z))), s(z)))))),
% 1.62/1.86 inference(monotonicity,[status(thm)],[4511])).
% 1.62/1.86 tff(4513,plain,
% 1.62/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.62/1.86 inference(transitivity,[status(thm)],[4512, 4510])).
% 1.62/1.86 tff(4514,plain,
% 1.62/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 1.62/1.86 inference(quant_inst,[status(thm)],[])).
% 1.62/1.86 tff(4515,plain,
% 1.62/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))),
% 1.62/1.86 inference(modus_ponens,[status(thm)],[4514, 4513])).
% 1.62/1.86 tff(4516,plain,
% 1.62/1.86 (~b(s(s(s(z))), z)),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[4515, 75, 372, 170, 1082])).
% 1.62/1.86 tff(4517,plain,
% 1.62/1.86 (r(s(s(s(z))), z)),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[1334, 58, 221, 4516])).
% 1.62/1.86 tff(4518,plain,
% 1.62/1.86 ($false),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[2467, 37, 155, 1061, 4517])).
% 1.62/1.86 tff(4519,plain,((~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~b(z, s(z))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.86 tff(4520,plain,
% 1.62/1.86 (~r(elem!1, z)),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[4519, 372, 1061, 114])).
% 1.62/1.86 tff(4521,plain,
% 1.62/1.86 (b(elem!1, z)),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[387, 4520, 353])).
% 1.62/1.86 tff(4522,plain,
% 1.62/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)))),
% 1.62/1.86 inference(rewrite,[status(thm)],[])).
% 1.62/1.86 tff(4523,plain,
% 1.62/1.86 (((~b(z, elem!1)) | (~b(s(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(z, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)))),
% 1.62/1.86 inference(rewrite,[status(thm)],[])).
% 1.62/1.86 tff(4524,plain,
% 1.62/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z))))),
% 1.62/1.86 inference(monotonicity,[status(thm)],[4523])).
% 1.62/1.86 tff(4525,plain,
% 1.62/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)))),
% 1.62/1.86 inference(transitivity,[status(thm)],[4524, 4522])).
% 1.62/1.86 tff(4526,plain,
% 1.62/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 1.62/1.86 inference(quant_inst,[status(thm)],[])).
% 1.62/1.86 tff(4527,plain,
% 1.62/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z))),
% 1.62/1.86 inference(modus_ponens,[status(thm)],[4526, 4525])).
% 1.62/1.86 tff(4528,plain,
% 1.62/1.86 ($false),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[4527, 75, 1518, 4521, 372, 107])).
% 1.62/1.86 tff(4529,plain,((~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (elem!1 = z) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.86 tff(4530,plain,
% 1.62/1.86 (~b(z, s(z))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[4529, 4509, 1518, 353, 1061, 114])).
% 1.62/1.86 tff(4531,plain,
% 1.62/1.86 (r(z, s(z))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[187, 4530])).
% 1.62/1.86 tff(4532,plain,
% 1.62/1.86 ((~(elem!1 = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 1.62/1.86 inference(monotonicity,[status(thm)],[240])).
% 1.62/1.86 tff(4533,plain,
% 1.62/1.86 (~(z = elem!1)),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[3606, 1061, 114, 107, 1031, 2217])).
% 1.62/1.86 tff(4534,plain,
% 1.62/1.86 (~(s(s(elem!1)) = s(s(z)))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[237, 4533])).
% 1.62/1.86 tff(4535,plain,
% 1.62/1.86 (~(s(z) = elem!1)),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[2724, 13, 506])).
% 1.62/1.86 tff(4536,plain,
% 1.62/1.86 (~(s(s(z)) = s(elem!1))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[3261, 4535])).
% 1.62/1.86 tff(4537,assumption,(s(s(s(z))) = s(s(elem!1))), introduced(assumption)).
% 1.62/1.86 tff(4538,plain,
% 1.62/1.86 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 1.62/1.86 inference(monotonicity,[status(thm)],[4537])).
% 1.62/1.86 tff(4539,plain,
% 1.62/1.86 (s(s(z)) = s(elem!1)),
% 1.62/1.86 inference(transitivity,[status(thm)],[254, 4538, 228])).
% 1.62/1.86 tff(4540,plain,
% 1.62/1.86 ($false),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[3284, 4539])).
% 1.62/1.86 tff(4541,plain,((~(s(s(s(z))) = s(s(elem!1)))) | (s(s(z)) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.86 tff(4542,plain,
% 1.62/1.86 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[4541, 4536])).
% 1.62/1.86 tff(4543,plain,
% 1.62/1.86 (~(elem!1 = z)),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[304, 4533])).
% 1.62/1.86 tff(4544,plain,
% 1.62/1.86 (b(elem!1, z)),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[387, 4543, 2745])).
% 1.62/1.86 tff(4545,plain,
% 1.62/1.86 (b(z, elem!1)),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[298, 4533, 13])).
% 1.62/1.86 tff(4546,plain,
% 1.62/1.86 (b(z, s(s(s(s(z))))) <=> b(z, elem!1)),
% 1.62/1.86 inference(monotonicity,[status(thm)],[4467])).
% 1.62/1.86 tff(4547,plain,
% 1.62/1.86 (b(z, elem!1) <=> b(z, s(s(s(s(z)))))),
% 1.62/1.86 inference(symmetry,[status(thm)],[4546])).
% 1.62/1.86 tff(4548,plain,
% 1.62/1.86 (b(z, s(s(s(s(z)))))),
% 1.62/1.86 inference(modus_ponens,[status(thm)],[1518, 4547])).
% 1.62/1.86 tff(4549,plain,
% 1.62/1.86 (b(s(s(s(s(z)))), z) <=> b(elem!1, z)),
% 1.62/1.86 inference(monotonicity,[status(thm)],[4467])).
% 1.62/1.86 tff(4550,plain,
% 1.62/1.86 (b(elem!1, z) <=> b(s(s(s(s(z)))), z)),
% 1.62/1.86 inference(symmetry,[status(thm)],[4549])).
% 1.62/1.86 tff(4551,plain,
% 1.62/1.86 (b(s(s(s(s(z)))), z)),
% 1.62/1.86 inference(modus_ponens,[status(thm)],[1958, 4550])).
% 1.62/1.86 tff(4552,plain,
% 1.62/1.86 (b(elem!1, s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.62/1.86 inference(monotonicity,[status(thm)],[270])).
% 1.62/1.86 tff(4553,plain,
% 1.62/1.86 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 1.62/1.86 inference(symmetry,[status(thm)],[4466])).
% 1.62/1.86 tff(4554,plain,
% 1.62/1.86 (b(s(s(s(z))), s(s(s(s(s(s(z))))))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.62/1.86 inference(monotonicity,[status(thm)],[4553])).
% 1.62/1.86 tff(4555,plain,
% 1.62/1.86 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.62/1.86 inference(symmetry,[status(thm)],[4554])).
% 1.62/1.86 tff(4556,plain,
% 1.62/1.86 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 1.62/1.86 inference(monotonicity,[status(thm)],[270])).
% 1.62/1.86 tff(4557,plain,
% 1.62/1.86 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.62/1.86 inference(modus_ponens,[status(thm)],[1061, 4556])).
% 1.62/1.86 tff(4558,plain,
% 1.62/1.86 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.62/1.86 inference(monotonicity,[status(thm)],[4553])).
% 1.62/1.86 tff(4559,plain,
% 1.62/1.86 (r(s(s(elem!1)), s(s(s(s(z))))) <=> r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.62/1.86 inference(symmetry,[status(thm)],[4558])).
% 1.62/1.86 tff(4560,plain,
% 1.62/1.86 ((elem!1 = s(s(elem!1))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 1.62/1.86 inference(monotonicity,[status(thm)],[270])).
% 1.62/1.86 tff(4561,plain,
% 1.62/1.86 ((elem!1 = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 1.62/1.86 inference(transitivity,[status(thm)],[4560, 3863])).
% 1.62/1.86 tff(4562,plain,
% 1.62/1.86 ((~(elem!1 = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(s(s(s(z))))))),
% 1.62/1.86 inference(monotonicity,[status(thm)],[4561])).
% 1.62/1.86 tff(4563,plain,
% 1.62/1.86 (~(elem!1 = s(s(elem!1)))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[4475, 270, 266])).
% 1.62/1.86 tff(4564,plain,
% 1.62/1.86 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 1.62/1.86 inference(modus_ponens,[status(thm)],[4563, 4562])).
% 1.62/1.86 tff(4565,plain,
% 1.62/1.86 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.62/1.86 inference(monotonicity,[status(thm)],[4553])).
% 1.62/1.86 tff(4566,plain,
% 1.62/1.86 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) <=> (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 1.62/1.86 inference(monotonicity,[status(thm)],[4565])).
% 1.62/1.86 tff(4567,plain,
% 1.62/1.86 (b(s(s(s(s(s(s(z)))))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.62/1.86 inference(monotonicity,[status(thm)],[4553])).
% 1.62/1.86 tff(4568,plain,
% 1.62/1.86 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(s(s(z)))))), s(z))),
% 1.62/1.86 inference(symmetry,[status(thm)],[4567])).
% 1.62/1.86 tff(4569,plain,
% 1.62/1.86 (b(elem!1, s(s(elem!1)))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[1617, 4563, 2217])).
% 1.62/1.86 tff(4570,plain,
% 1.62/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), 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(X1, 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)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)))),
% 1.62/1.86 inference(rewrite,[status(thm)],[])).
% 1.62/1.86 tff(4571,plain,
% 1.62/1.86 (((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)))),
% 1.62/1.86 inference(rewrite,[status(thm)],[])).
% 1.62/1.86 tff(4572,plain,
% 1.62/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1))))),
% 1.62/1.86 inference(monotonicity,[status(thm)],[4571])).
% 1.62/1.86 tff(4573,plain,
% 1.62/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)))),
% 1.62/1.86 inference(transitivity,[status(thm)],[4572, 4570])).
% 1.62/1.86 tff(4574,plain,
% 1.62/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)))),
% 1.62/1.86 inference(quant_inst,[status(thm)],[])).
% 1.62/1.86 tff(4575,plain,
% 1.62/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1))),
% 1.62/1.86 inference(modus_ponens,[status(thm)],[4574, 4573])).
% 1.62/1.86 tff(4576,plain,
% 1.62/1.86 ($false),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[4575, 75, 1518, 1620, 1957, 1954])).
% 1.62/1.86 tff(4577,plain,((~r(s(s(elem!1)), s(z))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.86 tff(4578,plain,
% 1.62/1.87 (~r(s(s(elem!1)), s(z))),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[4577, 4569, 1518, 506])).
% 1.62/1.87 tff(4579,plain,
% 1.62/1.87 (b(s(s(elem!1)), s(z))),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[561, 4578])).
% 1.62/1.87 tff(4580,plain,
% 1.62/1.87 (b(s(s(s(s(s(s(z)))))), s(z))),
% 1.62/1.87 inference(modus_ponens,[status(thm)],[4579, 4568])).
% 1.62/1.87 tff(4581,plain,
% 1.62/1.87 (b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) <=> b(elem!1, s(s(elem!1)))),
% 1.62/1.87 inference(monotonicity,[status(thm)],[4467, 4553])).
% 1.62/1.87 tff(4582,plain,
% 1.62/1.87 (b(elem!1, s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.62/1.87 inference(symmetry,[status(thm)],[4581])).
% 1.62/1.87 tff(4583,plain,
% 1.62/1.87 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.62/1.87 inference(modus_ponens,[status(thm)],[4569, 4582])).
% 1.62/1.87 tff(4584,plain,
% 1.62/1.87 (b(s(z), elem!1) <=> b(s(z), s(s(s(s(z)))))),
% 1.62/1.87 inference(monotonicity,[status(thm)],[270])).
% 1.62/1.87 tff(4585,plain,
% 1.62/1.87 (b(s(z), s(s(s(s(z)))))),
% 1.62/1.87 inference(modus_ponens,[status(thm)],[107, 4584])).
% 1.62/1.87 tff(4586,assumption,(b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))), introduced(assumption)).
% 1.62/1.87 tff(4587,assumption,(b(s(s(s(s(s(s(z)))))), s(z))), introduced(assumption)).
% 1.62/1.87 tff(4588,assumption,(b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.62/1.87 tff(4589,plain,
% 1.62/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.62/1.87 inference(rewrite,[status(thm)],[])).
% 1.62/1.87 tff(4590,plain,
% 1.62/1.87 (((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.62/1.87 inference(rewrite,[status(thm)],[])).
% 1.62/1.87 tff(4591,plain,
% 1.62/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 1.62/1.87 inference(monotonicity,[status(thm)],[4590])).
% 1.62/1.87 tff(4592,plain,
% 1.62/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.62/1.87 inference(transitivity,[status(thm)],[4591, 4589])).
% 1.62/1.87 tff(4593,plain,
% 1.62/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.62/1.87 inference(quant_inst,[status(thm)],[])).
% 1.62/1.87 tff(4594,plain,
% 1.62/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.62/1.87 inference(modus_ponens,[status(thm)],[4593, 4592])).
% 1.62/1.87 tff(4595,plain,
% 1.62/1.87 ($false),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[4594, 75, 578, 4588, 4587, 4586])).
% 1.62/1.87 tff(4596,plain,((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.87 tff(4597,plain,
% 1.62/1.87 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[4596, 4585, 4583, 4580])).
% 1.62/1.87 tff(4598,plain,
% 1.62/1.87 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.62/1.87 inference(modus_ponens,[status(thm)],[4597, 4566])).
% 1.62/1.87 tff(4599,plain,
% 1.62/1.87 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[1660, 4598, 4564])).
% 1.62/1.87 tff(4600,plain,
% 1.62/1.87 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.62/1.87 inference(modus_ponens,[status(thm)],[4599, 4559])).
% 1.62/1.87 tff(4601,assumption,(r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))), introduced(assumption)).
% 1.62/1.87 tff(4602,plain,
% 1.62/1.87 (r(s(s(s(z))), s(s(s(s(s(s(z))))))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 1.62/1.87 inference(monotonicity,[status(thm)],[4553])).
% 1.62/1.87 tff(4603,plain,
% 1.62/1.87 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.62/1.87 inference(symmetry,[status(thm)],[4602])).
% 1.62/1.87 tff(4604,plain,
% 1.62/1.87 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.62/1.87 inference(modus_ponens,[status(thm)],[27, 4603])).
% 1.62/1.87 tff(4605,plain,
% 1.62/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.62/1.87 inference(rewrite,[status(thm)],[])).
% 1.62/1.87 tff(4606,plain,
% 1.62/1.87 (((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.62/1.87 inference(rewrite,[status(thm)],[])).
% 1.62/1.87 tff(4607,plain,
% 1.62/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 1.62/1.87 inference(monotonicity,[status(thm)],[4606])).
% 1.62/1.87 tff(4608,plain,
% 1.62/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.62/1.87 inference(transitivity,[status(thm)],[4607, 4605])).
% 1.62/1.87 tff(4609,plain,
% 1.62/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.62/1.87 inference(quant_inst,[status(thm)],[])).
% 1.62/1.87 tff(4610,plain,
% 1.62/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 1.62/1.87 inference(modus_ponens,[status(thm)],[4609, 4608])).
% 1.62/1.87 tff(4611,plain,
% 1.62/1.87 ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[4610, 37, 1308])).
% 1.62/1.87 tff(4612,plain,
% 1.62/1.87 ($false),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[4611, 4604, 4601])).
% 1.62/1.87 tff(4613,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~(elem!1 = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.87 tff(4614,plain,
% 1.62/1.87 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[4613, 4600, 4557, 270])).
% 1.62/1.87 tff(4615,plain,
% 1.62/1.87 (b(s(s(s(z))), s(s(elem!1)))),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[62, 4614, 16])).
% 1.62/1.87 tff(4616,plain,
% 1.62/1.87 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.62/1.87 inference(modus_ponens,[status(thm)],[4615, 4555])).
% 1.62/1.87 tff(4617,assumption,(b(s(s(s(z))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.62/1.87 tff(4618,plain,
% 1.62/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.62/1.87 inference(rewrite,[status(thm)],[])).
% 1.62/1.87 tff(4619,plain,
% 1.62/1.87 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.62/1.87 inference(rewrite,[status(thm)],[])).
% 1.62/1.87 tff(4620,plain,
% 1.62/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 1.62/1.87 inference(monotonicity,[status(thm)],[4619])).
% 1.62/1.87 tff(4621,plain,
% 1.62/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.62/1.87 inference(transitivity,[status(thm)],[4620, 4618])).
% 1.62/1.87 tff(4622,plain,
% 1.62/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 1.62/1.87 inference(quant_inst,[status(thm)],[])).
% 1.62/1.87 tff(4623,plain,
% 1.62/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 1.62/1.87 inference(modus_ponens,[status(thm)],[4622, 4621])).
% 1.62/1.87 tff(4624,plain,
% 1.62/1.87 ($false),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[4623, 75, 984, 1053, 4587, 4617])).
% 1.62/1.87 tff(4625,plain,((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.87 tff(4626,plain,
% 1.62/1.87 (~b(s(z), s(s(s(z))))),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[4625, 4580, 1082, 4616])).
% 1.62/1.87 tff(4627,plain,
% 1.62/1.87 (r(s(z), s(s(s(z))))),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[1263, 4626])).
% 1.62/1.87 tff(4628,plain,
% 1.62/1.87 (~r(elem!1, s(s(s(z))))),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[1274, 4627, 114])).
% 1.62/1.87 tff(4629,plain,
% 1.62/1.87 (b(elem!1, s(s(s(z))))),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[1279, 4628, 1305])).
% 1.62/1.87 tff(4630,plain,
% 1.62/1.87 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.62/1.87 inference(modus_ponens,[status(thm)],[4629, 4552])).
% 1.62/1.87 tff(4631,plain,
% 1.62/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(z)))))))),
% 1.62/1.87 inference(rewrite,[status(thm)],[])).
% 1.62/1.87 tff(4632,plain,
% 1.62/1.87 (((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(z)))))))),
% 1.62/1.87 inference(rewrite,[status(thm)],[])).
% 1.62/1.87 tff(4633,plain,
% 1.62/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(z))))))))),
% 1.62/1.87 inference(monotonicity,[status(thm)],[4632])).
% 1.62/1.87 tff(4634,plain,
% 1.62/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(z)))))))),
% 1.62/1.88 inference(transitivity,[status(thm)],[4633, 4631])).
% 1.62/1.88 tff(4635,plain,
% 1.62/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.62/1.88 inference(quant_inst,[status(thm)],[])).
% 1.62/1.88 tff(4636,plain,
% 1.62/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(z))))))),
% 1.62/1.88 inference(modus_ponens,[status(thm)],[4635, 4634])).
% 1.62/1.88 tff(4637,plain,
% 1.62/1.88 ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[4636, 75, 4583, 4616])).
% 1.62/1.88 tff(4638,plain,
% 1.62/1.88 (~b(s(s(s(z))), z)),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[4637, 4630, 4551, 4548])).
% 1.62/1.88 tff(4639,plain,
% 1.62/1.88 (r(s(s(s(z))), z)),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[1334, 58, 221, 4638])).
% 1.62/1.88 tff(4640,plain,
% 1.62/1.88 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)))),
% 1.62/1.88 inference(rewrite,[status(thm)],[])).
% 1.62/1.88 tff(4641,plain,
% 1.62/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z))))),
% 1.62/1.88 inference(monotonicity,[status(thm)],[4640])).
% 1.62/1.88 tff(4642,plain,
% 1.62/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)))),
% 1.62/1.88 inference(transitivity,[status(thm)],[4641, 2618])).
% 1.62/1.88 tff(4643,plain,
% 1.62/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 1.62/1.88 inference(quant_inst,[status(thm)],[])).
% 1.62/1.88 tff(4644,plain,
% 1.62/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z))),
% 1.62/1.88 inference(modus_ponens,[status(thm)],[4643, 4642])).
% 1.62/1.88 tff(4645,plain,
% 1.62/1.88 (~b(s(z), z)),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[4644, 75, 1518, 1958, 107])).
% 1.62/1.88 tff(4646,plain,
% 1.62/1.88 (r(s(z), z)),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[169, 4645])).
% 1.62/1.88 tff(4647,plain,
% 1.62/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 1.62/1.88 inference(rewrite,[status(thm)],[])).
% 1.62/1.88 tff(4648,plain,
% 1.62/1.88 (((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 1.62/1.88 inference(rewrite,[status(thm)],[])).
% 1.62/1.88 tff(4649,plain,
% 1.62/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z))))),
% 1.62/1.88 inference(monotonicity,[status(thm)],[4648])).
% 1.62/1.88 tff(4650,plain,
% 1.62/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 1.62/1.88 inference(transitivity,[status(thm)],[4649, 4647])).
% 1.62/1.88 tff(4651,plain,
% 1.62/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 1.62/1.88 inference(quant_inst,[status(thm)],[])).
% 1.62/1.88 tff(4652,plain,
% 1.62/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z))),
% 1.62/1.88 inference(modus_ponens,[status(thm)],[4651, 4650])).
% 1.62/1.88 tff(4653,plain,
% 1.62/1.88 ($false),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[4652, 37, 4646, 4627, 4639])).
% 1.62/1.88 tff(4654,plain,((~(elem!1 = s(s(s(s(z)))))) | (elem!1 = s(s(s(z)))) | (~r(elem!1, s(z))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (s(s(s(z))) = s(s(elem!1))) | (~r(z, s(z))) | r(elem!1, s(s(elem!1))) | (s(s(elem!1)) = s(s(z))) | (~r(s(s(s(z))), elem!1)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.88 tff(4655,plain,
% 1.62/1.88 (~(elem!1 = s(s(s(s(z)))))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[4654, 3427, 114, 4545, 4544, 4542, 506, 2217, 4534, 1061, 107])).
% 1.62/1.88 tff(4656,plain,
% 1.62/1.88 (~(s(s(s(s(z)))) = elem!1)),
% 1.62/1.88 inference(modus_ponens,[status(thm)],[4655, 4532])).
% 1.62/1.88 tff(4657,plain,
% 1.62/1.88 (b(elem!1, s(s(s(s(z)))))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[278, 4655, 4148])).
% 1.62/1.88 tff(4658,plain,
% 1.62/1.88 (~b(s(z), z)),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[4644, 75, 4545, 4544, 107])).
% 1.62/1.88 tff(4659,plain,
% 1.62/1.88 (r(s(z), z)),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[169, 4658])).
% 1.62/1.88 tff(4660,plain,
% 1.62/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)))),
% 1.62/1.88 inference(rewrite,[status(thm)],[])).
% 1.62/1.88 tff(4661,plain,
% 1.62/1.88 (((~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)))),
% 1.62/1.88 inference(rewrite,[status(thm)],[])).
% 1.62/1.88 tff(4662,plain,
% 1.62/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z))))),
% 1.62/1.88 inference(monotonicity,[status(thm)],[4661])).
% 1.62/1.88 tff(4663,plain,
% 1.62/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)))),
% 1.62/1.88 inference(transitivity,[status(thm)],[4662, 4660])).
% 1.62/1.88 tff(4664,plain,
% 1.62/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.62/1.88 inference(quant_inst,[status(thm)],[])).
% 1.62/1.88 tff(4665,plain,
% 1.62/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z))),
% 1.62/1.88 inference(modus_ponens,[status(thm)],[4664, 4663])).
% 1.62/1.88 tff(4666,plain,
% 1.62/1.88 ($false),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[4665, 75, 1518, 1958, 286, 1423])).
% 1.62/1.88 tff(4667,plain,((~b(s(s(s(s(z)))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.88 tff(4668,plain,
% 1.62/1.88 (~b(s(s(s(s(z)))), z)),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[4667, 4545, 4544, 4657])).
% 1.62/1.88 tff(4669,plain,
% 1.62/1.88 (r(s(s(s(s(z)))), z)),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[1421, 58, 1143, 4668])).
% 1.62/1.88 tff(4670,plain,
% 1.62/1.88 (~r(s(z), s(s(s(s(z)))))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[2586, 4669, 4659])).
% 1.62/1.88 tff(4671,plain,
% 1.62/1.88 (b(s(z), s(s(s(s(z)))))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[488, 4670, 484])).
% 1.62/1.88 tff(4672,plain,
% 1.62/1.88 (~b(s(s(s(s(z)))), elem!1)),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[586, 4671, 107, 4657])).
% 1.62/1.88 tff(4673,plain,
% 1.62/1.88 (~r(s(s(s(s(z)))), elem!1)),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[3531, 4671, 1082, 1061])).
% 1.62/1.88 tff(4674,plain,
% 1.62/1.88 ($false),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[283, 4673, 4672, 4656])).
% 1.62/1.88 tff(4675,plain,((~r(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(z, s(z))) | r(elem!1, s(s(elem!1))) | (s(s(s(z))) = elem!1) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.62/1.88 tff(4676,plain,
% 1.62/1.88 (r(elem!1, s(s(elem!1)))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[4675, 4531, 4509, 114, 1061, 1031, 13])).
% 1.62/1.88 tff(4677,plain,
% 1.62/1.88 (~r(s(z), s(s(elem!1)))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[3615, 4676, 114])).
% 1.62/1.88 tff(4678,plain,
% 1.62/1.88 (b(s(z), s(s(elem!1)))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[1890, 4677])).
% 1.62/1.88 tff(4679,plain,
% 1.62/1.88 (~b(s(s(elem!1)), s(z))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[4506, 4678, 16, 1082, 1061, 2647])).
% 1.62/1.88 tff(4680,plain,
% 1.62/1.88 (r(s(s(elem!1)), s(z))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[561, 4679])).
% 1.62/1.88 tff(4681,plain,
% 1.62/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, 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)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 1.62/1.88 inference(rewrite,[status(thm)],[])).
% 1.62/1.88 tff(4682,plain,
% 1.62/1.88 (((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 1.62/1.88 inference(rewrite,[status(thm)],[])).
% 1.62/1.88 tff(4683,plain,
% 1.62/1.88 (((~![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(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)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))))),
% 1.62/1.88 inference(monotonicity,[status(thm)],[4682])).
% 1.62/1.88 tff(4684,plain,
% 1.62/1.88 (((~![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(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)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 1.62/1.88 inference(transitivity,[status(thm)],[4683, 4681])).
% 1.62/1.88 tff(4685,plain,
% 1.62/1.88 ((~![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(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 1.62/1.88 inference(quant_inst,[status(thm)],[])).
% 1.62/1.88 tff(4686,plain,
% 1.62/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))),
% 1.62/1.88 inference(modus_ponens,[status(thm)],[4685, 4684])).
% 1.62/1.88 tff(4687,plain,
% 1.62/1.88 ($false),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[4686, 37, 4680, 4676, 114, 2647])).
% 1.62/1.88 tff(4688,plain,((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(z))) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(s(s(z))), elem!1)) | (s(s(s(z))) = elem!1) | r(z, elem!1) | (~b(z, elem!1)) | (elem!1 = z) | (~(s(s(s(s(z)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.88 tff(4689,plain,
% 1.62/1.88 (~r(s(s(elem!1)), elem!1)),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[4688, 1061, 16, 114, 1031, 13, 1518, 353, 3285])).
% 1.62/1.88 tff(4690,plain,
% 1.62/1.88 (b(s(s(elem!1)), elem!1)),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[2673, 4689, 4477])).
% 1.62/1.88 tff(4691,plain,
% 1.62/1.88 (~b(s(s(elem!1)), z)),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[2795, 75, 1518, 1958, 707])).
% 1.62/1.88 tff(4692,plain,
% 1.62/1.88 (r(s(s(elem!1)), z)),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[2696, 4691])).
% 1.62/1.88 tff(4693,plain,
% 1.62/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)))),
% 1.62/1.88 inference(rewrite,[status(thm)],[])).
% 1.62/1.88 tff(4694,plain,
% 1.62/1.88 (((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(z))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)))),
% 1.62/1.88 inference(rewrite,[status(thm)],[])).
% 1.62/1.88 tff(4695,plain,
% 1.62/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1)), elem!1)) | (~b(elem!1, 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(X1, 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(z)))) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z))))),
% 1.62/1.88 inference(monotonicity,[status(thm)],[4694])).
% 1.62/1.88 tff(4696,plain,
% 1.62/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1)), elem!1)) | (~b(elem!1, 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(X1, 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(z)))) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)))),
% 1.62/1.88 inference(transitivity,[status(thm)],[4695, 4693])).
% 1.62/1.88 tff(4697,plain,
% 1.62/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.62/1.88 inference(quant_inst,[status(thm)],[])).
% 1.62/1.88 tff(4698,plain,
% 1.62/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z))),
% 1.62/1.88 inference(modus_ponens,[status(thm)],[4697, 4696])).
% 1.62/1.88 tff(4699,plain,
% 1.62/1.88 (~b(s(s(elem!1)), s(s(z)))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[4698, 75, 1518, 1958, 964, 707])).
% 1.62/1.88 tff(4700,plain,
% 1.62/1.88 (r(s(s(elem!1)), s(s(z)))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[1476, 4699, 266])).
% 1.62/1.88 tff(4701,plain,
% 1.62/1.88 ($false),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[2319, 37, 4387, 4700, 4692])).
% 1.62/1.88 tff(4702,plain,((~b(elem!1, z)) | (s(s(elem!1)) = s(s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.88 tff(4703,plain,
% 1.62/1.88 (~b(elem!1, z)),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[4702, 4690, 1518, 964, 266])).
% 1.62/1.88 tff(4704,plain,
% 1.62/1.88 (r(elem!1, z)),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[387, 4703, 353])).
% 1.62/1.88 tff(4705,plain,
% 1.62/1.88 (~r(z, s(z))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[177, 4704, 114])).
% 1.62/1.88 tff(4706,plain,
% 1.62/1.88 (~b(z, s(z))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[4519, 4704, 1061, 114])).
% 1.62/1.88 tff(4707,plain,
% 1.62/1.88 ($false),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[187, 4706, 4705])).
% 1.62/1.88 tff(4708,plain,((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(z))) | (elem!1 = z) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (s(s(elem!1)) = s(s(z))) | (s(s(s(z))) = s(s(elem!1))) | (s(s(s(z))) = elem!1) | r(z, elem!1) | (~(s(s(s(s(z)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.88 tff(4709,plain,
% 1.62/1.88 (~r(s(s(s(z))), elem!1)),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[4708, 3285, 353, 1518, 964, 266, 16, 1031, 13, 114])).
% 1.62/1.88 tff(4710,plain,
% 1.62/1.88 (b(s(s(s(z))), elem!1)),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[1115, 4709, 1031])).
% 1.62/1.88 tff(4711,plain,
% 1.62/1.88 (~b(s(s(elem!1)), z)),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[3694, 75, 1518, 1620, 707])).
% 1.62/1.88 tff(4712,plain,
% 1.62/1.88 (r(s(s(elem!1)), z)),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[518, 58, 515, 4711])).
% 1.62/1.88 tff(4713,plain,
% 1.62/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(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(X1, 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)), elem!1)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 1.62/1.88 inference(rewrite,[status(thm)],[])).
% 1.62/1.88 tff(4714,plain,
% 1.62/1.88 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(z))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 1.62/1.88 inference(rewrite,[status(thm)],[])).
% 1.62/1.89 tff(4715,plain,
% 1.62/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~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(X1, 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)), elem!1)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), elem!1))))),
% 1.62/1.89 inference(monotonicity,[status(thm)],[4714])).
% 1.62/1.89 tff(4716,plain,
% 1.62/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~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(X1, 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)), elem!1)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 1.62/1.89 inference(transitivity,[status(thm)],[4715, 4713])).
% 1.62/1.89 tff(4717,plain,
% 1.62/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.62/1.89 inference(quant_inst,[status(thm)],[])).
% 1.62/1.89 tff(4718,plain,
% 1.62/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), elem!1))),
% 1.62/1.89 inference(modus_ponens,[status(thm)],[4717, 4716])).
% 1.62/1.89 tff(4719,plain,
% 1.62/1.89 (~b(s(s(elem!1)), s(s(z)))),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[4718, 75, 1620, 964, 707])).
% 1.62/1.89 tff(4720,plain,
% 1.62/1.89 (r(s(s(elem!1)), s(s(z)))),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[1476, 4719, 266])).
% 1.62/1.89 tff(4721,plain,
% 1.62/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)))),
% 1.62/1.89 inference(rewrite,[status(thm)],[])).
% 1.62/1.89 tff(4722,plain,
% 1.62/1.89 (((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)))),
% 1.62/1.89 inference(rewrite,[status(thm)],[])).
% 1.62/1.89 tff(4723,plain,
% 1.62/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1))))),
% 1.62/1.89 inference(monotonicity,[status(thm)],[4722])).
% 1.62/1.89 tff(4724,plain,
% 1.62/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)))),
% 1.62/1.89 inference(transitivity,[status(thm)],[4723, 4721])).
% 1.62/1.89 tff(4725,plain,
% 1.62/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 1.62/1.89 inference(quant_inst,[status(thm)],[])).
% 1.62/1.89 tff(4726,plain,
% 1.62/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1))),
% 1.62/1.89 inference(modus_ponens,[status(thm)],[4725, 4724])).
% 1.62/1.89 tff(4727,plain,
% 1.62/1.89 (~b(s(s(z)), z)),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[4726, 75, 1518, 1620, 964, 707])).
% 1.62/1.89 tff(4728,plain,
% 1.62/1.89 (r(s(s(z)), z)),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[202, 4727])).
% 1.62/1.89 tff(4729,plain,
% 1.62/1.89 ($false),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[2319, 37, 4728, 4720, 4712])).
% 1.62/1.89 tff(4730,plain,((~b(s(s(elem!1)), elem!1)) | (s(s(elem!1)) = s(s(z))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.89 tff(4731,plain,
% 1.62/1.89 (~b(elem!1, s(s(elem!1)))),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[4730, 707, 964, 1518, 266])).
% 1.62/1.89 tff(4732,plain,
% 1.62/1.89 (r(elem!1, s(s(elem!1)))),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[1617, 4731, 4476])).
% 1.62/1.89 tff(4733,plain,
% 1.62/1.89 (~b(elem!1, z)),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[4702, 707, 1518, 964, 266])).
% 1.62/1.89 tff(4734,plain,
% 1.62/1.89 (r(elem!1, z)),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[387, 4733, 353])).
% 1.62/1.89 tff(4735,plain,
% 1.62/1.89 (~r(s(z), z)),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[162, 4734, 114])).
% 1.62/1.89 tff(4736,plain,
% 1.62/1.89 (b(s(z), z)),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[169, 4735])).
% 1.62/1.89 tff(4737,plain,
% 1.62/1.89 (~r(z, s(z))),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[177, 4734, 114])).
% 1.62/1.89 tff(4738,plain,
% 1.62/1.89 (b(z, s(z))),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[187, 4737])).
% 1.62/1.89 tff(4739,plain,
% 1.62/1.89 (r(s(s(s(s(z)))), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 1.62/1.89 inference(monotonicity,[status(thm)],[3285])).
% 1.62/1.89 tff(4740,plain,
% 1.62/1.89 (r(elem!1, s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.62/1.89 inference(symmetry,[status(thm)],[4739])).
% 1.62/1.89 tff(4741,plain,
% 1.62/1.89 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.62/1.89 inference(modus_ponens,[status(thm)],[4732, 4740])).
% 1.62/1.89 tff(4742,plain,
% 1.62/1.89 (r(s(s(s(s(z)))), z) <=> r(elem!1, z)),
% 1.62/1.89 inference(monotonicity,[status(thm)],[3285])).
% 1.62/1.89 tff(4743,plain,
% 1.62/1.89 (r(elem!1, z) <=> r(s(s(s(s(z)))), z)),
% 1.62/1.89 inference(symmetry,[status(thm)],[4742])).
% 1.62/1.89 tff(4744,plain,
% 1.62/1.89 (r(s(s(s(s(z)))), z)),
% 1.62/1.89 inference(modus_ponens,[status(thm)],[4734, 4743])).
% 1.62/1.89 tff(4745,plain,
% 1.62/1.89 (~r(s(s(elem!1)), z)),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[2707, 4744, 4741])).
% 1.62/1.89 tff(4746,plain,
% 1.62/1.89 (b(s(s(elem!1)), z)),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[2696, 4745])).
% 1.62/1.89 tff(4747,plain,
% 1.62/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), z)) | (~b(s(s(elem!1)), s(z))))),
% 1.62/1.89 inference(rewrite,[status(thm)],[])).
% 1.62/1.89 tff(4748,plain,
% 1.62/1.89 (((~b(z, s(z))) | (~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(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 1.62/1.89 inference(rewrite,[status(thm)],[])).
% 1.62/1.89 tff(4749,plain,
% 1.62/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), 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(X1, 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)), z)) | (~b(s(s(elem!1)), s(z)))))),
% 1.62/1.89 inference(monotonicity,[status(thm)],[4748])).
% 1.62/1.89 tff(4750,plain,
% 1.62/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), 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(X1, 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)), z)) | (~b(s(s(elem!1)), s(z))))),
% 1.62/1.89 inference(transitivity,[status(thm)],[4749, 4747])).
% 1.62/1.89 tff(4751,plain,
% 1.62/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))),
% 1.62/1.89 inference(quant_inst,[status(thm)],[])).
% 1.62/1.89 tff(4752,plain,
% 1.62/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z)))),
% 1.62/1.89 inference(modus_ponens,[status(thm)],[4751, 4750])).
% 1.62/1.89 tff(4753,plain,
% 1.62/1.89 ($false),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[4752, 75, 1457, 372, 371, 1892])).
% 1.62/1.89 tff(4754,plain,((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.89 tff(4755,plain,
% 1.62/1.89 (~b(s(s(elem!1)), s(z))),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[4754, 4746, 4738, 4736])).
% 1.62/1.89 tff(4756,plain,
% 1.62/1.89 (r(s(s(elem!1)), s(z))),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[561, 4755])).
% 1.62/1.89 tff(4757,plain,
% 1.62/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(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)))))),
% 1.62/1.89 inference(rewrite,[status(thm)],[])).
% 1.62/1.89 tff(4758,plain,
% 1.62/1.89 (((~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)))))),
% 1.62/1.89 inference(rewrite,[status(thm)],[])).
% 1.62/1.89 tff(4759,plain,
% 1.62/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(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))))))),
% 1.62/1.89 inference(monotonicity,[status(thm)],[4758])).
% 1.62/1.89 tff(4760,plain,
% 1.62/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(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)))))),
% 1.62/1.89 inference(transitivity,[status(thm)],[4759, 4757])).
% 1.62/1.89 tff(4761,plain,
% 1.62/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))))),
% 1.62/1.89 inference(quant_inst,[status(thm)],[])).
% 1.62/1.89 tff(4762,plain,
% 1.62/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1))))),
% 1.62/1.89 inference(modus_ponens,[status(thm)],[4761, 4760])).
% 1.62/1.89 tff(4763,plain,
% 1.62/1.89 ($false),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[4762, 37, 4756, 4732, 114])).
% 1.62/1.89 tff(4764,plain,((~b(s(s(elem!1)), elem!1)) | (~r(elem!1, s(z))) | (~(s(s(s(s(z)))) = elem!1)) | (elem!1 = z) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (s(s(elem!1)) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.89 tff(4765,plain,
% 1.62/1.89 (~b(s(s(elem!1)), elem!1)),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[4764, 3285, 114, 353, 1518, 964, 266])).
% 1.62/1.89 tff(4766,plain,
% 1.62/1.89 (r(s(s(elem!1)), elem!1)),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[2673, 4765, 4477])).
% 1.62/1.89 tff(4767,plain,
% 1.62/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(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(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))),
% 1.62/1.89 inference(rewrite,[status(thm)],[])).
% 1.62/1.89 tff(4768,plain,
% 1.62/1.89 (((~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))),
% 1.62/1.89 inference(rewrite,[status(thm)],[])).
% 1.62/1.89 tff(4769,plain,
% 1.62/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, 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(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1))))),
% 1.62/1.89 inference(monotonicity,[status(thm)],[4768])).
% 1.62/1.89 tff(4770,plain,
% 1.62/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, 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(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))),
% 1.62/1.89 inference(transitivity,[status(thm)],[4769, 4767])).
% 1.62/1.89 tff(4771,plain,
% 1.62/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)))),
% 1.62/1.89 inference(quant_inst,[status(thm)],[])).
% 1.62/1.89 tff(4772,plain,
% 1.62/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1))),
% 1.62/1.89 inference(modus_ponens,[status(thm)],[4771, 4770])).
% 1.62/1.89 tff(4773,plain,
% 1.62/1.89 ($false),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[4772, 37, 155, 2647, 2698])).
% 1.62/1.89 tff(4774,plain,((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.89 tff(4775,plain,
% 1.62/1.89 (~r(s(s(elem!1)), z)),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[4774, 155, 2647])).
% 1.62/1.89 tff(4776,plain,
% 1.62/1.89 (b(s(s(elem!1)), z)),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[2696, 4775])).
% 1.62/1.89 tff(4777,plain,
% 1.62/1.89 (~b(s(s(elem!1)), s(z))),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[4754, 4776, 188, 170])).
% 1.62/1.89 tff(4778,plain,
% 1.62/1.89 (r(s(s(elem!1)), s(z))),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[561, 4777])).
% 1.62/1.89 tff(4779,plain,
% 1.62/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(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)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)))),
% 1.62/1.89 inference(rewrite,[status(thm)],[])).
% 1.62/1.89 tff(4780,plain,
% 1.62/1.89 (((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)))),
% 1.62/1.89 inference(rewrite,[status(thm)],[])).
% 1.62/1.89 tff(4781,plain,
% 1.62/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(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)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1))))),
% 1.62/1.89 inference(monotonicity,[status(thm)],[4780])).
% 1.62/1.89 tff(4782,plain,
% 1.62/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(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)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)))),
% 1.62/1.89 inference(transitivity,[status(thm)],[4781, 4779])).
% 1.62/1.89 tff(4783,plain,
% 1.62/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)))),
% 1.62/1.89 inference(quant_inst,[status(thm)],[])).
% 1.62/1.89 tff(4784,plain,
% 1.62/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1))),
% 1.62/1.89 inference(modus_ponens,[status(thm)],[4783, 4782])).
% 1.62/1.89 tff(4785,plain,
% 1.62/1.89 ($false),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[4784, 37, 155, 4778, 114, 2647])).
% 1.62/1.89 tff(4786,plain,((~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.89 tff(4787,plain,
% 1.62/1.89 (~r(elem!1, z)),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[4786, 4766, 114])).
% 1.62/1.89 tff(4788,plain,
% 1.62/1.89 (b(elem!1, z)),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[387, 4787, 353])).
% 1.62/1.89 tff(4789,plain,
% 1.62/1.89 (~b(s(s(s(z))), z)),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[4030, 75, 1518, 4788, 4710])).
% 1.62/1.89 tff(4790,plain,
% 1.62/1.89 (r(s(s(s(z))), z)),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[1334, 58, 221, 4789])).
% 1.62/1.89 tff(4791,plain,
% 1.62/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.62/1.89 inference(rewrite,[status(thm)],[])).
% 1.62/1.89 tff(4792,plain,
% 1.62/1.89 (((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.62/1.89 inference(rewrite,[status(thm)],[])).
% 1.62/1.89 tff(4793,plain,
% 1.62/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, 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(X1, 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(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), s(s(s(z)))))))),
% 1.72/1.90 inference(monotonicity,[status(thm)],[4792])).
% 1.72/1.90 tff(4794,plain,
% 1.72/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, 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(X1, 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(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.72/1.90 inference(transitivity,[status(thm)],[4793, 4791])).
% 1.72/1.90 tff(4795,plain,
% 1.72/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.72/1.90 inference(quant_inst,[status(thm)],[])).
% 1.72/1.90 tff(4796,plain,
% 1.72/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), s(s(s(z)))))),
% 1.72/1.90 inference(modus_ponens,[status(thm)],[4795, 4794])).
% 1.72/1.90 tff(4797,plain,
% 1.72/1.90 (~b(s(s(z)), s(s(s(z))))),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[4796, 75, 1518, 4788, 964, 4710])).
% 1.72/1.90 tff(4798,plain,
% 1.72/1.90 (r(s(s(z)), s(s(s(z))))),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[1559, 58, 1556, 4797])).
% 1.72/1.90 tff(4799,plain,
% 1.72/1.90 (~b(s(s(z)), z)),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[4385, 75, 1518, 4788, 964])).
% 1.72/1.90 tff(4800,plain,
% 1.72/1.90 (r(s(s(z)), z)),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[202, 4799])).
% 1.72/1.90 tff(4801,plain,
% 1.72/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 1.72/1.90 inference(rewrite,[status(thm)],[])).
% 1.72/1.90 tff(4802,plain,
% 1.72/1.90 (((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 1.72/1.90 inference(rewrite,[status(thm)],[])).
% 1.72/1.90 tff(4803,plain,
% 1.72/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z))))),
% 1.72/1.90 inference(monotonicity,[status(thm)],[4802])).
% 1.72/1.90 tff(4804,plain,
% 1.72/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 1.72/1.90 inference(transitivity,[status(thm)],[4803, 4801])).
% 1.72/1.90 tff(4805,plain,
% 1.72/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 1.72/1.90 inference(quant_inst,[status(thm)],[])).
% 1.72/1.90 tff(4806,plain,
% 1.72/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z))),
% 1.72/1.90 inference(modus_ponens,[status(thm)],[4805, 4804])).
% 1.72/1.90 tff(4807,plain,
% 1.72/1.90 ($false),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[4806, 37, 4800, 4798, 4790])).
% 1.72/1.90 tff(4808,plain,((~(s(s(s(s(z)))) = elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (elem!1 = z) | (~r(elem!1, s(z))) | (s(s(elem!1)) = s(s(z))) | (s(s(s(z))) = elem!1) | (s(s(s(z))) = s(s(elem!1))) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.72/1.90 tff(4809,plain,
% 1.72/1.90 (~(s(s(s(s(z)))) = elem!1)),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[4808, 4317, 4142, 4316, 90, 4460, 4459, 16, 13])).
% 1.72/1.90 tff(4810,plain,
% 1.72/1.90 (b(s(s(s(s(z)))), elem!1)),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[283, 4809, 12])).
% 1.72/1.90 tff(4811,plain,
% 1.72/1.90 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[4421, 268, 12, 964, 1518, 267])).
% 1.72/1.90 tff(4812,plain,
% 1.72/1.90 (b(s(s(z)), s(s(s(s(z)))))),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[465, 4811])).
% 1.72/1.90 tff(4813,plain,
% 1.72/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(s(s(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(X1, 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(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.72/1.90 inference(rewrite,[status(thm)],[])).
% 1.72/1.90 tff(4814,plain,
% 1.72/1.90 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(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, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.72/1.90 inference(rewrite,[status(thm)],[])).
% 1.72/1.90 tff(4815,plain,
% 1.72/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.72/1.90 inference(monotonicity,[status(thm)],[4814])).
% 1.72/1.90 tff(4816,plain,
% 1.72/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.72/1.90 inference(transitivity,[status(thm)],[4815, 4813])).
% 1.72/1.90 tff(4817,plain,
% 1.72/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.72/1.90 inference(quant_inst,[status(thm)],[])).
% 1.72/1.90 tff(4818,plain,
% 1.72/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))),
% 1.72/1.90 inference(modus_ponens,[status(thm)],[4817, 4816])).
% 1.72/1.90 tff(4819,plain,
% 1.72/1.90 ($false),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[4818, 75, 964, 279, 2561, 4812])).
% 1.72/1.90 tff(4820,plain,(r(elem!1, s(s(s(s(z))))) | (~b(s(s(z)), elem!1)) | r(s(s(s(s(z)))), elem!1) | (~b(z, elem!1)) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.72/1.90 tff(4821,plain,
% 1.72/1.90 (r(elem!1, s(s(s(s(z)))))),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[4820, 4809, 12, 4317, 4142])).
% 1.72/1.90 tff(4822,plain,
% 1.72/1.90 (~r(s(s(s(z))), elem!1)),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[3255, 4821, 90])).
% 1.72/1.90 tff(4823,plain,
% 1.72/1.90 (b(s(s(s(z))), elem!1)),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[1115, 4822, 4459])).
% 1.72/1.90 tff(4824,plain,
% 1.72/1.90 (~b(elem!1, z)),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[4040, 4823, 4317, 4810])).
% 1.72/1.90 tff(4825,plain,
% 1.72/1.90 (r(elem!1, z)),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[387, 4824, 4316])).
% 1.72/1.90 tff(4826,plain,
% 1.72/1.90 (~r(z, s(z))),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[177, 4825, 90])).
% 1.72/1.90 tff(4827,plain,
% 1.72/1.90 (b(z, s(z))),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[187, 4826])).
% 1.72/1.90 tff(4828,plain,
% 1.72/1.90 (~r(s(z), s(s(s(s(z)))))),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[3203, 4821, 90])).
% 1.72/1.90 tff(4829,plain,
% 1.72/1.90 (b(s(z), s(s(s(s(z)))))),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[489, 4828])).
% 1.72/1.90 tff(4830,plain,
% 1.72/1.90 (~r(s(z), z)),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[162, 4825, 90])).
% 1.72/1.90 tff(4831,plain,
% 1.72/1.90 (b(s(z), z)),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[169, 4830])).
% 1.72/1.90 tff(4832,plain,
% 1.72/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.72/1.90 inference(rewrite,[status(thm)],[])).
% 1.72/1.90 tff(4833,plain,
% 1.72/1.90 (((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.72/1.90 inference(rewrite,[status(thm)],[])).
% 1.72/1.90 tff(4834,plain,
% 1.72/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))))),
% 1.72/1.90 inference(monotonicity,[status(thm)],[4833])).
% 1.72/1.90 tff(4835,plain,
% 1.72/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.72/1.90 inference(transitivity,[status(thm)],[4834, 4832])).
% 1.72/1.90 tff(4836,plain,
% 1.72/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.72/1.90 inference(quant_inst,[status(thm)],[])).
% 1.72/1.90 tff(4837,plain,
% 1.72/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 1.72/1.90 inference(modus_ponens,[status(thm)],[4836, 4835])).
% 1.72/1.90 tff(4838,plain,
% 1.72/1.90 ($false),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[4837, 75, 372, 371, 578, 1423])).
% 1.72/1.90 tff(4839,plain,((~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.90 tff(4840,plain,
% 1.72/1.90 (~b(s(s(s(s(z)))), z)),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[4839, 4831, 4829, 4827])).
% 1.72/1.90 tff(4841,plain,
% 1.72/1.90 (r(s(s(s(s(z)))), z)),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[1421, 58, 1143, 4840])).
% 1.72/1.90 tff(4842,plain,
% 1.72/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(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(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.72/1.90 inference(rewrite,[status(thm)],[])).
% 1.72/1.90 tff(4843,plain,
% 1.72/1.90 (((~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.72/1.90 inference(rewrite,[status(thm)],[])).
% 1.72/1.90 tff(4844,plain,
% 1.72/1.90 (((~![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(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))))),
% 1.72/1.90 inference(monotonicity,[status(thm)],[4843])).
% 1.72/1.90 tff(4845,plain,
% 1.72/1.90 (((~![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(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.72/1.90 inference(transitivity,[status(thm)],[4844, 4842])).
% 1.72/1.90 tff(4846,plain,
% 1.72/1.90 ((~![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(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.72/1.90 inference(quant_inst,[status(thm)],[])).
% 1.72/1.90 tff(4847,plain,
% 1.72/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 1.72/1.90 inference(modus_ponens,[status(thm)],[4846, 4845])).
% 1.72/1.90 tff(4848,plain,
% 1.72/1.90 ($false),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[4847, 37, 4825, 4821, 4841])).
% 1.72/1.90 tff(4849,plain,((s(s(s(z))) = s(s(elem!1))) | r(s(s(s(s(z)))), elem!1) | r(z, elem!1) | (s(s(z)) = elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.90 tff(4850,plain,
% 1.72/1.90 (s(s(s(z))) = s(s(elem!1))),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[4849, 15, 13, 12, 14])).
% 1.72/1.90 tff(4851,plain,
% 1.72/1.90 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.72/1.90 inference(monotonicity,[status(thm)],[4850])).
% 1.72/1.90 tff(4852,plain,
% 1.72/1.90 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.72/1.90 inference(symmetry,[status(thm)],[4851])).
% 1.72/1.90 tff(4853,plain,
% 1.72/1.90 (r(s(s(s(elem!1))), z) <=> r(s(s(s(s(z)))), z)),
% 1.72/1.90 inference(monotonicity,[status(thm)],[4852])).
% 1.72/1.90 tff(4854,plain,
% 1.72/1.90 (r(s(s(s(s(z)))), z) <=> r(s(s(s(elem!1))), z)),
% 1.72/1.90 inference(symmetry,[status(thm)],[4853])).
% 1.72/1.90 tff(4855,plain,
% 1.72/1.90 ((~r(s(s(s(s(z)))), z)) <=> (~r(s(s(s(elem!1))), z))),
% 1.72/1.90 inference(monotonicity,[status(thm)],[4854])).
% 1.72/1.90 tff(4856,plain,
% 1.72/1.90 (s(s(z)) = s(elem!1)),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[4541, 4850])).
% 1.72/1.90 tff(4857,plain,
% 1.72/1.90 (s(z) = elem!1),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[3261, 4856])).
% 1.72/1.90 tff(4858,plain,
% 1.72/1.90 (r(s(z), z) <=> r(elem!1, z)),
% 1.72/1.90 inference(monotonicity,[status(thm)],[4857])).
% 1.72/1.90 tff(4859,plain,
% 1.72/1.90 (r(elem!1, z) <=> r(s(z), z)),
% 1.72/1.90 inference(symmetry,[status(thm)],[4858])).
% 1.72/1.90 tff(4860,plain,
% 1.72/1.90 (s(s(elem!1)) = s(s(s(z)))),
% 1.72/1.90 inference(symmetry,[status(thm)],[4537])).
% 1.72/1.90 tff(4861,plain,
% 1.72/1.90 (s(s(z)) = s(s(s(z)))),
% 1.72/1.90 inference(transitivity,[status(thm)],[3571, 4860])).
% 1.72/1.90 tff(4862,plain,
% 1.72/1.90 (inj_0(s(s(z))) = inj_0(s(s(s(z))))),
% 1.72/1.90 inference(monotonicity,[status(thm)],[4861])).
% 1.72/1.90 tff(4863,plain,
% 1.72/1.90 (inj_0(s(s(s(z)))) = inj_0(s(s(z)))),
% 1.72/1.90 inference(symmetry,[status(thm)],[4862])).
% 1.72/1.90 tff(4864,plain,
% 1.72/1.90 (s(s(z)) = s(z)),
% 1.72/1.90 inference(transitivity,[status(thm)],[254, 4863, 133])).
% 1.72/1.90 tff(4865,plain,
% 1.72/1.90 ($false),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[148, 4864])).
% 1.72/1.90 tff(4866,plain,((~(s(s(s(z))) = s(s(elem!1)))) | (~(s(s(elem!1)) = s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.90 tff(4867,plain,
% 1.72/1.90 (~(s(s(elem!1)) = s(s(z)))),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[4866, 4850])).
% 1.72/1.90 tff(4868,plain,
% 1.72/1.90 (~(z = elem!1)),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[293, 4867])).
% 1.72/1.90 tff(4869,plain,
% 1.72/1.90 (~(elem!1 = z)),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[304, 4868])).
% 1.72/1.90 tff(4870,plain,
% 1.72/1.90 (b(z, elem!1)),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[298, 4868, 13])).
% 1.72/1.90 tff(4871,plain,
% 1.72/1.90 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 1.72/1.90 inference(monotonicity,[status(thm)],[4539])).
% 1.72/1.90 tff(4872,plain,
% 1.72/1.90 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 1.72/1.90 inference(symmetry,[status(thm)],[4871])).
% 1.72/1.90 tff(4873,plain,
% 1.72/1.90 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.72/1.90 inference(monotonicity,[status(thm)],[4537])).
% 1.72/1.90 tff(4874,plain,
% 1.72/1.90 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.72/1.90 inference(symmetry,[status(thm)],[4873])).
% 1.72/1.90 tff(4875,plain,
% 1.72/1.90 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 1.72/1.90 inference(monotonicity,[status(thm)],[4874])).
% 1.72/1.90 tff(4876,plain,
% 1.72/1.90 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 1.72/1.90 inference(transitivity,[status(thm)],[4875, 4872])).
% 1.72/1.90 tff(4877,plain,
% 1.72/1.90 ((~b(s(elem!1), s(s(s(elem!1))))) <=> (~b(s(s(z)), s(s(s(s(z))))))),
% 1.72/1.90 inference(monotonicity,[status(thm)],[4876])).
% 1.72/1.90 tff(4878,plain,
% 1.72/1.90 ((elem!1 = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(s(z)))))),
% 1.72/1.90 inference(monotonicity,[status(thm)],[4874])).
% 1.72/1.90 tff(4879,plain,
% 1.72/1.90 ((elem!1 = s(s(s(s(z))))) <=> (elem!1 = s(s(s(elem!1))))),
% 1.72/1.90 inference(symmetry,[status(thm)],[4878])).
% 1.72/1.90 tff(4880,plain,
% 1.72/1.90 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.72/1.90 inference(transitivity,[status(thm)],[4879, 3277])).
% 1.72/1.90 tff(4881,plain,
% 1.72/1.90 ((~(elem!1 = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.72/1.90 inference(monotonicity,[status(thm)],[4880])).
% 1.72/1.90 tff(4882,plain,
% 1.72/1.90 (s(s(z)) = s(elem!1)),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[4541, 4537])).
% 1.72/1.90 tff(4883,plain,
% 1.72/1.90 (s(z) = elem!1),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[3261, 4882])).
% 1.72/1.90 tff(4884,plain,
% 1.72/1.90 ((s(z) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(z)))))),
% 1.72/1.90 inference(monotonicity,[status(thm)],[4883])).
% 1.72/1.90 tff(4885,plain,
% 1.72/1.90 ((~(s(z) = s(s(s(s(z)))))) <=> (~(elem!1 = s(s(s(s(z))))))),
% 1.72/1.90 inference(monotonicity,[status(thm)],[4884])).
% 1.72/1.90 tff(4886,plain,
% 1.72/1.90 (~(elem!1 = s(s(s(s(z)))))),
% 1.72/1.90 inference(modus_ponens,[status(thm)],[484, 4885])).
% 1.72/1.90 tff(4887,plain,
% 1.72/1.90 (~(s(s(s(elem!1))) = elem!1)),
% 1.72/1.90 inference(modus_ponens,[status(thm)],[4886, 4881])).
% 1.72/1.90 tff(4888,plain,
% 1.72/1.90 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 1.72/1.90 inference(monotonicity,[status(thm)],[4874])).
% 1.72/1.90 tff(4889,plain,
% 1.72/1.90 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 1.72/1.90 inference(symmetry,[status(thm)],[4888])).
% 1.72/1.90 tff(4890,plain,
% 1.72/1.90 ((~r(s(s(s(s(z)))), elem!1)) <=> (~r(s(s(s(elem!1))), elem!1))),
% 1.72/1.90 inference(monotonicity,[status(thm)],[4889])).
% 1.72/1.90 tff(4891,plain,
% 1.72/1.90 (~r(s(s(s(elem!1))), elem!1)),
% 1.72/1.90 inference(modus_ponens,[status(thm)],[12, 4890])).
% 1.72/1.90 tff(4892,plain,
% 1.72/1.90 (b(s(s(s(elem!1))), elem!1)),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[3368, 58, 4891, 4887])).
% 1.72/1.90 tff(4893,plain,
% 1.72/1.90 (inj_0(s(s(elem!1))) = inj_0(s(s(s(z))))),
% 1.72/1.90 inference(symmetry,[status(thm)],[4538])).
% 1.72/1.90 tff(4894,plain,
% 1.72/1.90 (s(elem!1) = s(s(z))),
% 1.72/1.90 inference(transitivity,[status(thm)],[229, 4893, 253])).
% 1.72/1.90 tff(4895,plain,
% 1.72/1.90 (r(s(elem!1), elem!1) <=> r(s(s(z)), elem!1)),
% 1.72/1.91 inference(monotonicity,[status(thm)],[4894])).
% 1.72/1.91 tff(4896,plain,
% 1.72/1.91 ((~r(s(elem!1), elem!1)) <=> (~r(s(s(z)), elem!1))),
% 1.72/1.91 inference(monotonicity,[status(thm)],[4895])).
% 1.72/1.91 tff(4897,plain,
% 1.72/1.91 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[719, 4883])).
% 1.72/1.91 tff(4898,plain,
% 1.72/1.91 (~(s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[862, 4886])).
% 1.72/1.91 tff(4899,plain,
% 1.72/1.91 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[870, 4898])).
% 1.72/1.91 tff(4900,plain,
% 1.72/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.72/1.91 inference(rewrite,[status(thm)],[])).
% 1.72/1.91 tff(4901,plain,
% 1.72/1.91 (((~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))) <=> ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.72/1.91 inference(rewrite,[status(thm)],[])).
% 1.72/1.91 tff(4902,plain,
% 1.72/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 1.72/1.91 inference(monotonicity,[status(thm)],[4901])).
% 1.72/1.91 tff(4903,plain,
% 1.72/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.72/1.91 inference(transitivity,[status(thm)],[4902, 4900])).
% 1.72/1.91 tff(4904,plain,
% 1.72/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 1.72/1.91 inference(quant_inst,[status(thm)],[])).
% 1.72/1.91 tff(4905,plain,
% 1.72/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 1.72/1.91 inference(modus_ponens,[status(thm)],[4904, 4903])).
% 1.72/1.91 tff(4906,plain,
% 1.72/1.91 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[4905, 75, 1518, 1958, 1168, 922])).
% 1.72/1.91 tff(4907,assumption,(~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))), introduced(assumption)).
% 1.72/1.91 tff(4908,plain,
% 1.72/1.91 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[874, 58, 4907, 4906])).
% 1.72/1.91 tff(4909,plain,
% 1.72/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 1.72/1.91 inference(rewrite,[status(thm)],[])).
% 1.72/1.91 tff(4910,plain,
% 1.72/1.91 (((~b(z, elem!1)) | (~b(s(s(s(elem!1))), 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(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 1.72/1.91 inference(rewrite,[status(thm)],[])).
% 1.72/1.91 tff(4911,plain,
% 1.72/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1)))))))),
% 1.72/1.91 inference(monotonicity,[status(thm)],[4910])).
% 1.72/1.91 tff(4912,plain,
% 1.72/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 1.72/1.91 inference(transitivity,[status(thm)],[4911, 4909])).
% 1.72/1.91 tff(4913,plain,
% 1.72/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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))))))),
% 1.72/1.91 inference(quant_inst,[status(thm)],[])).
% 1.72/1.91 tff(4914,plain,
% 1.72/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1)))))),
% 1.72/1.91 inference(modus_ponens,[status(thm)],[4913, 4912])).
% 1.72/1.91 tff(4915,plain,
% 1.72/1.91 (~b(z, s(s(s(elem!1))))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[4914, 75, 1518, 1958, 922])).
% 1.72/1.91 tff(4916,plain,
% 1.72/1.91 ((z = s(s(s(elem!1)))) | r(z, s(s(s(elem!1))))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[674, 58, 4915])).
% 1.72/1.91 tff(4917,plain,
% 1.72/1.91 (r(z, s(s(s(elem!1))))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[4916, 663])).
% 1.72/1.91 tff(4918,plain,
% 1.72/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(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(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 1.72/1.91 inference(rewrite,[status(thm)],[])).
% 1.72/1.91 tff(4919,plain,
% 1.72/1.91 (((~r(s(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(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 1.72/1.91 inference(rewrite,[status(thm)],[])).
% 1.72/1.91 tff(4920,plain,
% 1.72/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))))),
% 1.72/1.91 inference(monotonicity,[status(thm)],[4919])).
% 1.72/1.91 tff(4921,plain,
% 1.72/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 1.72/1.91 inference(transitivity,[status(thm)],[4920, 4918])).
% 1.72/1.91 tff(4922,plain,
% 1.72/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.72/1.91 inference(quant_inst,[status(thm)],[])).
% 1.72/1.91 tff(4923,plain,
% 1.72/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 1.72/1.91 inference(modus_ponens,[status(thm)],[4922, 4921])).
% 1.72/1.91 tff(4924,plain,
% 1.72/1.91 ($false),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[4923, 37, 4917, 2838, 2830, 4908])).
% 1.72/1.91 tff(4925,plain,((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.91 tff(4926,plain,
% 1.72/1.91 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[4925, 1958, 1518, 4899, 4892])).
% 1.72/1.91 tff(4927,plain,
% 1.72/1.91 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[813, 4926, 4897])).
% 1.72/1.91 tff(4928,plain,
% 1.72/1.91 ((elem!1 = s(s(elem!1))) <=> (s(s(elem!1)) = elem!1)),
% 1.72/1.91 inference(symmetry,[status(thm)],[3428])).
% 1.72/1.91 tff(4929,plain,
% 1.72/1.91 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 1.72/1.91 inference(monotonicity,[status(thm)],[4883])).
% 1.72/1.91 tff(4930,plain,
% 1.72/1.91 ((s(s(elem!1)) = s(z)) <=> (elem!1 = s(s(elem!1)))),
% 1.72/1.91 inference(transitivity,[status(thm)],[4929, 3428])).
% 1.72/1.91 tff(4931,plain,
% 1.72/1.91 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 1.72/1.91 inference(transitivity,[status(thm)],[4930, 4928])).
% 1.72/1.91 tff(4932,plain,
% 1.72/1.91 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = elem!1))),
% 1.72/1.91 inference(monotonicity,[status(thm)],[4931])).
% 1.72/1.91 tff(4933,plain,
% 1.72/1.91 (~(s(s(elem!1)) = elem!1)),
% 1.72/1.91 inference(modus_ponens,[status(thm)],[556, 4932])).
% 1.72/1.91 tff(4934,plain,
% 1.72/1.91 (elem!1 = s(z)),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[97, 4883])).
% 1.72/1.91 tff(4935,plain,
% 1.72/1.91 ((s(z) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 1.72/1.91 inference(transitivity,[status(thm)],[4884, 240])).
% 1.72/1.91 tff(4936,plain,
% 1.72/1.91 ((~(s(z) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 1.72/1.91 inference(monotonicity,[status(thm)],[4935])).
% 1.72/1.91 tff(4937,plain,
% 1.72/1.91 (~(s(s(s(s(z)))) = elem!1)),
% 1.72/1.91 inference(modus_ponens,[status(thm)],[484, 4936])).
% 1.72/1.91 tff(4938,plain,
% 1.72/1.91 (b(s(s(s(s(z)))), elem!1)),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[283, 4937, 12])).
% 1.72/1.91 tff(4939,plain,
% 1.72/1.91 (~b(s(s(s(z))), elem!1)),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[4040, 1958, 1518, 4938])).
% 1.72/1.91 tff(4940,plain,
% 1.72/1.91 (~b(s(s(elem!1)), elem!1)),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[3645, 4939, 4934])).
% 1.72/1.91 tff(4941,plain,
% 1.72/1.91 (r(s(s(elem!1)), elem!1)),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[2673, 4940, 4933])).
% 1.72/1.91 tff(4942,plain,
% 1.72/1.91 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(s(z)))),
% 1.72/1.91 inference(monotonicity,[status(thm)],[4894])).
% 1.72/1.91 tff(4943,plain,
% 1.72/1.91 ((~r(s(s(elem!1)), s(elem!1))) <=> (~r(s(s(elem!1)), s(s(z))))),
% 1.72/1.91 inference(monotonicity,[status(thm)],[4942])).
% 1.72/1.91 tff(4944,plain,
% 1.72/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(s(elem!1)), s(elem!1))))),
% 1.72/1.91 inference(rewrite,[status(thm)],[])).
% 1.72/1.91 tff(4945,plain,
% 1.72/1.91 (((~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(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.72/1.91 inference(rewrite,[status(thm)],[])).
% 1.72/1.91 tff(4946,plain,
% 1.72/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), 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(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))))),
% 1.72/1.91 inference(monotonicity,[status(thm)],[4945])).
% 1.72/1.91 tff(4947,plain,
% 1.72/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), 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(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.72/1.91 inference(transitivity,[status(thm)],[4946, 4944])).
% 1.72/1.91 tff(4948,plain,
% 1.72/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.72/1.91 inference(quant_inst,[status(thm)],[])).
% 1.72/1.91 tff(4949,plain,
% 1.72/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.72/1.91 inference(modus_ponens,[status(thm)],[4948, 4947])).
% 1.72/1.91 tff(4950,plain,
% 1.72/1.91 (~r(s(s(elem!1)), s(elem!1))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[4949, 37, 752, 2647])).
% 1.72/1.91 tff(4951,plain,
% 1.72/1.91 (~r(s(s(elem!1)), s(s(z)))),
% 1.72/1.91 inference(modus_ponens,[status(thm)],[4950, 4943])).
% 1.72/1.91 tff(4952,plain,
% 1.72/1.91 (~(s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[3006, 4883])).
% 1.72/1.91 tff(4953,plain,
% 1.72/1.91 (~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[836, 4883])).
% 1.72/1.91 tff(4954,plain,
% 1.72/1.91 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[736, 4883])).
% 1.72/1.91 tff(4955,plain,
% 1.72/1.91 (~b(s(s(elem!1)), s(elem!1))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[3071, 752, 4954, 4953, 2647, 4952, 738])).
% 1.72/1.91 tff(4956,plain,
% 1.72/1.91 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(s(z)))),
% 1.72/1.91 inference(monotonicity,[status(thm)],[18])).
% 1.72/1.91 tff(4957,plain,
% 1.72/1.91 ((~b(s(s(elem!1)), s(elem!1))) <=> (~b(s(s(elem!1)), s(s(z))))),
% 1.72/1.91 inference(monotonicity,[status(thm)],[4956])).
% 1.72/1.91 tff(4958,plain,
% 1.72/1.91 (~b(s(s(elem!1)), s(s(z)))),
% 1.72/1.91 inference(modus_ponens,[status(thm)],[1863, 4957])).
% 1.72/1.91 tff(4959,plain,
% 1.72/1.91 ((z = elem!1) <=> (z = s(z))),
% 1.72/1.91 inference(monotonicity,[status(thm)],[17])).
% 1.72/1.91 tff(4960,plain,
% 1.72/1.91 ((z = elem!1) <=> (s(z) = z)),
% 1.72/1.91 inference(transitivity,[status(thm)],[4959, 179])).
% 1.72/1.91 tff(4961,plain,
% 1.72/1.91 ((s(z) = z) <=> (z = elem!1)),
% 1.72/1.91 inference(symmetry,[status(thm)],[4960])).
% 1.72/1.91 tff(4962,plain,
% 1.72/1.91 ((~(s(z) = z)) <=> (~(z = elem!1))),
% 1.72/1.91 inference(monotonicity,[status(thm)],[4961])).
% 1.72/1.91 tff(4963,plain,
% 1.72/1.91 (~(z = elem!1)),
% 1.72/1.91 inference(modus_ponens,[status(thm)],[165, 4962])).
% 1.72/1.91 tff(4964,plain,
% 1.72/1.91 (~(s(s(elem!1)) = s(s(z)))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[237, 4963])).
% 1.72/1.91 tff(4965,plain,
% 1.72/1.91 ($false),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[1476, 4964, 4958, 1473])).
% 1.72/1.91 tff(4966,plain,((~(elem!1 = s(z))) | r(s(s(elem!1)), s(s(z))) | b(s(s(elem!1)), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.91 tff(4967,plain,
% 1.72/1.91 (r(s(s(elem!1)), s(s(z)))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[4966, 4955, 4934])).
% 1.72/1.91 tff(4968,plain,
% 1.72/1.91 ($false),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[4967, 4951])).
% 1.72/1.91 tff(4969,plain,((~r(s(elem!1), elem!1)) | (~(s(s(s(z))) = s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.91 tff(4970,plain,
% 1.72/1.91 (~r(s(elem!1), elem!1)),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[4969, 4941, 4537, 4927])).
% 1.72/1.91 tff(4971,plain,
% 1.72/1.91 (~r(s(s(z)), elem!1)),
% 1.72/1.91 inference(modus_ponens,[status(thm)],[4970, 4896])).
% 1.72/1.91 tff(4972,plain,
% 1.72/1.91 (b(s(s(z)), elem!1)),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[104, 4971, 15])).
% 1.72/1.91 tff(4973,plain,
% 1.72/1.91 (b(s(elem!1), elem!1)),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[968, 4972, 4883])).
% 1.72/1.91 tff(4974,plain,
% 1.72/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.72/1.91 inference(rewrite,[status(thm)],[])).
% 1.72/1.91 tff(4975,plain,
% 1.72/1.91 (((~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.72/1.91 inference(rewrite,[status(thm)],[])).
% 1.72/1.91 tff(4976,plain,
% 1.72/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~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(X1, 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(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1))))),
% 1.72/1.91 inference(monotonicity,[status(thm)],[4975])).
% 1.72/1.91 tff(4977,plain,
% 1.72/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~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(X1, 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(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.72/1.91 inference(transitivity,[status(thm)],[4976, 4974])).
% 1.72/1.91 tff(4978,plain,
% 1.72/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.72/1.92 inference(quant_inst,[status(thm)],[])).
% 1.72/1.92 tff(4979,plain,
% 1.72/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[4978, 4977])).
% 1.72/1.92 tff(4980,plain,
% 1.72/1.92 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[4979, 75, 1518, 1958, 4973, 4892])).
% 1.72/1.92 tff(4981,plain,
% 1.72/1.92 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[4980, 4877])).
% 1.72/1.92 tff(4982,plain,
% 1.72/1.92 (~(s(s(elem!1)) = s(s(z)))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[4866, 4537])).
% 1.72/1.92 tff(4983,plain,
% 1.72/1.92 (r(s(z), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[4883])).
% 1.72/1.92 tff(4984,plain,
% 1.72/1.92 (r(elem!1, s(s(s(s(z))))) <=> r(s(z), s(s(s(s(z)))))),
% 1.72/1.92 inference(symmetry,[status(thm)],[4983])).
% 1.72/1.92 tff(4985,plain,
% 1.72/1.92 (r(elem!1, s(s(s(s(z)))))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[4820, 4972, 12, 1518, 4937])).
% 1.72/1.92 tff(4986,plain,
% 1.72/1.92 (r(s(z), s(s(s(s(z)))))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[4985, 4984])).
% 1.72/1.92 tff(4987,plain,
% 1.72/1.92 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(z)))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[619])).
% 1.72/1.92 tff(4988,plain,
% 1.72/1.92 (b(elem!1, s(s(z))) <=> b(elem!1, s(elem!1))),
% 1.72/1.92 inference(symmetry,[status(thm)],[4987])).
% 1.72/1.92 tff(4989,plain,
% 1.72/1.92 (b(s(z), s(s(z))) <=> b(elem!1, s(s(z)))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[93])).
% 1.72/1.92 tff(4990,plain,
% 1.72/1.92 (b(s(z), s(s(z))) <=> b(elem!1, s(elem!1))),
% 1.72/1.92 inference(transitivity,[status(thm)],[4989, 4988])).
% 1.72/1.92 tff(4991,plain,
% 1.72/1.92 (r(s(z), s(s(z))) <=> r(elem!1, s(s(z)))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[93])).
% 1.72/1.92 tff(4992,plain,
% 1.72/1.92 (r(elem!1, s(s(z))) <=> r(s(z), s(s(z)))),
% 1.72/1.92 inference(symmetry,[status(thm)],[4991])).
% 1.72/1.92 tff(4993,plain,
% 1.72/1.92 (r(elem!1, s(s(z))) <=> r(elem!1, s(elem!1))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[609])).
% 1.72/1.92 tff(4994,plain,
% 1.72/1.92 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(z)))),
% 1.72/1.92 inference(symmetry,[status(thm)],[4993])).
% 1.72/1.92 tff(4995,plain,
% 1.72/1.92 (r(elem!1, s(elem!1)) <=> r(s(z), s(s(z)))),
% 1.72/1.92 inference(transitivity,[status(thm)],[4994, 4992])).
% 1.72/1.92 tff(4996,plain,
% 1.72/1.92 ((~r(elem!1, s(elem!1))) <=> (~r(s(z), s(s(z))))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[4995])).
% 1.72/1.92 tff(4997,plain,
% 1.72/1.92 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[612])).
% 1.72/1.92 tff(4998,plain,
% 1.72/1.92 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 1.72/1.92 inference(symmetry,[status(thm)],[4997])).
% 1.72/1.92 tff(4999,plain,
% 1.72/1.92 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[609])).
% 1.72/1.92 tff(5000,plain,
% 1.72/1.92 (r(s(elem!1), s(s(s(s(z)))))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[467, 4999])).
% 1.72/1.92 tff(5001,plain,
% 1.72/1.92 (r(s(elem!1), s(s(s(elem!1))))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[5000, 4998])).
% 1.72/1.92 tff(5002,plain,
% 1.72/1.92 (r(elem!1, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(s(z)))))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[612])).
% 1.72/1.92 tff(5003,plain,
% 1.72/1.92 (r(elem!1, s(s(s(s(z))))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.72/1.92 inference(symmetry,[status(thm)],[5002])).
% 1.72/1.92 tff(5004,plain,
% 1.72/1.92 (r(s(z), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[93])).
% 1.72/1.92 tff(5005,plain,
% 1.72/1.92 (r(elem!1, s(s(s(s(z)))))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[468, 5004])).
% 1.72/1.92 tff(5006,plain,
% 1.72/1.92 (r(elem!1, s(s(s(elem!1))))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[5005, 5003])).
% 1.72/1.92 tff(5007,plain,
% 1.72/1.92 (((~![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))))))),
% 1.72/1.92 inference(rewrite,[status(thm)],[])).
% 1.72/1.92 tff(5008,plain,
% 1.72/1.92 (((~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))))))),
% 1.72/1.92 inference(rewrite,[status(thm)],[])).
% 1.72/1.92 tff(5009,plain,
% 1.72/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), 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)))))))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[5008])).
% 1.72/1.92 tff(5010,plain,
% 1.72/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), 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))))))),
% 1.72/1.92 inference(transitivity,[status(thm)],[5009, 5007])).
% 1.72/1.92 tff(5011,plain,
% 1.72/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), 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))))),
% 1.72/1.92 inference(quant_inst,[status(thm)],[])).
% 1.72/1.92 tff(5012,plain,
% 1.72/1.92 ((~![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)))))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[5011, 5010])).
% 1.72/1.92 tff(5013,plain,
% 1.72/1.92 (~r(elem!1, s(elem!1))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[5012, 37, 5006, 5001])).
% 1.72/1.92 tff(5014,plain,
% 1.72/1.92 (~r(s(z), s(s(z)))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[5013, 4996])).
% 1.72/1.92 tff(5015,plain,
% 1.72/1.92 (b(s(z), s(s(z)))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[416, 5014])).
% 1.72/1.92 tff(5016,plain,
% 1.72/1.92 (b(elem!1, s(elem!1))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[5015, 4990])).
% 1.72/1.92 tff(5017,plain,
% 1.72/1.92 (b(s(elem!1), elem!1)),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[968, 93, 964])).
% 1.72/1.92 tff(5018,plain,
% 1.72/1.92 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 1.72/1.92 inference(monotonicity,[status(thm)],[93])).
% 1.72/1.92 tff(5019,plain,
% 1.72/1.92 ((s(s(elem!1)) = s(z)) <=> (elem!1 = s(s(elem!1)))),
% 1.72/1.92 inference(transitivity,[status(thm)],[5018, 3428])).
% 1.72/1.92 tff(5020,plain,
% 1.72/1.92 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 1.72/1.92 inference(transitivity,[status(thm)],[5019, 4928])).
% 1.72/1.92 tff(5021,plain,
% 1.72/1.92 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = elem!1))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[5020])).
% 1.72/1.92 tff(5022,plain,
% 1.72/1.92 (~(s(s(elem!1)) = elem!1)),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[556, 5021])).
% 1.72/1.92 tff(5023,plain,
% 1.72/1.92 (b(s(s(s(s(z)))), elem!1)),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[283, 618, 12])).
% 1.72/1.92 tff(5024,plain,
% 1.72/1.92 (b(s(s(s(elem!1))), elem!1)),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[935, 5023, 93])).
% 1.72/1.92 tff(5025,plain,
% 1.72/1.92 ((s(elem!1) = s(s(elem!1))) <=> (s(s(z)) = s(s(elem!1)))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[619])).
% 1.72/1.92 tff(5026,plain,
% 1.72/1.92 ((s(elem!1) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(z)))),
% 1.72/1.92 inference(transitivity,[status(thm)],[5025, 2229])).
% 1.72/1.92 tff(5027,plain,
% 1.72/1.92 ((s(s(elem!1)) = s(s(z))) <=> (s(elem!1) = s(s(elem!1)))),
% 1.72/1.92 inference(symmetry,[status(thm)],[5026])).
% 1.72/1.92 tff(5028,plain,
% 1.72/1.92 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[5027])).
% 1.72/1.92 tff(5029,plain,
% 1.72/1.92 (~(s(elem!1) = s(s(elem!1)))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[266, 5028])).
% 1.72/1.92 tff(5030,plain,
% 1.72/1.92 ((~(s(s(elem!1)) = s(z))) <=> (~(elem!1 = s(s(elem!1))))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[5019])).
% 1.72/1.92 tff(5031,plain,
% 1.72/1.92 (~(elem!1 = s(s(elem!1)))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[556, 5030])).
% 1.72/1.92 tff(5032,plain,
% 1.72/1.92 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[612])).
% 1.72/1.92 tff(5033,plain,
% 1.72/1.92 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.72/1.92 inference(symmetry,[status(thm)],[5032])).
% 1.72/1.92 tff(5034,plain,
% 1.72/1.92 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[610])).
% 1.72/1.92 tff(5035,plain,
% 1.72/1.92 (r(elem!1, s(s(s(elem!1))))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[3195, 5003])).
% 1.72/1.92 tff(5036,plain,
% 1.72/1.92 (s(s(elem!1)) = s(s(s(z)))),
% 1.72/1.92 inference(symmetry,[status(thm)],[610])).
% 1.72/1.92 tff(5037,plain,
% 1.72/1.92 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[612, 5036])).
% 1.72/1.92 tff(5038,plain,
% 1.72/1.92 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.72/1.92 inference(symmetry,[status(thm)],[5037])).
% 1.72/1.92 tff(5039,assumption,(r(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 1.72/1.92 tff(5040,plain,
% 1.72/1.92 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[5039, 5038])).
% 1.72/1.92 tff(5041,plain,
% 1.72/1.92 (((~![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)))))),
% 1.72/1.92 inference(rewrite,[status(thm)],[])).
% 1.72/1.92 tff(5042,plain,
% 1.72/1.92 (((~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)))))),
% 1.72/1.92 inference(rewrite,[status(thm)],[])).
% 1.72/1.92 tff(5043,plain,
% 1.72/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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))))))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[5042])).
% 1.72/1.92 tff(5044,plain,
% 1.72/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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)))))),
% 1.72/1.92 inference(transitivity,[status(thm)],[5043, 5041])).
% 1.72/1.92 tff(5045,plain,
% 1.72/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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))))))),
% 1.72/1.92 inference(quant_inst,[status(thm)],[])).
% 1.72/1.92 tff(5046,plain,
% 1.72/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[5045, 5044])).
% 1.72/1.92 tff(5047,plain,
% 1.72/1.92 ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[5046, 37, 1490])).
% 1.72/1.92 tff(5048,plain,
% 1.72/1.92 ($false),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[5047, 5040, 5035])).
% 1.72/1.92 tff(5049,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(elem!1)))) | (~(s(z) = elem!1)) | (~r(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.92 tff(5050,plain,
% 1.72/1.92 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[5049, 1490, 93, 3195])).
% 1.72/1.92 tff(5051,plain,
% 1.72/1.92 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[2898, 5050])).
% 1.72/1.92 tff(5052,plain,
% 1.72/1.92 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[5051, 5034])).
% 1.72/1.92 tff(5053,plain,
% 1.72/1.92 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[5052, 5033])).
% 1.72/1.92 tff(5054,plain,
% 1.72/1.92 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[5036])).
% 1.72/1.92 tff(5055,plain,
% 1.72/1.92 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.72/1.92 inference(symmetry,[status(thm)],[5054])).
% 1.72/1.92 tff(5056,plain,
% 1.72/1.92 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[610, 612])).
% 1.72/1.92 tff(5057,plain,
% 1.72/1.92 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 1.72/1.92 inference(symmetry,[status(thm)],[5056])).
% 1.72/1.92 tff(5058,plain,
% 1.72/1.92 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[610])).
% 1.72/1.92 tff(5059,plain,
% 1.72/1.92 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 1.72/1.92 inference(transitivity,[status(thm)],[5058, 3863])).
% 1.72/1.92 tff(5060,plain,
% 1.72/1.92 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(s(z))))))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[5059])).
% 1.72/1.92 tff(5061,plain,
% 1.72/1.92 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[264, 5060])).
% 1.72/1.92 tff(5062,plain,
% 1.72/1.92 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[3811, 1490, 3195])).
% 1.72/1.92 tff(5063,plain,
% 1.72/1.92 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[1660, 5062, 5061])).
% 1.72/1.92 tff(5064,plain,
% 1.72/1.92 (b(s(s(s(z))), s(s(s(elem!1))))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[5063, 5057])).
% 1.72/1.92 tff(5065,plain,
% 1.72/1.92 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[5064, 5055])).
% 1.72/1.92 tff(5066,plain,
% 1.72/1.92 (r(s(elem!1), s(s(s(elem!1))))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[1167, 4998])).
% 1.72/1.92 tff(5067,plain,
% 1.72/1.92 (~r(elem!1, s(elem!1))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[5012, 37, 5035, 5066])).
% 1.72/1.92 tff(5068,plain,
% 1.72/1.92 (~r(s(z), s(s(z)))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[5067, 4996])).
% 1.72/1.92 tff(5069,plain,
% 1.72/1.92 (b(s(z), s(s(z)))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[416, 5068])).
% 1.72/1.92 tff(5070,plain,
% 1.72/1.92 (b(elem!1, s(elem!1))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[5069, 4990])).
% 1.72/1.92 tff(5071,assumption,(b(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 1.72/1.92 tff(5072,plain,
% 1.72/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))) | (~b(s(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(X1, 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(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.72/1.92 inference(rewrite,[status(thm)],[])).
% 1.72/1.92 tff(5073,plain,
% 1.72/1.92 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, 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(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.72/1.92 inference(rewrite,[status(thm)],[])).
% 1.72/1.92 tff(5074,plain,
% 1.72/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), elem!1)) | (~b(elem!1, 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(X1, 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(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[5073])).
% 1.72/1.92 tff(5075,plain,
% 1.72/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), elem!1)) | (~b(elem!1, 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(X1, 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(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.72/1.92 inference(transitivity,[status(thm)],[5074, 5072])).
% 1.72/1.92 tff(5076,plain,
% 1.72/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), elem!1)) | (~b(elem!1, 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))))))),
% 1.72/1.92 inference(quant_inst,[status(thm)],[])).
% 1.72/1.92 tff(5077,plain,
% 1.72/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[5076, 5075])).
% 1.72/1.92 tff(5078,plain,
% 1.72/1.92 ($false),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[5077, 75, 921, 707, 922, 2609, 5071])).
% 1.72/1.92 tff(5079,plain,((~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(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.92 tff(5080,plain,
% 1.72/1.92 (~b(s(s(elem!1)), elem!1)),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[5079, 5070, 922, 921, 5065])).
% 1.72/1.92 tff(5081,plain,
% 1.72/1.92 (r(s(s(elem!1)), elem!1)),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[2673, 5080, 5022])).
% 1.72/1.92 tff(5082,plain,
% 1.72/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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, 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(X1, 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, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 1.72/1.92 inference(rewrite,[status(thm)],[])).
% 1.72/1.92 tff(5083,plain,
% 1.72/1.92 (((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z))) <=> ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 1.72/1.92 inference(rewrite,[status(thm)],[])).
% 1.72/1.92 tff(5084,plain,
% 1.72/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~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(X1, 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, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z))))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[5083])).
% 1.72/1.92 tff(5085,plain,
% 1.72/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~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(X1, 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, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 1.72/1.92 inference(transitivity,[status(thm)],[5084, 5082])).
% 1.72/1.92 tff(5086,plain,
% 1.72/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 1.72/1.92 inference(quant_inst,[status(thm)],[])).
% 1.72/1.92 tff(5087,plain,
% 1.72/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[5086, 5085])).
% 1.72/1.92 tff(5088,plain,
% 1.72/1.92 (~b(s(s(s(elem!1))), z)),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[5087, 75, 1518, 921, 922, 2609])).
% 1.72/1.92 tff(5089,plain,
% 1.72/1.92 (r(s(s(s(elem!1))), z)),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[948, 58, 662, 5088])).
% 1.72/1.92 tff(5090,assumption,(r(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 1.72/1.92 tff(5091,plain,
% 1.72/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1), z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1), z)) | (~b(elem!1, s(elem!1))))),
% 1.72/1.92 inference(rewrite,[status(thm)],[])).
% 1.72/1.92 tff(5092,plain,
% 1.72/1.92 (((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))) <=> ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))))),
% 1.72/1.92 inference(rewrite,[status(thm)],[])).
% 1.72/1.92 tff(5093,plain,
% 1.72/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(elem!1, 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(X1, 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(elem!1), z)) | (~b(elem!1, s(elem!1)))))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[5092])).
% 1.72/1.92 tff(5094,plain,
% 1.72/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(elem!1, 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(X1, 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(elem!1), z)) | (~b(elem!1, s(elem!1))))),
% 1.72/1.92 inference(transitivity,[status(thm)],[5093, 5091])).
% 1.72/1.93 tff(5095,plain,
% 1.72/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 1.72/1.93 inference(quant_inst,[status(thm)],[])).
% 1.72/1.93 tff(5096,plain,
% 1.72/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1), z)) | (~b(elem!1, s(elem!1)))),
% 1.72/1.93 inference(modus_ponens,[status(thm)],[5095, 5094])).
% 1.72/1.93 tff(5097,plain,
% 1.72/1.93 (~b(s(elem!1), z)),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[5096, 75, 1518, 921, 2609])).
% 1.72/1.93 tff(5098,plain,
% 1.72/1.93 (r(s(elem!1), z)),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[766, 5097])).
% 1.72/1.93 tff(5099,plain,
% 1.72/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 1.72/1.93 inference(rewrite,[status(thm)],[])).
% 1.72/1.93 tff(5100,plain,
% 1.72/1.93 (((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), s(s(s(elem!1)))))) <=> ((~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 1.72/1.93 inference(rewrite,[status(thm)],[])).
% 1.72/1.93 tff(5101,plain,
% 1.72/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~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), z)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z))))),
% 1.72/1.93 inference(monotonicity,[status(thm)],[5100])).
% 1.72/1.93 tff(5102,plain,
% 1.72/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~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), z)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 1.72/1.93 inference(transitivity,[status(thm)],[5101, 5099])).
% 1.72/1.93 tff(5103,plain,
% 1.72/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.72/1.93 inference(quant_inst,[status(thm)],[])).
% 1.72/1.93 tff(5104,plain,
% 1.72/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z))),
% 1.72/1.93 inference(modus_ponens,[status(thm)],[5103, 5102])).
% 1.72/1.93 tff(5105,plain,
% 1.72/1.93 ($false),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[5104, 37, 5098, 5090, 5089])).
% 1.72/1.93 tff(5106,plain,((~b(z, elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.93 tff(5107,plain,
% 1.72/1.93 (~b(z, elem!1)),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[5106, 5066, 921, 922, 5070])).
% 1.72/1.93 tff(5108,plain,
% 1.72/1.93 (r(z, elem!1)),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[298, 5107, 235])).
% 1.72/1.93 tff(5109,plain,
% 1.72/1.93 (((~![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)), 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(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))),
% 1.72/1.93 inference(rewrite,[status(thm)],[])).
% 1.72/1.93 tff(5110,plain,
% 1.72/1.93 (((~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)), z)) | (~r(s(s(elem!1)), elem!1)))),
% 1.72/1.93 inference(rewrite,[status(thm)],[])).
% 1.72/1.93 tff(5111,plain,
% 1.72/1.93 (((~![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)), z)) | (~r(s(s(elem!1)), elem!1))))),
% 1.72/1.93 inference(monotonicity,[status(thm)],[5110])).
% 1.72/1.93 tff(5112,plain,
% 1.72/1.93 (((~![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)), z)) | (~r(s(s(elem!1)), elem!1)))),
% 1.72/1.93 inference(transitivity,[status(thm)],[5111, 5109])).
% 1.72/1.93 tff(5113,plain,
% 1.72/1.93 ((~![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)))),
% 1.72/1.93 inference(quant_inst,[status(thm)],[])).
% 1.72/1.93 tff(5114,plain,
% 1.72/1.93 ((~![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)), z)) | (~r(s(s(elem!1)), elem!1))),
% 1.72/1.93 inference(modus_ponens,[status(thm)],[5113, 5112])).
% 1.72/1.93 tff(5115,plain,
% 1.72/1.93 (~r(s(s(elem!1)), z)),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[5114, 37, 5108, 5081])).
% 1.72/1.93 tff(5116,plain,
% 1.72/1.93 (b(s(s(elem!1)), z)),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[2696, 5115])).
% 1.72/1.93 tff(5117,plain,
% 1.72/1.93 (~r(z, s(s(elem!1)))),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[2372, 5108, 1490])).
% 1.72/1.93 tff(5118,plain,
% 1.72/1.93 ((z = s(s(elem!1))) | b(z, s(s(elem!1)))),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[1834, 58, 5117])).
% 1.72/1.93 tff(5119,plain,
% 1.72/1.93 (b(z, s(s(elem!1)))),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[5118, 1824])).
% 1.72/1.93 tff(5120,plain,
% 1.72/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(X1, 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))))))),
% 1.72/1.93 inference(rewrite,[status(thm)],[])).
% 1.72/1.93 tff(5121,plain,
% 1.72/1.93 (((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(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))))))),
% 1.72/1.93 inference(rewrite,[status(thm)],[])).
% 1.72/1.93 tff(5122,plain,
% 1.72/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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)))))))),
% 1.72/1.93 inference(monotonicity,[status(thm)],[5121])).
% 1.72/1.93 tff(5123,plain,
% 1.72/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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))))))),
% 1.72/1.93 inference(transitivity,[status(thm)],[5122, 5120])).
% 1.72/1.93 tff(5124,plain,
% 1.72/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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))))))),
% 1.72/1.93 inference(quant_inst,[status(thm)],[])).
% 1.72/1.93 tff(5125,plain,
% 1.72/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))))),
% 1.72/1.93 inference(modus_ponens,[status(thm)],[5124, 5123])).
% 1.72/1.93 tff(5126,plain,
% 1.72/1.93 (~b(z, s(s(s(elem!1))))),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[5125, 75, 5119, 5116, 5053])).
% 1.72/1.93 tff(5127,plain,
% 1.72/1.93 ((z = s(s(s(elem!1)))) | r(z, s(s(s(elem!1))))),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[674, 58, 5126])).
% 1.72/1.93 tff(5128,plain,
% 1.72/1.93 (r(z, s(s(s(elem!1))))),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[5127, 663])).
% 1.72/1.93 tff(5129,plain,
% 1.72/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, 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, elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))),
% 1.72/1.93 inference(rewrite,[status(thm)],[])).
% 1.72/1.93 tff(5130,plain,
% 1.72/1.93 (((~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))),
% 1.72/1.93 inference(rewrite,[status(thm)],[])).
% 1.72/1.93 tff(5131,plain,
% 1.72/1.93 (((~![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(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1)))))))),
% 1.72/1.93 inference(monotonicity,[status(thm)],[5130])).
% 1.72/1.93 tff(5132,plain,
% 1.72/1.93 (((~![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(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))),
% 1.72/1.93 inference(transitivity,[status(thm)],[5131, 5129])).
% 1.72/1.93 tff(5133,plain,
% 1.72/1.93 ((~![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(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)))),
% 1.72/1.93 inference(quant_inst,[status(thm)],[])).
% 1.72/1.93 tff(5134,plain,
% 1.72/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1)))))),
% 1.72/1.93 inference(modus_ponens,[status(thm)],[5133, 5132])).
% 1.72/1.93 tff(5135,plain,
% 1.72/1.93 ($false),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[5134, 37, 5108, 1490, 5035, 5128])).
% 1.72/1.93 tff(5136,plain,((~r(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (z = elem!1) | (~(s(z) = elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.93 tff(5137,plain,
% 1.72/1.93 (~r(elem!1, s(s(elem!1)))),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[5136, 5024, 5017, 294, 93, 5000, 5005])).
% 1.72/1.93 tff(5138,plain,
% 1.72/1.93 (b(elem!1, s(s(elem!1)))),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[1617, 5137, 5031])).
% 1.72/1.93 tff(5139,plain,
% 1.72/1.93 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.72/1.93 inference(symmetry,[status(thm)],[5034])).
% 1.72/1.93 tff(5140,plain,
% 1.72/1.93 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.72/1.93 inference(transitivity,[status(thm)],[5032, 5139])).
% 1.72/1.93 tff(5141,plain,
% 1.72/1.93 ((~b(s(s(s(elem!1))), s(s(elem!1)))) <=> (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.72/1.93 inference(monotonicity,[status(thm)],[5140])).
% 1.72/1.93 tff(5142,plain,
% 1.72/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), 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(X1, 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)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.72/1.93 inference(rewrite,[status(thm)],[])).
% 1.72/1.93 tff(5143,plain,
% 1.72/1.93 (((~b(s(s(elem!1)), elem!1)) | (~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(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)))))),
% 1.72/1.93 inference(rewrite,[status(thm)],[])).
% 1.72/1.93 tff(5144,plain,
% 1.72/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), 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(X1, 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)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 1.72/1.93 inference(monotonicity,[status(thm)],[5143])).
% 1.72/1.93 tff(5145,plain,
% 1.72/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), 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(X1, 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)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.72/1.93 inference(transitivity,[status(thm)],[5144, 5142])).
% 1.72/1.93 tff(5146,plain,
% 1.72/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), 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)))))),
% 1.72/1.93 inference(quant_inst,[status(thm)],[])).
% 1.72/1.93 tff(5147,plain,
% 1.72/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 1.72/1.93 inference(modus_ponens,[status(thm)],[5146, 5145])).
% 1.72/1.93 tff(5148,plain,
% 1.72/1.93 ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[5147, 75, 1620, 707])).
% 1.72/1.93 tff(5149,plain,
% 1.72/1.93 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[5148, 922])).
% 1.72/1.93 tff(5150,plain,
% 1.72/1.93 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.72/1.93 inference(modus_ponens,[status(thm)],[5149, 5141])).
% 1.72/1.93 tff(5151,plain,
% 1.72/1.93 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[2898, 5150])).
% 1.72/1.93 tff(5152,plain,
% 1.72/1.93 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.72/1.93 inference(modus_ponens,[status(thm)],[5151, 5038])).
% 1.72/1.93 tff(5153,plain,
% 1.72/1.93 (~b(s(elem!1), s(s(elem!1)))),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[3713, 75, 1620, 921, 707])).
% 1.72/1.93 tff(5154,plain,
% 1.72/1.93 (r(s(elem!1), s(s(elem!1)))),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[1851, 5153, 1845])).
% 1.72/1.93 tff(5155,plain,
% 1.72/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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)))))),
% 1.72/1.93 inference(rewrite,[status(thm)],[])).
% 1.72/1.93 tff(5156,plain,
% 1.72/1.93 (((~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)))))),
% 1.72/1.93 inference(rewrite,[status(thm)],[])).
% 1.72/1.93 tff(5157,plain,
% 1.72/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(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))))))),
% 1.72/1.93 inference(monotonicity,[status(thm)],[5156])).
% 1.72/1.93 tff(5158,plain,
% 1.72/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(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)))))),
% 1.72/1.93 inference(transitivity,[status(thm)],[5157, 5155])).
% 1.72/1.93 tff(5159,plain,
% 1.72/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(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))))),
% 1.72/1.93 inference(quant_inst,[status(thm)],[])).
% 1.72/1.93 tff(5160,plain,
% 1.72/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.72/1.93 inference(modus_ponens,[status(thm)],[5159, 5158])).
% 1.72/1.93 tff(5161,plain,
% 1.72/1.93 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[5160, 37, 5154, 5152])).
% 1.72/1.93 tff(5162,plain,
% 1.72/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), 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)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), 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)))),
% 1.72/1.94 inference(rewrite,[status(thm)],[])).
% 1.72/1.94 tff(5163,plain,
% 1.72/1.94 (((~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(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(elem!1)))) | (~b(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)))),
% 1.72/1.94 inference(rewrite,[status(thm)],[])).
% 1.72/1.94 tff(5164,plain,
% 1.72/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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)), 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))))),
% 1.72/1.94 inference(monotonicity,[status(thm)],[5163])).
% 1.72/1.94 tff(5165,plain,
% 1.72/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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)), 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)))),
% 1.72/1.94 inference(transitivity,[status(thm)],[5164, 5162])).
% 1.72/1.94 tff(5166,plain,
% 1.72/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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))))),
% 1.72/1.94 inference(quant_inst,[status(thm)],[])).
% 1.72/1.94 tff(5167,plain,
% 1.72/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1))),
% 1.72/1.94 inference(modus_ponens,[status(thm)],[5166, 5165])).
% 1.72/1.94 tff(5168,plain,
% 1.72/1.94 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[5167, 75, 1620, 921, 707, 922])).
% 1.72/1.94 tff(5169,plain,
% 1.72/1.94 ((s(s(s(elem!1))) = s(elem!1)) | r(s(s(s(elem!1))), s(elem!1))),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[655, 58, 5168])).
% 1.72/1.94 tff(5170,plain,
% 1.72/1.94 ($false),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[5169, 5161, 645])).
% 1.72/1.94 tff(5171,plain,((~b(s(elem!1), elem!1)) | (~(s(z) = elem!1)) | (s(elem!1) = s(s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.94 tff(5172,plain,
% 1.72/1.94 (~b(s(s(elem!1)), elem!1)),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[5171, 5138, 93, 5017, 5029, 5024])).
% 1.72/1.94 tff(5173,plain,
% 1.72/1.94 (r(s(s(elem!1)), elem!1)),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[2673, 5172, 5022])).
% 1.72/1.94 tff(5174,plain,
% 1.72/1.94 (~b(z, elem!1)),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[5106, 5016, 5017, 5024, 5001])).
% 1.72/1.94 tff(5175,plain,
% 1.72/1.94 (r(z, elem!1)),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[298, 5174, 294])).
% 1.72/1.94 tff(5176,plain,
% 1.72/1.94 (~r(s(s(elem!1)), z)),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[5114, 37, 300, 2647])).
% 1.72/1.94 tff(5177,plain,
% 1.72/1.94 (b(s(s(elem!1)), z)),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[2696, 5176])).
% 1.72/1.94 tff(5178,plain,
% 1.72/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 1.72/1.94 inference(rewrite,[status(thm)],[])).
% 1.72/1.94 tff(5179,plain,
% 1.72/1.94 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 1.72/1.94 inference(rewrite,[status(thm)],[])).
% 1.72/1.94 tff(5180,plain,
% 1.72/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 1.72/1.94 inference(monotonicity,[status(thm)],[5179])).
% 1.72/1.94 tff(5181,plain,
% 1.72/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 1.72/1.94 inference(transitivity,[status(thm)],[5180, 5178])).
% 1.72/1.94 tff(5182,plain,
% 1.72/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 1.72/1.94 inference(quant_inst,[status(thm)],[])).
% 1.72/1.94 tff(5183,plain,
% 1.72/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 1.72/1.94 inference(modus_ponens,[status(thm)],[5182, 5181])).
% 1.72/1.94 tff(5184,plain,
% 1.72/1.94 ($false),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[5183, 75, 5177, 782, 751, 3068])).
% 1.72/1.94 tff(5185,plain,((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.94 tff(5186,plain,
% 1.72/1.94 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[5185, 837, 5175, 5173])).
% 1.72/1.94 tff(5187,plain,
% 1.72/1.94 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[813, 5186, 720])).
% 1.72/1.94 tff(5188,plain,
% 1.72/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.72/1.94 inference(rewrite,[status(thm)],[])).
% 1.72/1.94 tff(5189,plain,
% 1.72/1.94 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.72/1.94 inference(rewrite,[status(thm)],[])).
% 1.72/1.94 tff(5190,plain,
% 1.72/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 1.72/1.94 inference(monotonicity,[status(thm)],[5189])).
% 1.72/1.94 tff(5191,plain,
% 1.72/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.72/1.94 inference(transitivity,[status(thm)],[5190, 5188])).
% 1.72/1.94 tff(5192,plain,
% 1.72/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.72/1.94 inference(quant_inst,[status(thm)],[])).
% 1.72/1.94 tff(5193,plain,
% 1.72/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 1.72/1.94 inference(modus_ponens,[status(thm)],[5192, 5191])).
% 1.72/1.94 tff(5194,plain,
% 1.72/1.94 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[5193, 75, 5187, 5017, 5016])).
% 1.72/1.94 tff(5195,plain,
% 1.72/1.94 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[793, 58, 737, 5194])).
% 1.72/1.94 tff(5196,plain,
% 1.72/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.72/1.94 inference(rewrite,[status(thm)],[])).
% 1.72/1.94 tff(5197,plain,
% 1.72/1.94 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.72/1.94 inference(rewrite,[status(thm)],[])).
% 1.72/1.94 tff(5198,plain,
% 1.72/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(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(X1, 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(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 1.72/1.94 inference(monotonicity,[status(thm)],[5197])).
% 1.72/1.94 tff(5199,plain,
% 1.72/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(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(X1, 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(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.72/1.94 inference(transitivity,[status(thm)],[5198, 5196])).
% 1.72/1.94 tff(5200,plain,
% 1.72/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 1.72/1.94 inference(quant_inst,[status(thm)],[])).
% 1.72/1.94 tff(5201,plain,
% 1.72/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 1.72/1.94 inference(modus_ponens,[status(thm)],[5200, 5199])).
% 1.72/1.94 tff(5202,plain,
% 1.72/1.94 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[5201, 75, 5187, 5017, 5024, 5016])).
% 1.72/1.94 tff(5203,plain,
% 1.72/1.94 (r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[874, 58, 871, 5202])).
% 1.72/1.94 tff(5204,plain,
% 1.72/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.72/1.94 inference(rewrite,[status(thm)],[])).
% 1.72/1.94 tff(5205,plain,
% 1.72/1.94 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(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(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.72/1.95 inference(rewrite,[status(thm)],[])).
% 1.72/1.95 tff(5206,plain,
% 1.72/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 1.72/1.95 inference(monotonicity,[status(thm)],[5205])).
% 1.72/1.95 tff(5207,plain,
% 1.72/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.72/1.95 inference(transitivity,[status(thm)],[5206, 5204])).
% 1.72/1.95 tff(5208,plain,
% 1.72/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.72/1.95 inference(quant_inst,[status(thm)],[])).
% 1.72/1.95 tff(5209,plain,
% 1.72/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 1.72/1.95 inference(modus_ponens,[status(thm)],[5208, 5207])).
% 1.72/1.95 tff(5210,plain,
% 1.72/1.95 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[5209, 75, 5187, 5017, 5016])).
% 1.72/1.95 tff(5211,plain,
% 1.72/1.95 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[3010, 58, 3007, 5210])).
% 1.72/1.95 tff(5212,plain,
% 1.72/1.95 (((~![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(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(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(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 1.72/1.95 inference(rewrite,[status(thm)],[])).
% 1.72/1.95 tff(5213,plain,
% 1.72/1.95 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 1.72/1.95 inference(rewrite,[status(thm)],[])).
% 1.72/1.95 tff(5214,plain,
% 1.72/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))))),
% 1.72/1.95 inference(monotonicity,[status(thm)],[5213])).
% 1.72/1.95 tff(5215,plain,
% 1.72/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 1.72/1.95 inference(transitivity,[status(thm)],[5214, 5212])).
% 1.72/1.95 tff(5216,plain,
% 1.72/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.72/1.95 inference(quant_inst,[status(thm)],[])).
% 1.72/1.95 tff(5217,plain,
% 1.72/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 1.72/1.95 inference(modus_ponens,[status(thm)],[5216, 5215])).
% 1.72/1.95 tff(5218,plain,
% 1.72/1.95 ($false),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[5217, 37, 5001, 5211, 5203, 5195])).
% 1.72/1.95 tff(5219,plain,((~(s(z) = elem!1)) | r(s(s(s(s(z)))), elem!1) | (~r(s(s(z)), s(s(s(s(z)))))) | (s(s(elem!1)) = s(s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.95 tff(5220,plain,
% 1.72/1.95 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[5219, 4986, 12, 4883, 4982, 4972])).
% 1.72/1.95 tff(5221,plain,
% 1.72/1.95 (b(s(s(z)), s(s(s(s(z)))))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[465, 5220])).
% 1.72/1.95 tff(5222,plain,
% 1.72/1.95 ($false),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[5221, 4981])).
% 1.72/1.95 tff(5223,plain,((~b(elem!1, z)) | (~(s(s(s(z))) = s(s(elem!1)))) | r(s(s(s(s(z)))), elem!1) | (~b(z, elem!1)) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.72/1.95 tff(5224,plain,
% 1.72/1.95 (~b(elem!1, z)),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[5223, 4850, 12, 4870, 15])).
% 1.72/1.95 tff(5225,plain,
% 1.72/1.95 (r(elem!1, z)),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[387, 5224, 4869])).
% 1.72/1.95 tff(5226,plain,
% 1.72/1.95 (r(s(z), z)),
% 1.72/1.95 inference(modus_ponens,[status(thm)],[5225, 4859])).
% 1.72/1.95 tff(5227,plain,
% 1.72/1.95 (r(s(z), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 1.72/1.95 inference(monotonicity,[status(thm)],[4857])).
% 1.72/1.95 tff(5228,plain,
% 1.72/1.95 (r(elem!1, s(s(s(s(z))))) <=> r(s(z), s(s(s(s(z)))))),
% 1.72/1.95 inference(symmetry,[status(thm)],[5227])).
% 1.72/1.95 tff(5229,plain,
% 1.72/1.95 ((s(z) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(z)))))),
% 1.72/1.95 inference(monotonicity,[status(thm)],[4857])).
% 1.72/1.95 tff(5230,plain,
% 1.72/1.95 ((s(z) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 1.72/1.95 inference(transitivity,[status(thm)],[5229, 240])).
% 1.72/1.95 tff(5231,plain,
% 1.72/1.95 ((~(s(z) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 1.72/1.95 inference(monotonicity,[status(thm)],[5230])).
% 1.72/1.95 tff(5232,plain,
% 1.72/1.95 (~(s(s(s(s(z)))) = elem!1)),
% 1.72/1.95 inference(modus_ponens,[status(thm)],[484, 5231])).
% 1.72/1.95 tff(5233,plain,
% 1.72/1.95 ((s(s(s(z))) = elem!1) <=> (s(s(elem!1)) = elem!1)),
% 1.72/1.95 inference(monotonicity,[status(thm)],[4850])).
% 1.72/1.95 tff(5234,plain,
% 1.72/1.95 ((s(s(s(z))) = elem!1) <=> (elem!1 = s(s(elem!1)))),
% 1.72/1.95 inference(transitivity,[status(thm)],[5233, 3428])).
% 1.72/1.95 tff(5235,plain,
% 1.72/1.95 ((elem!1 = s(s(elem!1))) <=> (s(s(s(z))) = elem!1)),
% 1.72/1.95 inference(symmetry,[status(thm)],[5234])).
% 1.72/1.95 tff(5236,plain,
% 1.72/1.95 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 1.72/1.95 inference(monotonicity,[status(thm)],[4857])).
% 1.72/1.95 tff(5237,plain,
% 1.72/1.95 ((s(s(elem!1)) = s(z)) <=> (elem!1 = s(s(elem!1)))),
% 1.72/1.95 inference(transitivity,[status(thm)],[5236, 3428])).
% 1.72/1.95 tff(5238,plain,
% 1.72/1.95 ((s(s(elem!1)) = s(z)) <=> (s(s(s(z))) = elem!1)),
% 1.72/1.95 inference(transitivity,[status(thm)],[5237, 5235])).
% 1.72/1.95 tff(5239,plain,
% 1.72/1.95 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(s(z))) = elem!1))),
% 1.72/1.95 inference(monotonicity,[status(thm)],[5238])).
% 1.72/1.95 tff(5240,plain,
% 1.72/1.95 (~(s(s(s(z))) = elem!1)),
% 1.72/1.95 inference(modus_ponens,[status(thm)],[556, 5239])).
% 1.72/1.95 tff(5241,plain,
% 1.72/1.95 (b(s(s(s(z))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.72/1.95 inference(monotonicity,[status(thm)],[4850])).
% 1.72/1.95 tff(5242,plain,
% 1.72/1.95 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(z))), elem!1)),
% 1.72/1.95 inference(symmetry,[status(thm)],[5241])).
% 1.72/1.95 tff(5243,plain,
% 1.72/1.95 ((~b(s(s(elem!1)), elem!1)) <=> (~b(s(s(s(z))), elem!1))),
% 1.72/1.95 inference(monotonicity,[status(thm)],[5242])).
% 1.72/1.95 tff(5244,plain,
% 1.72/1.95 (b(s(s(s(s(z)))), elem!1)),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[283, 5232, 12])).
% 1.72/1.95 tff(5245,plain,
% 1.72/1.95 (~r(z, s(z))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[2724, 4857, 13])).
% 1.72/1.95 tff(5246,plain,
% 1.72/1.95 (b(z, s(z))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[187, 5245])).
% 1.72/1.95 tff(5247,assumption,(z = s(s(elem!1))), introduced(assumption)).
% 1.72/1.95 tff(5248,plain,
% 1.72/1.95 (s(s(elem!1)) = z),
% 1.72/1.95 inference(symmetry,[status(thm)],[5247])).
% 1.72/1.95 tff(5249,plain,
% 1.72/1.95 ($false),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[515, 5248])).
% 1.72/1.95 tff(5250,plain,(~(z = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.95 tff(5251,plain,
% 1.72/1.95 (r(s(z), z) <=> r(elem!1, z)),
% 1.72/1.95 inference(monotonicity,[status(thm)],[4883])).
% 1.72/1.95 tff(5252,plain,
% 1.72/1.95 (r(elem!1, z) <=> r(s(z), z)),
% 1.72/1.95 inference(symmetry,[status(thm)],[5251])).
% 1.72/1.95 tff(5253,plain,
% 1.72/1.95 (r(s(z), z)),
% 1.72/1.95 inference(modus_ponens,[status(thm)],[155, 5252])).
% 1.72/1.95 tff(5254,plain,
% 1.72/1.95 (r(s(z), s(s(s(z)))) <=> r(s(z), s(s(elem!1)))),
% 1.72/1.95 inference(monotonicity,[status(thm)],[4537])).
% 1.72/1.95 tff(5255,plain,
% 1.72/1.95 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(z)))), elem!1)),
% 1.72/1.95 inference(monotonicity,[status(thm)],[4883])).
% 1.72/1.95 tff(5256,plain,
% 1.72/1.95 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(z))),
% 1.72/1.95 inference(symmetry,[status(thm)],[5255])).
% 1.72/1.95 tff(5257,plain,
% 1.72/1.95 (b(s(s(s(s(z)))), s(z))),
% 1.72/1.95 inference(modus_ponens,[status(thm)],[287, 5256])).
% 1.72/1.95 tff(5258,plain,
% 1.72/1.95 (b(s(s(s(z))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.72/1.95 inference(monotonicity,[status(thm)],[4537])).
% 1.72/1.95 tff(5259,plain,
% 1.72/1.95 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(z))), s(z))),
% 1.72/1.95 inference(symmetry,[status(thm)],[5258])).
% 1.72/1.95 tff(5260,plain,
% 1.72/1.95 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 1.72/1.95 inference(monotonicity,[status(thm)],[4883])).
% 1.72/1.95 tff(5261,plain,
% 1.72/1.95 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(z))),
% 1.72/1.95 inference(symmetry,[status(thm)],[5260])).
% 1.72/1.95 tff(5262,plain,
% 1.72/1.95 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(z))), s(z))),
% 1.72/1.95 inference(transitivity,[status(thm)],[5261, 5259])).
% 1.72/1.95 tff(5263,plain,
% 1.72/1.95 (b(s(s(s(z))), s(z))),
% 1.72/1.95 inference(modus_ponens,[status(thm)],[707, 5262])).
% 1.72/1.95 tff(5264,plain,
% 1.72/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(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(X1, 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(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.72/1.95 inference(rewrite,[status(thm)],[])).
% 1.72/1.95 tff(5265,plain,
% 1.72/1.95 (((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(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)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.72/1.95 inference(rewrite,[status(thm)],[])).
% 1.72/1.95 tff(5266,plain,
% 1.72/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(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(X1, 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(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), z))))),
% 1.72/1.95 inference(monotonicity,[status(thm)],[5265])).
% 1.72/1.95 tff(5267,plain,
% 1.72/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(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(X1, 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(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.72/1.95 inference(transitivity,[status(thm)],[5266, 5264])).
% 1.72/1.95 tff(5268,plain,
% 1.72/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.72/1.95 inference(quant_inst,[status(thm)],[])).
% 1.72/1.95 tff(5269,plain,
% 1.72/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), z))),
% 1.72/1.95 inference(modus_ponens,[status(thm)],[5268, 5267])).
% 1.72/1.95 tff(5270,plain,
% 1.72/1.95 (~b(s(s(s(s(z)))), z)),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[5269, 75, 372, 984, 1053, 982])).
% 1.72/1.95 tff(5271,plain,
% 1.72/1.95 (r(s(s(s(s(z)))), z)),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[1421, 58, 1143, 5270])).
% 1.72/1.95 tff(5272,plain,
% 1.72/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.72/1.95 inference(rewrite,[status(thm)],[])).
% 1.72/1.95 tff(5273,plain,
% 1.72/1.95 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.72/1.95 inference(rewrite,[status(thm)],[])).
% 1.72/1.95 tff(5274,plain,
% 1.72/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 1.72/1.95 inference(monotonicity,[status(thm)],[5273])).
% 1.72/1.95 tff(5275,plain,
% 1.72/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.72/1.95 inference(transitivity,[status(thm)],[5274, 5272])).
% 1.72/1.95 tff(5276,plain,
% 1.72/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 1.72/1.95 inference(quant_inst,[status(thm)],[])).
% 1.72/1.95 tff(5277,plain,
% 1.72/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 1.72/1.95 inference(modus_ponens,[status(thm)],[5276, 5275])).
% 1.72/1.95 tff(5278,plain,
% 1.72/1.95 (~b(z, s(s(s(z))))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[5277, 75, 372, 984, 1053])).
% 1.72/1.95 tff(5279,plain,
% 1.72/1.95 ((z = s(s(s(z)))) | r(z, s(s(s(z))))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[2884, 58, 5278])).
% 1.72/1.95 tff(5280,plain,
% 1.72/1.95 (r(z, s(s(s(z))))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[5279, 2874])).
% 1.72/1.95 tff(5281,plain,
% 1.72/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.72/1.95 inference(rewrite,[status(thm)],[])).
% 1.72/1.95 tff(5282,plain,
% 1.72/1.95 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(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(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.72/1.95 inference(rewrite,[status(thm)],[])).
% 1.72/1.95 tff(5283,plain,
% 1.72/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.72/1.95 inference(monotonicity,[status(thm)],[5282])).
% 1.72/1.95 tff(5284,plain,
% 1.72/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.72/1.95 inference(transitivity,[status(thm)],[5283, 5281])).
% 1.72/1.95 tff(5285,plain,
% 1.72/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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))))))),
% 1.72/1.95 inference(quant_inst,[status(thm)],[])).
% 1.72/1.95 tff(5286,plain,
% 1.72/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.72/1.96 inference(modus_ponens,[status(thm)],[5285, 5284])).
% 1.72/1.96 tff(5287,plain,
% 1.72/1.96 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[5286, 75, 984, 1053, 982])).
% 1.72/1.96 tff(5288,plain,
% 1.72/1.96 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[2897, 5287, 264])).
% 1.72/1.96 tff(5289,plain,
% 1.72/1.96 ($false),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[4038, 37, 5288, 5280, 5271])).
% 1.72/1.96 tff(5290,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.96 tff(5291,plain,
% 1.72/1.96 (~b(s(z), s(s(s(z))))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[5290, 5263, 372, 5257])).
% 1.72/1.96 tff(5292,plain,
% 1.72/1.96 (r(s(z), s(s(s(z))))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[1263, 5291])).
% 1.72/1.96 tff(5293,plain,
% 1.72/1.96 (r(s(z), s(s(elem!1)))),
% 1.72/1.96 inference(modus_ponens,[status(thm)],[5292, 5254])).
% 1.72/1.96 tff(5294,plain,
% 1.72/1.96 (((~![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(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), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))))),
% 1.72/1.96 inference(rewrite,[status(thm)],[])).
% 1.72/1.96 tff(5295,plain,
% 1.72/1.96 (((~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))))),
% 1.72/1.96 inference(rewrite,[status(thm)],[])).
% 1.72/1.96 tff(5296,plain,
% 1.72/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1))))))),
% 1.72/1.96 inference(monotonicity,[status(thm)],[5295])).
% 1.72/1.96 tff(5297,plain,
% 1.72/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))))),
% 1.72/1.96 inference(transitivity,[status(thm)],[5296, 5294])).
% 1.72/1.96 tff(5298,plain,
% 1.72/1.96 ((~![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)))),
% 1.72/1.96 inference(quant_inst,[status(thm)],[])).
% 1.72/1.96 tff(5299,plain,
% 1.72/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1))))),
% 1.72/1.96 inference(modus_ponens,[status(thm)],[5298, 5297])).
% 1.72/1.96 tff(5300,plain,
% 1.72/1.96 ($false),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[5299, 37, 1561, 1871, 2364])).
% 1.72/1.96 tff(5301,plain,((~r(s(z), s(s(elem!1)))) | (~r(s(z), z)) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.96 tff(5302,plain,
% 1.72/1.96 (~r(z, s(s(elem!1)))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[5301, 5293, 5253])).
% 1.72/1.96 tff(5303,plain,
% 1.72/1.96 (b(s(s(s(z))), elem!1)),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[3645, 707, 4934])).
% 1.72/1.96 tff(5304,plain,
% 1.72/1.96 (~b(elem!1, s(s(s(s(z)))))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[2543, 5303, 1518, 287])).
% 1.72/1.96 tff(5305,plain,
% 1.72/1.96 (r(elem!1, s(s(s(s(z)))))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[278, 5304, 4886])).
% 1.72/1.96 tff(5306,assumption,(~r(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 1.72/1.96 tff(5307,plain,
% 1.72/1.96 ($false),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[5306, 5035])).
% 1.72/1.96 tff(5308,plain,(r(elem!1, s(s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.96 tff(5309,plain,
% 1.72/1.96 (r(elem!1, s(s(s(elem!1))))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[5308, 5305, 4883])).
% 1.72/1.96 tff(5310,assumption,(r(z, s(s(s(elem!1))))), introduced(assumption)).
% 1.72/1.96 tff(5311,assumption,(r(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 1.72/1.96 tff(5312,plain,
% 1.72/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, 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(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))),
% 1.72/1.96 inference(rewrite,[status(thm)],[])).
% 1.72/1.96 tff(5313,plain,
% 1.72/1.96 (((~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))),
% 1.72/1.96 inference(rewrite,[status(thm)],[])).
% 1.72/1.96 tff(5314,plain,
% 1.72/1.96 (((~![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(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1)))))))),
% 1.72/1.96 inference(monotonicity,[status(thm)],[5313])).
% 1.72/1.96 tff(5315,plain,
% 1.72/1.96 (((~![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(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))),
% 1.72/1.96 inference(transitivity,[status(thm)],[5314, 5312])).
% 1.72/1.96 tff(5316,plain,
% 1.72/1.96 ((~![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(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)))),
% 1.72/1.96 inference(quant_inst,[status(thm)],[])).
% 1.72/1.96 tff(5317,plain,
% 1.72/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1)))))),
% 1.72/1.96 inference(modus_ponens,[status(thm)],[5316, 5315])).
% 1.72/1.96 tff(5318,plain,
% 1.72/1.96 ($false),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[5317, 37, 155, 5311, 5310])).
% 1.72/1.96 tff(5319,plain,((~r(z, s(s(s(elem!1))))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.96 tff(5320,plain,
% 1.72/1.96 (~r(z, s(s(s(elem!1))))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[5319, 5309, 155])).
% 1.72/1.96 tff(5321,plain,
% 1.72/1.96 ((z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1))))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[674, 58, 5320])).
% 1.72/1.96 tff(5322,plain,
% 1.72/1.96 (b(z, s(s(s(elem!1))))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[5321, 663])).
% 1.72/1.96 tff(5323,plain,
% 1.72/1.96 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.72/1.96 inference(monotonicity,[status(thm)],[4874])).
% 1.72/1.96 tff(5324,plain,
% 1.72/1.96 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.72/1.96 inference(symmetry,[status(thm)],[5323])).
% 1.72/1.96 tff(5325,plain,
% 1.72/1.96 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.72/1.96 inference(monotonicity,[status(thm)],[4537])).
% 1.72/1.96 tff(5326,plain,
% 1.72/1.96 (r(s(z), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 1.72/1.96 inference(monotonicity,[status(thm)],[4883])).
% 1.72/1.96 tff(5327,plain,
% 1.72/1.96 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 1.72/1.96 inference(transitivity,[status(thm)],[5254, 5326])).
% 1.72/1.96 tff(5328,plain,
% 1.72/1.96 (r(elem!1, s(s(elem!1)))),
% 1.72/1.96 inference(modus_ponens,[status(thm)],[5292, 5327])).
% 1.72/1.96 tff(5329,plain,
% 1.72/1.96 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[5049, 5328, 4883, 5305])).
% 1.72/1.96 tff(5330,plain,
% 1.72/1.96 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[2898, 5329])).
% 1.72/1.96 tff(5331,plain,
% 1.72/1.96 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.72/1.96 inference(modus_ponens,[status(thm)],[5330, 5325])).
% 1.72/1.96 tff(5332,plain,
% 1.72/1.96 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.72/1.96 inference(modus_ponens,[status(thm)],[5331, 5324])).
% 1.72/1.96 tff(5333,plain,
% 1.72/1.96 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.72/1.96 inference(monotonicity,[status(thm)],[4873])).
% 1.72/1.96 tff(5334,plain,
% 1.72/1.96 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.72/1.96 inference(monotonicity,[status(thm)],[4537])).
% 1.72/1.96 tff(5335,plain,
% 1.72/1.96 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.72/1.96 inference(transitivity,[status(thm)],[5334, 5333])).
% 1.72/1.96 tff(5336,plain,
% 1.72/1.96 (r(s(z), s(s(s(s(z)))))),
% 1.72/1.96 inference(modus_ponens,[status(thm)],[5305, 4984])).
% 1.72/1.96 tff(5337,plain,
% 1.72/1.96 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[1316, 5292, 5336])).
% 1.72/1.96 tff(5338,plain,
% 1.72/1.96 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[575, 5337])).
% 1.72/1.96 tff(5339,plain,
% 1.72/1.96 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.72/1.96 inference(modus_ponens,[status(thm)],[5338, 5335])).
% 1.72/1.96 tff(5340,plain,
% 1.72/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(elem!1)), s(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(X1, 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(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 1.72/1.96 inference(rewrite,[status(thm)],[])).
% 1.72/1.96 tff(5341,plain,
% 1.72/1.96 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, 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))))) | (~b(z, s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(z, 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(s(elem!1))))))),
% 1.72/1.96 inference(rewrite,[status(thm)],[])).
% 1.72/1.96 tff(5342,plain,
% 1.72/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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, 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))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))))),
% 1.72/1.96 inference(monotonicity,[status(thm)],[5341])).
% 1.72/1.96 tff(5343,plain,
% 1.72/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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, 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))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 1.72/1.96 inference(transitivity,[status(thm)],[5342, 5340])).
% 1.72/1.96 tff(5344,plain,
% 1.72/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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, 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))))) | (~b(z, s(s(elem!1)))))),
% 1.72/1.96 inference(quant_inst,[status(thm)],[])).
% 1.72/1.96 tff(5345,plain,
% 1.72/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))),
% 1.72/1.96 inference(modus_ponens,[status(thm)],[5344, 5343])).
% 1.72/1.96 tff(5346,plain,
% 1.72/1.96 ((~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[5345, 75, 1518, 707, 5339, 5332])).
% 1.72/1.96 tff(5347,plain,
% 1.72/1.96 (~b(z, s(s(elem!1)))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[5346, 5322])).
% 1.72/1.96 tff(5348,plain,
% 1.72/1.96 ($false),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[1834, 58, 5347, 5302, 5250])).
% 1.72/1.96 tff(5349,plain,((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~r(elem!1, z)) | (~(s(s(s(z))) = s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.96 tff(5350,plain,
% 1.72/1.96 (~b(s(s(elem!1)), elem!1)),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[5349, 4870, 5225, 4850, 5246, 5244])).
% 1.72/1.96 tff(5351,plain,
% 1.72/1.96 (~b(s(s(s(z))), elem!1)),
% 1.72/1.96 inference(modus_ponens,[status(thm)],[5350, 5243])).
% 1.72/1.96 tff(5352,plain,
% 1.72/1.96 (r(s(s(s(z))), elem!1)),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[1115, 5351, 5240])).
% 1.72/1.96 tff(5353,plain,
% 1.72/1.96 (r(s(s(s(elem!1))), z) <=> r(s(s(s(s(z)))), z)),
% 1.72/1.96 inference(monotonicity,[status(thm)],[4874])).
% 1.72/1.96 tff(5354,plain,
% 1.72/1.96 (r(s(s(s(s(z)))), z) <=> r(s(s(s(elem!1))), z)),
% 1.72/1.96 inference(symmetry,[status(thm)],[5353])).
% 1.72/1.96 tff(5355,plain,
% 1.72/1.96 ((~r(s(s(s(s(z)))), z)) <=> (~r(s(s(s(elem!1))), z))),
% 1.72/1.96 inference(monotonicity,[status(thm)],[5354])).
% 1.72/1.96 tff(5356,plain,
% 1.72/1.96 (~(z = elem!1)),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[293, 4982])).
% 1.72/1.96 tff(5357,plain,
% 1.72/1.96 (~(elem!1 = z)),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[304, 5356])).
% 1.72/1.96 tff(5358,plain,
% 1.72/1.96 (~b(elem!1, z)),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[5223, 4537, 12, 1518, 15])).
% 1.72/1.96 tff(5359,plain,
% 1.72/1.96 (r(elem!1, z)),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[387, 5358, 5357])).
% 1.72/1.96 tff(5360,plain,
% 1.72/1.96 (r(s(z), z)),
% 1.72/1.96 inference(modus_ponens,[status(thm)],[5359, 5252])).
% 1.72/1.96 tff(5361,plain,
% 1.72/1.96 (~b(s(z), s(s(s(s(z)))))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[3680, 105, 4937, 1061, 1518, 14, 12, 4982, 99])).
% 1.72/1.96 tff(5362,plain,
% 1.72/1.96 (r(s(z), s(s(s(s(z)))))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[489, 5361])).
% 1.72/1.96 tff(5363,plain,
% 1.72/1.96 (~r(s(s(s(s(z)))), z)),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[2586, 5362, 5360])).
% 1.72/1.96 tff(5364,plain,
% 1.72/1.96 (~r(s(s(s(elem!1))), z)),
% 1.72/1.96 inference(modus_ponens,[status(thm)],[5363, 5355])).
% 1.72/1.96 tff(5365,plain,
% 1.72/1.96 (r(elem!1, s(s(s(s(z)))))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[3193, 99, 12, 4937, 4982])).
% 1.72/1.96 tff(5366,plain,
% 1.72/1.96 (r(elem!1, s(s(s(elem!1))))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[5308, 5365, 4883])).
% 1.72/1.96 tff(5367,plain,
% 1.72/1.96 (~r(z, s(s(s(elem!1))))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[5319, 5366, 5359])).
% 1.72/1.96 tff(5368,plain,
% 1.72/1.96 (~b(s(s(z)), s(z))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[358, 99, 4934])).
% 1.72/1.96 tff(5369,plain,
% 1.72/1.96 (r(s(s(z)), s(z))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[153, 5368])).
% 1.72/1.96 tff(5370,plain,
% 1.72/1.96 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[476, 5369, 5362])).
% 1.72/1.96 tff(5371,plain,
% 1.72/1.96 (b(s(s(z)), s(s(s(s(z)))))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[465, 5370])).
% 1.72/1.96 tff(5372,assumption,(~b(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 1.72/1.96 tff(5373,plain,
% 1.72/1.96 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.72/1.96 inference(modus_ponens,[status(thm)],[5372, 4877])).
% 1.72/1.96 tff(5374,plain,
% 1.72/1.96 ($false),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[895, 5373])).
% 1.72/1.96 tff(5375,plain,(b(s(elem!1), s(s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~(s(s(s(z))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.96 tff(5376,plain,
% 1.72/1.96 (b(s(elem!1), s(s(s(elem!1))))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[5375, 5371, 4537])).
% 1.72/1.96 tff(5377,plain,
% 1.72/1.96 (r(s(s(z)), elem!1) <=> r(s(elem!1), elem!1)),
% 1.72/1.96 inference(symmetry,[status(thm)],[4895])).
% 1.72/1.96 tff(5378,plain,
% 1.72/1.96 (r(s(elem!1), elem!1)),
% 1.72/1.96 inference(modus_ponens,[status(thm)],[105, 5377])).
% 1.72/1.96 tff(5379,plain,
% 1.72/1.96 (~r(s(elem!1), z)),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[2988, 5378, 5359])).
% 1.72/1.96 tff(5380,plain,
% 1.72/1.96 (b(s(elem!1), z)),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[766, 5379])).
% 1.72/1.96 tff(5381,assumption,(~r(z, s(s(s(elem!1))))), introduced(assumption)).
% 1.72/1.96 tff(5382,plain,
% 1.72/1.96 ((z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1))))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[674, 58, 5381])).
% 1.72/1.96 tff(5383,plain,
% 1.72/1.96 (b(z, s(s(s(elem!1))))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[5382, 663])).
% 1.72/1.96 tff(5384,assumption,(b(s(s(s(elem!1))), z)), introduced(assumption)).
% 1.72/1.96 tff(5385,plain,
% 1.72/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), z)) | (~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(X1, 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), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 1.72/1.96 inference(rewrite,[status(thm)],[])).
% 1.72/1.96 tff(5386,plain,
% 1.72/1.96 (((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 1.72/1.96 inference(rewrite,[status(thm)],[])).
% 1.72/1.96 tff(5387,plain,
% 1.72/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))))),
% 1.72/1.96 inference(monotonicity,[status(thm)],[5386])).
% 1.72/1.96 tff(5388,plain,
% 1.72/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 1.72/1.96 inference(transitivity,[status(thm)],[5387, 5385])).
% 1.72/1.96 tff(5389,plain,
% 1.72/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)))),
% 1.72/1.96 inference(quant_inst,[status(thm)],[])).
% 1.72/1.96 tff(5390,plain,
% 1.72/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))),
% 1.72/1.96 inference(modus_ponens,[status(thm)],[5389, 5388])).
% 1.72/1.96 tff(5391,plain,
% 1.72/1.96 ($false),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[5390, 75, 798, 920, 5384, 5383])).
% 1.72/1.96 tff(5392,plain,((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | r(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.96 tff(5393,plain,
% 1.72/1.96 (~b(s(s(s(elem!1))), z)),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[5392, 5380, 5376, 5367])).
% 1.72/1.96 tff(5394,plain,
% 1.72/1.96 (r(s(s(s(elem!1))), z)),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[948, 58, 662, 5393])).
% 1.72/1.96 tff(5395,plain,
% 1.72/1.96 ($false),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[5394, 5364])).
% 1.72/1.96 tff(5396,plain,(b(s(s(z)), elem!1) | (~(s(s(s(z))) = s(s(elem!1)))) | (~r(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | b(elem!1, s(z)) | r(s(s(s(s(z)))), elem!1) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.72/1.96 tff(5397,plain,
% 1.72/1.96 (b(s(s(z)), elem!1)),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[5396, 4850, 5352, 4870, 14, 12, 15])).
% 1.72/1.96 tff(5398,plain,
% 1.72/1.96 (r(elem!1, s(s(s(s(z)))))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[4820, 5397, 12, 4870, 5232])).
% 1.72/1.96 tff(5399,plain,
% 1.72/1.96 (r(s(z), s(s(s(s(z)))))),
% 1.72/1.96 inference(modus_ponens,[status(thm)],[5398, 5228])).
% 1.72/1.96 tff(5400,plain,
% 1.72/1.96 (~r(s(s(s(s(z)))), z)),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[2586, 5399, 5226])).
% 1.72/1.96 tff(5401,plain,
% 1.72/1.96 (~r(s(s(s(elem!1))), z)),
% 1.72/1.96 inference(modus_ponens,[status(thm)],[5400, 4855])).
% 1.72/1.96 tff(5402,plain,
% 1.72/1.96 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[5219, 5399, 12, 4857, 4867, 5397])).
% 1.72/1.96 tff(5403,plain,
% 1.72/1.96 (b(s(s(z)), s(s(s(s(z)))))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[465, 5402])).
% 1.72/1.96 tff(5404,plain,
% 1.72/1.96 (b(s(elem!1), s(s(s(elem!1))))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[5375, 5403, 4850])).
% 1.72/1.96 tff(5405,plain,
% 1.72/1.96 (r(elem!1, s(s(s(elem!1))))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[5308, 5398, 4857])).
% 1.72/1.96 tff(5406,plain,
% 1.72/1.96 (~r(z, s(s(s(elem!1))))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[5319, 5405, 5225])).
% 1.72/1.96 tff(5407,plain,
% 1.72/1.96 (r(s(z), s(elem!1)) <=> r(elem!1, s(elem!1))),
% 1.72/1.96 inference(monotonicity,[status(thm)],[4857])).
% 1.72/1.96 tff(5408,plain,
% 1.72/1.96 (r(elem!1, s(elem!1)) <=> r(s(z), s(elem!1))),
% 1.72/1.96 inference(symmetry,[status(thm)],[5407])).
% 1.72/1.96 tff(5409,plain,
% 1.72/1.96 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 1.72/1.96 inference(monotonicity,[status(thm)],[4850])).
% 1.72/1.96 tff(5410,plain,
% 1.72/1.96 (s(s(z)) = s(elem!1)),
% 1.72/1.96 inference(transitivity,[status(thm)],[254, 5409, 228])).
% 1.72/1.96 tff(5411,plain,
% 1.72/1.96 (r(elem!1, s(s(z))) <=> r(elem!1, s(elem!1))),
% 1.72/1.96 inference(monotonicity,[status(thm)],[5410])).
% 1.72/1.96 tff(5412,plain,
% 1.72/1.96 (r(s(z), s(s(z))) <=> r(elem!1, s(s(z)))),
% 1.72/1.96 inference(monotonicity,[status(thm)],[4857])).
% 1.72/1.96 tff(5413,plain,
% 1.72/1.96 (r(s(z), s(s(z))) <=> r(s(z), s(elem!1))),
% 1.72/1.96 inference(transitivity,[status(thm)],[5412, 5411, 5408])).
% 1.72/1.96 tff(5414,plain,
% 1.72/1.96 (~b(elem!1, s(s(z)))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[2255, 5403, 5397, 5244])).
% 1.72/1.96 tff(5415,plain,
% 1.72/1.96 (b(elem!1, s(s(z)))),
% 1.72/1.96 inference(modus_ponens,[status(thm)],[402, 4989])).
% 1.72/1.96 tff(5416,assumption,(~b(elem!1, s(s(z)))), introduced(assumption)).
% 1.72/1.96 tff(5417,plain,
% 1.72/1.96 ($false),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[5416, 5415])).
% 1.72/1.96 tff(5418,plain,((~b(s(z), s(s(z)))) | b(elem!1, s(s(z))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.96 tff(5419,plain,
% 1.72/1.96 (~b(s(z), s(s(z)))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[5418, 5414, 4857])).
% 1.72/1.96 tff(5420,plain,
% 1.72/1.96 (r(s(z), s(s(z)))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[416, 5419])).
% 1.72/1.96 tff(5421,plain,
% 1.72/1.96 (r(s(z), s(elem!1))),
% 1.72/1.96 inference(modus_ponens,[status(thm)],[5420, 5413])).
% 1.72/1.96 tff(5422,plain,
% 1.72/1.96 (~r(s(elem!1), z)),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[1761, 5421, 5226])).
% 1.72/1.96 tff(5423,plain,
% 1.72/1.96 (b(s(elem!1), z)),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[766, 5422])).
% 1.72/1.96 tff(5424,plain,
% 1.72/1.96 (~b(s(s(s(elem!1))), z)),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[5392, 5423, 5406, 5404])).
% 1.72/1.96 tff(5425,plain,
% 1.72/1.96 (r(s(s(s(elem!1))), z)),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[948, 58, 662, 5424])).
% 1.72/1.96 tff(5426,plain,
% 1.72/1.96 ($false),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[5425, 5401])).
% 1.72/1.96 tff(5427,plain,((s(s(z)) = elem!1) | r(s(s(s(s(z)))), elem!1) | b(elem!1, s(z)) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.72/1.96 tff(5428,plain,
% 1.72/1.96 (s(s(z)) = elem!1),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[5427, 14, 12, 13])).
% 1.72/1.96 tff(5429,plain,
% 1.72/1.96 (r(s(s(z)), s(z)) <=> r(elem!1, s(z))),
% 1.72/1.97 inference(monotonicity,[status(thm)],[5428])).
% 1.72/1.97 tff(5430,plain,
% 1.72/1.97 (~b(s(s(z)), s(z))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[316, 5428, 14])).
% 1.72/1.97 tff(5431,plain,
% 1.72/1.97 (r(s(s(z)), s(z))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[153, 5430])).
% 1.72/1.97 tff(5432,plain,
% 1.72/1.97 (r(elem!1, s(z))),
% 1.72/1.97 inference(modus_ponens,[status(thm)],[5431, 5429])).
% 1.72/1.97 tff(5433,plain,
% 1.72/1.97 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[1013, 5428])).
% 1.72/1.97 tff(5434,plain,
% 1.72/1.97 (s(s(s(s(z)))) = s(s(z))),
% 1.72/1.97 inference(transitivity,[status(thm)],[1021, 225])).
% 1.72/1.97 tff(5435,plain,
% 1.72/1.97 (inj_0(s(s(s(s(z))))) = inj_0(s(s(z)))),
% 1.72/1.97 inference(monotonicity,[status(thm)],[5434])).
% 1.72/1.97 tff(5436,plain,
% 1.72/1.97 (s(s(s(z))) = s(z)),
% 1.72/1.97 inference(transitivity,[status(thm)],[451, 5435, 133])).
% 1.72/1.97 tff(5437,plain,
% 1.72/1.97 ($false),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[1255, 5436])).
% 1.72/1.97 tff(5438,plain,((~(s(s(elem!1)) = s(s(s(s(z)))))) | (s(s(s(z))) = s(z)) | (~(s(s(elem!1)) = s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.97 tff(5439,plain,
% 1.72/1.97 ((~(s(s(elem!1)) = s(s(s(s(z)))))) | (~(s(s(elem!1)) = s(s(z))))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[5438, 457])).
% 1.72/1.97 tff(5440,plain,
% 1.72/1.97 (~(s(s(elem!1)) = s(s(z)))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[5439, 5433])).
% 1.72/1.97 tff(5441,plain,
% 1.72/1.97 (~(z = elem!1)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[293, 5440])).
% 1.72/1.97 tff(5442,plain,
% 1.72/1.97 (~(elem!1 = z)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[304, 5441])).
% 1.72/1.97 tff(5443,plain,
% 1.72/1.97 ((s(s(z)) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(z)))))),
% 1.72/1.97 inference(monotonicity,[status(thm)],[5428])).
% 1.72/1.97 tff(5444,plain,
% 1.72/1.97 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 1.72/1.97 inference(transitivity,[status(thm)],[5443, 240])).
% 1.72/1.97 tff(5445,plain,
% 1.72/1.97 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 1.72/1.97 inference(monotonicity,[status(thm)],[5444])).
% 1.72/1.97 tff(5446,plain,
% 1.72/1.97 (~(s(s(s(s(z)))) = elem!1)),
% 1.72/1.97 inference(modus_ponens,[status(thm)],[459, 5445])).
% 1.72/1.97 tff(5447,plain,
% 1.72/1.97 (b(s(s(s(s(z)))), elem!1)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[283, 5446, 12])).
% 1.72/1.97 tff(5448,plain,
% 1.72/1.97 (b(z, elem!1)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[298, 5441, 13])).
% 1.72/1.97 tff(5449,plain,
% 1.72/1.97 ((s(s(z)) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 1.72/1.97 inference(monotonicity,[status(thm)],[5428])).
% 1.72/1.97 tff(5450,plain,
% 1.72/1.97 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 1.72/1.97 inference(transitivity,[status(thm)],[5449, 1028])).
% 1.72/1.97 tff(5451,plain,
% 1.72/1.97 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = elem!1))),
% 1.72/1.97 inference(monotonicity,[status(thm)],[5450])).
% 1.72/1.97 tff(5452,plain,
% 1.72/1.97 (~(s(s(s(z))) = elem!1)),
% 1.72/1.97 inference(modus_ponens,[status(thm)],[1556, 5451])).
% 1.72/1.97 tff(5453,plain,
% 1.72/1.97 (b(s(s(z)), elem!1) <=> b(elem!1, elem!1)),
% 1.72/1.97 inference(monotonicity,[status(thm)],[5428])).
% 1.72/1.97 tff(5454,plain,
% 1.72/1.97 (b(elem!1, elem!1) <=> b(s(s(z)), elem!1)),
% 1.72/1.97 inference(symmetry,[status(thm)],[5453])).
% 1.72/1.97 tff(5455,plain,
% 1.72/1.97 ((~b(elem!1, elem!1)) <=> (~b(s(s(z)), elem!1))),
% 1.72/1.97 inference(monotonicity,[status(thm)],[5454])).
% 1.72/1.97 tff(5456,plain,
% 1.72/1.97 (~b(s(s(z)), elem!1)),
% 1.72/1.97 inference(modus_ponens,[status(thm)],[1389, 5455])).
% 1.72/1.97 tff(5457,plain,
% 1.72/1.97 (r(elem!1, s(s(s(s(z)))))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[3193, 5456, 12, 5446, 5440])).
% 1.72/1.97 tff(5458,plain,
% 1.72/1.97 (~r(s(s(s(z))), elem!1)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[3255, 5457, 5432])).
% 1.72/1.97 tff(5459,plain,
% 1.72/1.97 (b(s(s(s(z))), elem!1)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[1115, 5458, 5452])).
% 1.72/1.97 tff(5460,plain,
% 1.72/1.97 (~b(elem!1, z)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[4040, 5459, 5448, 5447])).
% 1.72/1.97 tff(5461,plain,
% 1.72/1.97 (r(elem!1, z)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[387, 5460, 5442])).
% 1.72/1.97 tff(5462,plain,
% 1.72/1.97 (~r(z, s(z))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[177, 5461, 5432])).
% 1.72/1.97 tff(5463,plain,
% 1.72/1.97 (b(z, s(z))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[187, 5462])).
% 1.72/1.97 tff(5464,plain,
% 1.72/1.97 (~r(s(z), s(s(s(s(z)))))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[3203, 5432, 5457])).
% 1.72/1.97 tff(5465,plain,
% 1.72/1.97 (b(s(z), s(s(s(s(z)))))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[489, 5464])).
% 1.72/1.97 tff(5466,plain,
% 1.72/1.97 (~r(s(z), z)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[162, 5461, 5432])).
% 1.72/1.97 tff(5467,plain,
% 1.72/1.97 (b(s(z), z)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[169, 5466])).
% 1.72/1.97 tff(5468,plain,
% 1.72/1.97 (~b(s(s(s(s(z)))), z)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[4839, 5467, 5465, 5463])).
% 1.72/1.97 tff(5469,plain,
% 1.72/1.97 (r(s(s(s(s(z)))), z)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[1421, 58, 1143, 5468])).
% 1.72/1.97 tff(5470,plain,
% 1.72/1.97 ($false),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[4847, 37, 5461, 5457, 5469])).
% 1.72/1.97 tff(5471,plain,(b(elem!1, s(z)) | r(s(s(s(s(z)))), elem!1) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.72/1.97 tff(5472,plain,
% 1.72/1.97 (b(elem!1, s(z))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[5471, 12, 13])).
% 1.72/1.97 tff(5473,assumption,(s(s(s(elem!1))) = elem!1), introduced(assumption)).
% 1.72/1.97 tff(5474,plain,
% 1.72/1.97 (s(s(s(elem!1))) = z),
% 1.72/1.97 inference(transitivity,[status(thm)],[5473, 3962])).
% 1.72/1.97 tff(5475,plain,
% 1.72/1.97 ($false),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[662, 5474])).
% 1.72/1.97 tff(5476,plain,((~(s(s(s(elem!1))) = elem!1)) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.97 tff(5477,plain,
% 1.72/1.97 (~(s(s(s(elem!1))) = elem!1)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[5476, 288])).
% 1.72/1.97 tff(5478,plain,
% 1.72/1.97 (r(s(z), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 1.72/1.97 inference(monotonicity,[status(thm)],[289])).
% 1.72/1.97 tff(5479,plain,
% 1.72/1.97 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[5439, 3839])).
% 1.72/1.97 tff(5480,plain,
% 1.72/1.97 (~(s(s(z)) = elem!1)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[1013, 5479])).
% 1.72/1.97 tff(5481,plain,
% 1.72/1.97 (r(s(s(z)), elem!1)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[104, 99, 5480])).
% 1.72/1.97 tff(5482,plain,
% 1.72/1.97 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 1.72/1.97 inference(transitivity,[status(thm)],[3430, 4928])).
% 1.72/1.97 tff(5483,plain,
% 1.72/1.97 ((~(s(s(elem!1)) = z)) <=> (~(s(s(elem!1)) = elem!1))),
% 1.72/1.97 inference(monotonicity,[status(thm)],[5482])).
% 1.72/1.97 tff(5484,plain,
% 1.72/1.97 (~(s(s(elem!1)) = elem!1)),
% 1.72/1.97 inference(modus_ponens,[status(thm)],[515, 5483])).
% 1.72/1.97 tff(5485,plain,
% 1.72/1.97 (~b(s(s(elem!1)), elem!1)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[3652, 99, 288])).
% 1.72/1.97 tff(5486,plain,
% 1.72/1.97 (r(s(s(elem!1)), elem!1)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[2673, 5485, 5484])).
% 1.72/1.97 tff(5487,plain,
% 1.72/1.97 (b(s(s(s(z))), z) <=> b(s(s(s(z))), elem!1)),
% 1.72/1.97 inference(monotonicity,[status(thm)],[288])).
% 1.72/1.97 tff(5488,plain,
% 1.72/1.97 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), z)),
% 1.72/1.97 inference(symmetry,[status(thm)],[5487])).
% 1.72/1.97 tff(5489,plain,
% 1.72/1.97 (b(s(s(s(z))), z)),
% 1.72/1.97 inference(modus_ponens,[status(thm)],[1119, 5488])).
% 1.72/1.97 tff(5490,plain,
% 1.72/1.97 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 1.72/1.97 inference(monotonicity,[status(thm)],[3417])).
% 1.72/1.97 tff(5491,plain,
% 1.72/1.97 (b(s(s(s(elem!1))), elem!1)),
% 1.72/1.97 inference(modus_ponens,[status(thm)],[1119, 5490])).
% 1.72/1.97 tff(5492,plain,
% 1.72/1.97 (~(s(s(z)) = s(elem!1))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[3261, 2478])).
% 1.72/1.97 tff(5493,plain,
% 1.72/1.97 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[4541, 5492])).
% 1.72/1.97 tff(5494,plain,
% 1.72/1.97 (r(s(s(s(z))), s(z)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.72/1.97 inference(monotonicity,[status(thm)],[3417, 289])).
% 1.72/1.97 tff(5495,plain,
% 1.72/1.97 (b(z, s(z)) <=> b(elem!1, s(z))),
% 1.72/1.97 inference(monotonicity,[status(thm)],[288])).
% 1.72/1.97 tff(5496,plain,
% 1.72/1.97 (b(elem!1, s(z)) <=> b(z, s(z))),
% 1.72/1.97 inference(symmetry,[status(thm)],[5495])).
% 1.72/1.97 tff(5497,plain,
% 1.72/1.97 (b(z, s(z))),
% 1.72/1.97 inference(modus_ponens,[status(thm)],[1391, 5496])).
% 1.72/1.97 tff(5498,assumption,(~b(z, s(z))), introduced(assumption)).
% 1.72/1.97 tff(5499,plain,
% 1.72/1.97 ($false),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[5498, 5497])).
% 1.72/1.97 tff(5500,plain,((~(z = elem!1)) | b(z, s(z)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.97 tff(5501,plain,
% 1.72/1.97 (b(z, s(z))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[5500, 288, 1391])).
% 1.72/1.97 tff(5502,plain,
% 1.72/1.97 (~b(s(z), s(s(s(s(z)))))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[1438, 286, 1391, 287])).
% 1.72/1.97 tff(5503,plain,
% 1.72/1.97 (r(s(z), s(s(s(s(z)))))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[489, 5502])).
% 1.72/1.97 tff(5504,plain,
% 1.72/1.97 (~r(s(z), s(s(s(z))))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[1316, 3979, 5503])).
% 1.72/1.97 tff(5505,plain,
% 1.72/1.97 (b(s(z), s(s(s(z))))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[1263, 5504])).
% 1.72/1.97 tff(5506,plain,
% 1.72/1.97 (~b(s(s(s(z))), s(z))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[1091, 5505, 5501, 1083])).
% 1.72/1.97 tff(5507,plain,
% 1.72/1.97 (r(s(s(s(z))), s(z))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[1081, 5506])).
% 1.72/1.97 tff(5508,plain,
% 1.72/1.97 (r(s(s(s(elem!1))), s(elem!1))),
% 1.72/1.97 inference(modus_ponens,[status(thm)],[5507, 5494])).
% 1.72/1.97 tff(5509,plain,
% 1.72/1.97 (r(s(elem!1), s(s(s(s(z)))))),
% 1.72/1.97 inference(modus_ponens,[status(thm)],[5503, 5478])).
% 1.72/1.97 tff(5510,plain,
% 1.72/1.97 (((~![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(s(s(z)))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.72/1.97 inference(rewrite,[status(thm)],[])).
% 1.72/1.97 tff(5511,plain,
% 1.72/1.97 (((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(elem!1)))) <=> ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.72/1.97 inference(rewrite,[status(thm)],[])).
% 1.72/1.97 tff(5512,plain,
% 1.72/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~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(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 1.72/1.97 inference(monotonicity,[status(thm)],[5511])).
% 1.72/1.97 tff(5513,plain,
% 1.72/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~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(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.72/1.97 inference(transitivity,[status(thm)],[5512, 5510])).
% 1.72/1.97 tff(5514,plain,
% 1.72/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.72/1.97 inference(quant_inst,[status(thm)],[])).
% 1.72/1.97 tff(5515,plain,
% 1.72/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z))))))),
% 1.72/1.97 inference(modus_ponens,[status(thm)],[5514, 5513])).
% 1.72/1.97 tff(5516,plain,
% 1.72/1.97 ($false),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[5515, 37, 5509, 5508, 3980])).
% 1.72/1.97 tff(5517,plain,((~b(elem!1, s(s(s(s(z)))))) | (~(z = elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.97 tff(5518,plain,
% 1.72/1.97 (~b(elem!1, s(s(s(s(z)))))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[5517, 1083, 288, 287, 922, 1391])).
% 1.72/1.97 tff(5519,plain,
% 1.72/1.97 (r(elem!1, s(s(s(s(z)))))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[278, 5518, 3522])).
% 1.72/1.97 tff(5520,plain,
% 1.72/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~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(X1, 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(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.72/1.97 inference(rewrite,[status(thm)],[])).
% 1.72/1.97 tff(5521,plain,
% 1.72/1.97 (((~b(s(z), elem!1)) | (~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(z), elem!1)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.72/1.97 inference(rewrite,[status(thm)],[])).
% 1.72/1.97 tff(5522,plain,
% 1.72/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z))))))))),
% 1.72/1.97 inference(monotonicity,[status(thm)],[5521])).
% 1.72/1.97 tff(5523,plain,
% 1.72/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.72/1.97 inference(transitivity,[status(thm)],[5522, 5520])).
% 1.72/1.97 tff(5524,plain,
% 1.72/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))))))),
% 1.72/1.97 inference(quant_inst,[status(thm)],[])).
% 1.72/1.97 tff(5525,plain,
% 1.72/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z))))))),
% 1.72/1.97 inference(modus_ponens,[status(thm)],[5524, 5523])).
% 1.72/1.97 tff(5526,plain,
% 1.72/1.97 ($false),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[5525, 75, 107, 1391, 578, 287])).
% 1.72/1.97 tff(5527,plain,((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.97 tff(5528,plain,
% 1.72/1.97 (~b(s(z), elem!1)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[5527, 578, 1391, 287])).
% 1.72/1.97 tff(5529,plain,
% 1.72/1.97 (r(s(z), elem!1)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[601, 5528, 2478])).
% 1.72/1.97 tff(5530,plain,
% 1.72/1.97 ((~b(s(s(z)), elem!1)) <=> (~b(s(s(elem!1)), elem!1))),
% 1.72/1.97 inference(monotonicity,[status(thm)],[3648])).
% 1.72/1.97 tff(5531,plain,
% 1.72/1.97 (b(s(elem!1), s(s(s(s(z)))))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[3857, 578, 288])).
% 1.72/1.97 tff(5532,plain,
% 1.72/1.97 (r(s(z), z) <=> r(s(z), elem!1)),
% 1.72/1.97 inference(monotonicity,[status(thm)],[288])).
% 1.72/1.97 tff(5533,plain,
% 1.72/1.97 (r(s(z), elem!1) <=> r(s(z), z)),
% 1.72/1.97 inference(symmetry,[status(thm)],[5532])).
% 1.72/1.97 tff(5534,plain,
% 1.72/1.97 (r(s(z), z)),
% 1.72/1.97 inference(modus_ponens,[status(thm)],[588, 5533])).
% 1.72/1.97 tff(5535,plain,
% 1.72/1.97 (b(z, s(z))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[5500, 1391, 288])).
% 1.72/1.97 tff(5536,plain,
% 1.72/1.97 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 1.72/1.97 inference(monotonicity,[status(thm)],[3418])).
% 1.72/1.97 tff(5537,plain,
% 1.72/1.97 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.72/1.97 inference(symmetry,[status(thm)],[5536])).
% 1.72/1.97 tff(5538,plain,
% 1.72/1.97 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 1.72/1.97 inference(monotonicity,[status(thm)],[288])).
% 1.72/1.97 tff(5539,plain,
% 1.72/1.97 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), z)),
% 1.72/1.97 inference(symmetry,[status(thm)],[5538])).
% 1.72/1.97 tff(5540,plain,
% 1.72/1.97 (b(s(s(z)), elem!1) <=> b(s(s(elem!1)), z)),
% 1.72/1.97 inference(transitivity,[status(thm)],[3648, 5539])).
% 1.72/1.97 tff(5541,plain,
% 1.72/1.97 (b(s(s(elem!1)), z)),
% 1.72/1.97 inference(modus_ponens,[status(thm)],[964, 5540])).
% 1.72/1.97 tff(5542,plain,
% 1.72/1.97 (r(s(z), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.72/1.97 inference(monotonicity,[status(thm)],[289])).
% 1.72/1.97 tff(5543,plain,
% 1.72/1.97 (r(s(elem!1), s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 1.72/1.97 inference(symmetry,[status(thm)],[5542])).
% 1.72/1.97 tff(5544,plain,
% 1.72/1.97 (b(s(s(z)), z) <=> b(s(s(z)), elem!1)),
% 1.72/1.97 inference(monotonicity,[status(thm)],[288])).
% 1.72/1.97 tff(5545,plain,
% 1.72/1.97 (b(s(s(z)), elem!1) <=> b(s(s(z)), z)),
% 1.72/1.97 inference(symmetry,[status(thm)],[5544])).
% 1.72/1.97 tff(5546,plain,
% 1.72/1.97 (b(s(s(z)), z)),
% 1.72/1.97 inference(modus_ponens,[status(thm)],[964, 5545])).
% 1.72/1.97 tff(5547,plain,
% 1.72/1.97 (b(z, s(s(z))) <=> b(elem!1, s(s(z)))),
% 1.72/1.97 inference(monotonicity,[status(thm)],[288])).
% 1.72/1.97 tff(5548,plain,
% 1.72/1.97 (b(elem!1, s(s(z))) <=> b(z, s(s(z)))),
% 1.72/1.97 inference(symmetry,[status(thm)],[5547])).
% 1.72/1.97 tff(5549,plain,
% 1.72/1.97 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(z)))),
% 1.72/1.97 inference(transitivity,[status(thm)],[4269, 5548])).
% 1.72/1.97 tff(5550,plain,
% 1.72/1.97 (b(s(elem!1), s(s(elem!1)))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[1851, 1844, 3438])).
% 1.72/1.97 tff(5551,plain,
% 1.72/1.97 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[4280, 5550, 3862, 4272])).
% 1.72/1.97 tff(5552,plain,
% 1.72/1.97 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[1660, 5551, 5479])).
% 1.72/1.97 tff(5553,plain,
% 1.72/1.97 (~r(elem!1, s(s(elem!1)))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[3811, 5552, 3195])).
% 1.72/1.97 tff(5554,plain,
% 1.72/1.97 (b(elem!1, s(s(elem!1)))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[1617, 5553, 3432])).
% 1.72/1.97 tff(5555,plain,
% 1.72/1.97 (b(z, s(s(z)))),
% 1.72/1.97 inference(modus_ponens,[status(thm)],[5554, 5549])).
% 1.72/1.97 tff(5556,plain,
% 1.72/1.97 (r(s(elem!1), s(s(elem!1))) <=> r(s(z), s(s(z)))),
% 1.72/1.97 inference(symmetry,[status(thm)],[3411])).
% 1.72/1.97 tff(5557,plain,
% 1.72/1.97 ((~r(s(elem!1), s(s(elem!1)))) <=> (~r(s(z), s(s(z))))),
% 1.72/1.97 inference(monotonicity,[status(thm)],[5556])).
% 1.72/1.97 tff(5558,plain,
% 1.72/1.97 (~r(s(z), s(s(z)))),
% 1.72/1.97 inference(modus_ponens,[status(thm)],[1844, 5557])).
% 1.72/1.97 tff(5559,plain,
% 1.72/1.97 (b(s(z), s(s(z)))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[416, 5558])).
% 1.72/1.97 tff(5560,plain,
% 1.72/1.97 (~b(z, s(s(z)))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[410, 5559, 372, 401])).
% 1.72/1.97 tff(5561,plain,
% 1.72/1.97 ($false),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[5560, 5555])).
% 1.72/1.97 tff(5562,plain,(r(s(elem!1), s(s(elem!1))) | (~(z = elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(z))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.97 tff(5563,plain,
% 1.72/1.97 (r(s(elem!1), s(s(elem!1)))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[5562, 5546, 3195, 3862, 4272, 372, 288])).
% 1.72/1.97 tff(5564,plain,
% 1.72/1.97 (r(s(z), s(s(elem!1)))),
% 1.72/1.97 inference(modus_ponens,[status(thm)],[5563, 5543])).
% 1.72/1.97 tff(5565,plain,
% 1.72/1.97 (~r(z, s(s(elem!1)))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[5301, 5564, 1561])).
% 1.72/1.97 tff(5566,assumption,(~r(z, s(s(elem!1)))), introduced(assumption)).
% 1.72/1.97 tff(5567,plain,
% 1.72/1.97 ((z = s(s(elem!1))) | b(z, s(s(elem!1)))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[1834, 58, 5566])).
% 1.72/1.97 tff(5568,plain,
% 1.72/1.97 (b(z, s(s(elem!1)))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[5567, 1824])).
% 1.72/1.97 tff(5569,plain,
% 1.72/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.72/1.97 inference(rewrite,[status(thm)],[])).
% 1.72/1.97 tff(5570,plain,
% 1.72/1.97 (((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.72/1.97 inference(rewrite,[status(thm)],[])).
% 1.72/1.97 tff(5571,plain,
% 1.72/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), z)) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 1.72/1.97 inference(monotonicity,[status(thm)],[5570])).
% 1.72/1.97 tff(5572,plain,
% 1.72/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.72/1.97 inference(transitivity,[status(thm)],[5571, 5569])).
% 1.72/1.97 tff(5573,plain,
% 1.72/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.72/1.97 inference(quant_inst,[status(thm)],[])).
% 1.72/1.97 tff(5574,plain,
% 1.72/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1))))),
% 1.72/1.97 inference(modus_ponens,[status(thm)],[5573, 5572])).
% 1.72/1.97 tff(5575,plain,
% 1.72/1.97 ($false),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[5574, 75, 3628, 5568, 1892, 1083])).
% 1.72/1.97 tff(5576,plain,((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | r(z, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.97 tff(5577,plain,
% 1.72/1.97 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[5576, 5565, 5541, 1083])).
% 1.72/1.97 tff(5578,plain,
% 1.72/1.97 (r(s(s(s(z))), s(s(elem!1)))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[62, 5577, 16])).
% 1.72/1.97 tff(5579,plain,
% 1.72/1.97 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.72/1.97 inference(modus_ponens,[status(thm)],[5578, 5537])).
% 1.72/1.97 tff(5580,plain,
% 1.72/1.97 (r(s(z), s(s(s(z)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 1.72/1.97 inference(monotonicity,[status(thm)],[289, 3417])).
% 1.72/1.97 tff(5581,plain,
% 1.72/1.97 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(z), s(s(s(z))))),
% 1.72/1.97 inference(symmetry,[status(thm)],[3831])).
% 1.72/1.97 tff(5582,plain,
% 1.72/1.97 ((~b(s(elem!1), s(s(s(elem!1))))) <=> (~b(s(z), s(s(s(z)))))),
% 1.72/1.97 inference(monotonicity,[status(thm)],[5581])).
% 1.72/1.97 tff(5583,plain,
% 1.72/1.97 ((~r(s(s(s(elem!1))), s(elem!1))) <=> (~r(s(s(s(z))), s(z)))),
% 1.72/1.97 inference(monotonicity,[status(thm)],[3423])).
% 1.72/1.97 tff(5584,plain,
% 1.72/1.97 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.72/1.97 inference(monotonicity,[status(thm)],[3418])).
% 1.72/1.97 tff(5585,plain,
% 1.72/1.97 ((~b(s(s(s(elem!1))), s(s(elem!1)))) <=> (~b(s(s(s(z))), s(s(elem!1))))),
% 1.72/1.97 inference(monotonicity,[status(thm)],[5584])).
% 1.72/1.97 tff(5586,plain,
% 1.72/1.97 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.72/1.97 inference(monotonicity,[status(thm)],[3417])).
% 1.72/1.97 tff(5587,plain,
% 1.72/1.97 ((s(s(s(z))) = z) <=> (elem!1 = s(s(s(z))))),
% 1.72/1.97 inference(transitivity,[status(thm)],[4143, 3425])).
% 1.72/1.97 tff(5588,plain,
% 1.72/1.97 ((~(s(s(s(z))) = z)) <=> (~(elem!1 = s(s(s(z)))))),
% 1.72/1.97 inference(monotonicity,[status(thm)],[5587])).
% 1.72/1.97 tff(5589,plain,
% 1.72/1.97 (~(elem!1 = s(s(s(z))))),
% 1.72/1.97 inference(modus_ponens,[status(thm)],[221, 5588])).
% 1.72/1.98 tff(5590,plain,
% 1.72/1.98 (r(elem!1, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(z))))),
% 1.72/1.98 inference(monotonicity,[status(thm)],[3418])).
% 1.72/1.98 tff(5591,plain,
% 1.72/1.98 ((~r(elem!1, s(s(s(elem!1))))) <=> (~r(elem!1, s(s(s(z)))))),
% 1.72/1.98 inference(monotonicity,[status(thm)],[5590])).
% 1.72/1.98 tff(5592,plain,
% 1.72/1.98 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.72/1.98 inference(modus_ponens,[status(thm)],[1308, 3976])).
% 1.72/1.98 tff(5593,plain,
% 1.72/1.98 (((~![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(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~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(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.72/1.98 inference(rewrite,[status(thm)],[])).
% 1.72/1.98 tff(5594,plain,
% 1.72/1.98 (((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.72/1.98 inference(rewrite,[status(thm)],[])).
% 1.72/1.98 tff(5595,plain,
% 1.72/1.98 (((~![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(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~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(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(elem!1)))))))),
% 1.72/1.98 inference(monotonicity,[status(thm)],[5594])).
% 1.72/1.98 tff(5596,plain,
% 1.72/1.98 (((~![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(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~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(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.72/1.98 inference(transitivity,[status(thm)],[5595, 5593])).
% 1.72/1.98 tff(5597,plain,
% 1.72/1.98 ((~![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(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.72/1.98 inference(quant_inst,[status(thm)],[])).
% 1.72/1.98 tff(5598,plain,
% 1.72/1.98 ((~![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(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(elem!1)))))),
% 1.72/1.98 inference(modus_ponens,[status(thm)],[5597, 5596])).
% 1.72/1.98 tff(5599,plain,
% 1.72/1.98 ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(elem!1)))))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[5598, 37, 3195])).
% 1.72/1.98 tff(5600,plain,
% 1.72/1.98 (~r(elem!1, s(s(s(elem!1))))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[5599, 5592])).
% 1.72/1.98 tff(5601,plain,
% 1.72/1.98 (~r(elem!1, s(s(s(z))))),
% 1.72/1.98 inference(modus_ponens,[status(thm)],[5600, 5591])).
% 1.72/1.98 tff(5602,plain,
% 1.72/1.98 (b(elem!1, s(s(s(z))))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[1279, 5601, 5589])).
% 1.72/1.98 tff(5603,plain,
% 1.72/1.98 (b(elem!1, s(s(s(elem!1))))),
% 1.72/1.98 inference(modus_ponens,[status(thm)],[5602, 5586])).
% 1.72/1.98 tff(5604,plain,
% 1.72/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), s(s(elem!1)))))),
% 1.72/1.98 inference(rewrite,[status(thm)],[])).
% 1.72/1.98 tff(5605,plain,
% 1.72/1.98 (((~b(s(s(s(elem!1))), 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(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))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.72/1.98 inference(rewrite,[status(thm)],[])).
% 1.72/1.98 tff(5606,plain,
% 1.72/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(elem!1))), s(s(elem!1))))))),
% 1.72/1.98 inference(monotonicity,[status(thm)],[5605])).
% 1.72/1.98 tff(5607,plain,
% 1.72/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(elem!1))), s(s(elem!1)))))),
% 1.72/1.98 inference(transitivity,[status(thm)],[5606, 5604])).
% 1.72/1.98 tff(5608,plain,
% 1.72/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))))),
% 1.72/1.98 inference(quant_inst,[status(thm)],[])).
% 1.72/1.98 tff(5609,plain,
% 1.72/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), s(s(elem!1))))),
% 1.72/1.98 inference(modus_ponens,[status(thm)],[5608, 5607])).
% 1.72/1.98 tff(5610,plain,
% 1.72/1.98 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[5609, 75, 707, 5603, 922])).
% 1.72/1.98 tff(5611,plain,
% 1.72/1.98 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.72/1.98 inference(modus_ponens,[status(thm)],[5610, 5585])).
% 1.72/1.98 tff(5612,plain,
% 1.72/1.98 (r(s(s(s(z))), s(s(elem!1)))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[62, 5611, 16])).
% 1.72/1.98 tff(5613,plain,
% 1.72/1.98 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.72/1.98 inference(modus_ponens,[status(thm)],[5612, 5537])).
% 1.72/1.98 tff(5614,plain,
% 1.72/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(s(s(elem!1))))))),
% 1.72/1.98 inference(rewrite,[status(thm)],[])).
% 1.72/1.98 tff(5615,plain,
% 1.72/1.98 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(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(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.72/1.98 inference(rewrite,[status(thm)],[])).
% 1.72/1.98 tff(5616,plain,
% 1.72/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(elem!1)), s(s(s(elem!1)))))))),
% 1.72/1.98 inference(monotonicity,[status(thm)],[5615])).
% 1.72/1.98 tff(5617,plain,
% 1.72/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(elem!1)), s(s(s(elem!1))))))),
% 1.72/1.98 inference(transitivity,[status(thm)],[5616, 5614])).
% 1.72/1.98 tff(5618,plain,
% 1.72/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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))))))),
% 1.72/1.98 inference(quant_inst,[status(thm)],[])).
% 1.72/1.98 tff(5619,plain,
% 1.72/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(s(s(elem!1)))))),
% 1.72/1.98 inference(modus_ponens,[status(thm)],[5618, 5617])).
% 1.72/1.98 tff(5620,plain,
% 1.72/1.98 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[5619, 75, 707, 5603, 922])).
% 1.72/1.98 tff(5621,plain,
% 1.72/1.98 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.72/1.98 inference(modus_ponens,[status(thm)],[5620, 4224])).
% 1.72/1.98 tff(5622,plain,
% 1.72/1.98 (r(s(s(elem!1)), s(s(s(z))))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[1936, 5621, 4222])).
% 1.72/1.98 tff(5623,plain,
% 1.72/1.98 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[4241, 5622, 1308])).
% 1.72/1.98 tff(5624,plain,
% 1.72/1.98 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[1660, 5623, 5479])).
% 1.72/1.98 tff(5625,plain,
% 1.72/1.98 (~b(s(elem!1), s(s(elem!1)))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[4278, 75, 5624, 3862, 4272])).
% 1.72/1.98 tff(5626,plain,
% 1.72/1.98 (r(s(elem!1), s(s(elem!1)))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[1851, 5625, 3438])).
% 1.72/1.98 tff(5627,plain,
% 1.72/1.98 ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[5160, 37, 5626])).
% 1.72/1.98 tff(5628,plain,
% 1.72/1.98 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[5627, 5613])).
% 1.72/1.98 tff(5629,plain,
% 1.72/1.98 (~r(s(s(s(z))), s(z))),
% 1.72/1.98 inference(modus_ponens,[status(thm)],[5628, 5583])).
% 1.72/1.98 tff(5630,plain,
% 1.72/1.98 (b(s(s(s(z))), s(z))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[1081, 5629])).
% 1.72/1.98 tff(5631,plain,
% 1.72/1.98 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(z), s(s(s(z))))),
% 1.72/1.98 inference(symmetry,[status(thm)],[5580])).
% 1.72/1.98 tff(5632,plain,
% 1.72/1.98 ((~r(s(elem!1), s(s(s(elem!1))))) <=> (~r(s(z), s(s(s(z)))))),
% 1.72/1.98 inference(monotonicity,[status(thm)],[5631])).
% 1.72/1.98 tff(5633,plain,
% 1.72/1.98 (((~![X0: $i, 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)))))),
% 1.72/1.98 inference(rewrite,[status(thm)],[])).
% 1.72/1.98 tff(5634,plain,
% 1.72/1.98 (((~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)))))),
% 1.72/1.98 inference(rewrite,[status(thm)],[])).
% 1.72/1.98 tff(5635,plain,
% 1.72/1.98 (((~![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(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))))))),
% 1.72/1.98 inference(monotonicity,[status(thm)],[5634])).
% 1.72/1.98 tff(5636,plain,
% 1.72/1.98 (((~![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(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)))))),
% 1.72/1.98 inference(transitivity,[status(thm)],[5635, 5633])).
% 1.72/1.98 tff(5637,plain,
% 1.72/1.98 ((~![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(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))))))),
% 1.72/1.98 inference(quant_inst,[status(thm)],[])).
% 1.72/1.98 tff(5638,plain,
% 1.72/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.72/1.98 inference(modus_ponens,[status(thm)],[5637, 5636])).
% 1.72/1.98 tff(5639,plain,
% 1.72/1.98 ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[5638, 37, 5626])).
% 1.72/1.98 tff(5640,plain,
% 1.72/1.98 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[5639, 5613])).
% 1.72/1.98 tff(5641,plain,
% 1.72/1.98 (~r(s(z), s(s(s(z))))),
% 1.72/1.98 inference(modus_ponens,[status(thm)],[5640, 5632])).
% 1.72/1.98 tff(5642,plain,
% 1.72/1.98 (b(s(z), s(s(s(z))))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[1263, 5641])).
% 1.72/1.98 tff(5643,plain,
% 1.72/1.98 ($false),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[1091, 5642, 5630, 1083, 372])).
% 1.72/1.98 tff(5644,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~(z = elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (s(s(s(z))) = s(s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.98 tff(5645,plain,
% 1.72/1.98 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[5644, 4146, 372, 288, 3862, 4272, 16, 1083, 922, 3195])).
% 1.72/1.98 tff(5646,plain,
% 1.72/1.98 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[575, 5645])).
% 1.72/1.98 tff(5647,plain,
% 1.72/1.98 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.72/1.98 inference(modus_ponens,[status(thm)],[5646, 3832])).
% 1.72/1.98 tff(5648,plain,
% 1.72/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(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(X1, 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(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.72/1.98 inference(rewrite,[status(thm)],[])).
% 1.72/1.98 tff(5649,plain,
% 1.72/1.98 (((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.72/1.98 inference(rewrite,[status(thm)],[])).
% 1.72/1.98 tff(5650,plain,
% 1.72/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 1.72/1.98 inference(monotonicity,[status(thm)],[5649])).
% 1.72/1.98 tff(5651,plain,
% 1.72/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.72/1.98 inference(transitivity,[status(thm)],[5650, 5648])).
% 1.72/1.98 tff(5652,plain,
% 1.72/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.72/1.98 inference(quant_inst,[status(thm)],[])).
% 1.72/1.98 tff(5653,plain,
% 1.72/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 1.72/1.98 inference(modus_ponens,[status(thm)],[5652, 5651])).
% 1.72/1.98 tff(5654,plain,
% 1.72/1.98 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[5653, 75, 5647, 3862, 4272])).
% 1.72/1.98 tff(5655,plain,
% 1.72/1.98 (~b(s(z), s(s(s(z))))),
% 1.72/1.98 inference(modus_ponens,[status(thm)],[5654, 5582])).
% 1.72/1.98 tff(5656,plain,
% 1.72/1.98 (r(s(z), s(s(s(z))))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[1263, 5655])).
% 1.72/1.98 tff(5657,plain,
% 1.72/1.98 (r(s(elem!1), s(s(s(elem!1))))),
% 1.72/1.98 inference(modus_ponens,[status(thm)],[5656, 5580])).
% 1.72/1.98 tff(5658,plain,
% 1.72/1.98 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[5638, 37, 5563, 5657])).
% 1.72/1.98 tff(5659,plain,
% 1.72/1.98 ($false),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[5658, 5579])).
% 1.72/1.98 tff(5660,plain,((~b(s(s(z)), elem!1)) | (~(z = elem!1)) | (s(s(s(z))) = s(s(elem!1))) | (~b(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.98 tff(5661,plain,
% 1.72/1.98 (~b(s(s(z)), elem!1)),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[5660, 5535, 16, 1083, 5534, 3195, 5531, 4272, 288, 922])).
% 1.72/1.99 tff(5662,plain,
% 1.72/1.99 (~b(s(s(elem!1)), elem!1)),
% 1.72/1.99 inference(modus_ponens,[status(thm)],[5661, 5530])).
% 1.72/1.99 tff(5663,plain,
% 1.72/1.99 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(z))),
% 1.72/1.99 inference(monotonicity,[status(thm)],[3422])).
% 1.72/1.99 tff(5664,plain,
% 1.72/1.99 (b(s(s(s(s(z)))), s(z))),
% 1.72/1.99 inference(modus_ponens,[status(thm)],[4272, 5663])).
% 1.72/1.99 tff(5665,plain,
% 1.72/1.99 (r(s(s(z)), elem!1)),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[104, 5661, 5480])).
% 1.72/1.99 tff(5666,plain,
% 1.72/1.99 (~r(s(s(z)), s(z))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[596, 5665, 588])).
% 1.72/1.99 tff(5667,plain,
% 1.72/1.99 (b(s(s(z)), s(z))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[153, 5666])).
% 1.72/1.99 tff(5668,plain,
% 1.72/1.99 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[3906, 5667, 5664, 578])).
% 1.72/1.99 tff(5669,plain,
% 1.72/1.99 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[3926, 5668, 3839])).
% 1.72/1.99 tff(5670,plain,
% 1.72/1.99 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[1660, 5669, 5479])).
% 1.72/1.99 tff(5671,plain,
% 1.72/1.99 (~r(elem!1, s(s(elem!1)))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[3811, 5670, 3195])).
% 1.72/1.99 tff(5672,plain,
% 1.72/1.99 (b(elem!1, s(s(elem!1)))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[1617, 5671, 3432])).
% 1.72/1.99 tff(5673,plain,
% 1.72/1.99 (~r(s(z), s(s(elem!1)))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[3753, 2647, 588])).
% 1.72/1.99 tff(5674,plain,
% 1.72/1.99 (b(s(z), s(s(elem!1)))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[1890, 5673])).
% 1.72/1.99 tff(5675,plain,
% 1.72/1.99 (((~![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)), s(z))) | (~r(s(z), 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)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 1.72/1.99 inference(rewrite,[status(thm)],[])).
% 1.72/1.99 tff(5676,plain,
% 1.72/1.99 (((~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 1.72/1.99 inference(rewrite,[status(thm)],[])).
% 1.72/1.99 tff(5677,plain,
% 1.72/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1))))),
% 1.72/1.99 inference(monotonicity,[status(thm)],[5676])).
% 1.72/1.99 tff(5678,plain,
% 1.72/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 1.72/1.99 inference(transitivity,[status(thm)],[5677, 5675])).
% 1.72/1.99 tff(5679,plain,
% 1.72/1.99 ((~![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))))),
% 1.72/1.99 inference(quant_inst,[status(thm)],[])).
% 1.72/1.99 tff(5680,plain,
% 1.72/1.99 ((~![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)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1))),
% 1.72/1.99 inference(modus_ponens,[status(thm)],[5679, 5678])).
% 1.72/1.99 tff(5681,plain,
% 1.72/1.99 (~r(s(s(elem!1)), s(z))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[5680, 37, 588, 2647])).
% 1.72/1.99 tff(5682,plain,
% 1.72/1.99 (b(s(s(elem!1)), s(z))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[561, 5681])).
% 1.72/1.99 tff(5683,plain,
% 1.72/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), s(z))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), s(z))) | (~b(elem!1, s(z))))),
% 1.72/1.99 inference(rewrite,[status(thm)],[])).
% 1.72/1.99 tff(5684,plain,
% 1.72/1.99 (((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))))),
% 1.72/1.99 inference(rewrite,[status(thm)],[])).
% 1.72/1.99 tff(5685,plain,
% 1.72/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), s(z))) | (~b(elem!1, s(z)))))),
% 1.72/1.99 inference(monotonicity,[status(thm)],[5684])).
% 1.72/1.99 tff(5686,plain,
% 1.72/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), s(z))) | (~b(elem!1, s(z))))),
% 1.72/1.99 inference(transitivity,[status(thm)],[5685, 5683])).
% 1.72/1.99 tff(5687,plain,
% 1.72/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 1.72/1.99 inference(quant_inst,[status(thm)],[])).
% 1.72/1.99 tff(5688,plain,
% 1.72/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z)))),
% 1.72/1.99 inference(modus_ponens,[status(thm)],[5687, 5686])).
% 1.72/1.99 tff(5689,plain,
% 1.72/1.99 ($false),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[5688, 75, 5682, 1620, 1391, 5674])).
% 1.72/1.99 tff(5690,plain,((~r(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.99 tff(5691,plain,
% 1.72/1.99 (~r(s(s(elem!1)), elem!1)),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[5690, 5672, 588, 1391])).
% 1.72/1.99 tff(5692,plain,
% 1.72/1.99 (b(s(s(elem!1)), elem!1)),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[2673, 5691, 5484])).
% 1.72/1.99 tff(5693,plain,
% 1.72/1.99 ($false),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[5692, 5662])).
% 1.72/1.99 tff(5694,plain,((~b(elem!1, s(z))) | (~(z = elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (s(s(s(z))) = s(s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.99 tff(5695,plain,
% 1.72/1.99 (~b(s(s(s(s(z)))), s(elem!1))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[5694, 5529, 1391, 922, 5519, 5493, 1083, 578, 288])).
% 1.72/1.99 tff(5696,plain,
% 1.72/1.99 (r(s(s(s(s(z)))), s(elem!1))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[4263, 58, 5695, 4260])).
% 1.72/1.99 tff(5697,assumption,(s(s(s(s(z)))) = s(s(elem!1))), introduced(assumption)).
% 1.72/1.99 tff(5698,plain,
% 1.72/1.99 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.72/1.99 inference(symmetry,[status(thm)],[5697])).
% 1.72/1.99 tff(5699,plain,
% 1.72/1.99 ($false),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[1011, 5698])).
% 1.72/1.99 tff(5700,plain,((~(s(s(s(s(z)))) = s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.99 tff(5701,plain,
% 1.72/1.99 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[5700, 5479])).
% 1.72/1.99 tff(5702,plain,
% 1.72/1.99 (~b(elem!1, s(s(elem!1)))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[5690, 5529, 1391, 2647])).
% 1.72/1.99 tff(5703,plain,
% 1.72/1.99 (r(elem!1, s(s(elem!1)))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[1617, 5702, 3432])).
% 1.72/1.99 tff(5704,plain,
% 1.72/1.99 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[3811, 5703, 5519])).
% 1.72/1.99 tff(5705,plain,
% 1.72/1.99 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[1660, 5704, 5479])).
% 1.72/1.99 tff(5706,plain,
% 1.72/1.99 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), s(elem!1))),
% 1.72/1.99 inference(monotonicity,[status(thm)],[289])).
% 1.72/1.99 tff(5707,plain,
% 1.72/1.99 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(z))),
% 1.72/1.99 inference(symmetry,[status(thm)],[5706])).
% 1.72/1.99 tff(5708,plain,
% 1.72/1.99 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.72/1.99 inference(transitivity,[status(thm)],[3570, 5707])).
% 1.72/1.99 tff(5709,plain,
% 1.72/1.99 (~r(s(s(z)), s(z))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[596, 5529, 106])).
% 1.72/1.99 tff(5710,plain,
% 1.72/1.99 (b(s(s(z)), s(z))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[153, 5709])).
% 1.72/1.99 tff(5711,plain,
% 1.72/1.99 (b(s(s(elem!1)), s(z))),
% 1.72/1.99 inference(modus_ponens,[status(thm)],[5710, 5708])).
% 1.72/1.99 tff(5712,assumption,(b(s(s(s(s(z)))), s(s(elem!1)))), introduced(assumption)).
% 1.72/1.99 tff(5713,plain,
% 1.72/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.72/1.99 inference(rewrite,[status(thm)],[])).
% 1.72/1.99 tff(5714,plain,
% 1.72/1.99 (((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.72/1.99 inference(rewrite,[status(thm)],[])).
% 1.72/1.99 tff(5715,plain,
% 1.72/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))))),
% 1.72/1.99 inference(monotonicity,[status(thm)],[5714])).
% 1.72/1.99 tff(5716,plain,
% 1.72/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.72/1.99 inference(transitivity,[status(thm)],[5715, 5713])).
% 1.72/1.99 tff(5717,plain,
% 1.72/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))))),
% 1.72/1.99 inference(quant_inst,[status(thm)],[])).
% 1.72/1.99 tff(5718,plain,
% 1.72/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 1.72/1.99 inference(modus_ponens,[status(thm)],[5717, 5716])).
% 1.72/1.99 tff(5719,plain,
% 1.72/1.99 ($false),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[5718, 75, 1457, 578, 1619, 5712])).
% 1.72/1.99 tff(5720,plain,((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.99 tff(5721,plain,
% 1.72/1.99 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[5720, 5711, 578, 5705])).
% 1.72/1.99 tff(5722,plain,
% 1.72/1.99 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[3876, 58, 5721, 5701])).
% 1.72/1.99 tff(5723,plain,
% 1.72/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), 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(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(s(elem!1)))))),
% 1.72/1.99 inference(rewrite,[status(thm)],[])).
% 1.72/1.99 tff(5724,plain,
% 1.72/1.99 (((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(s(elem!1)))))),
% 1.72/1.99 inference(rewrite,[status(thm)],[])).
% 1.72/1.99 tff(5725,plain,
% 1.72/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(s(elem!1))))))),
% 1.72/1.99 inference(monotonicity,[status(thm)],[5724])).
% 1.72/1.99 tff(5726,plain,
% 1.72/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(s(elem!1)))))),
% 1.72/1.99 inference(transitivity,[status(thm)],[5725, 5723])).
% 1.72/1.99 tff(5727,plain,
% 1.72/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.72/1.99 inference(quant_inst,[status(thm)],[])).
% 1.72/1.99 tff(5728,plain,
% 1.72/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(elem!1, s(s(elem!1))))),
% 1.72/1.99 inference(modus_ponens,[status(thm)],[5727, 5726])).
% 1.72/1.99 tff(5729,plain,
% 1.72/1.99 ($false),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[5728, 37, 5703, 5519, 5722, 5696])).
% 1.72/1.99 tff(5730,plain,((~b(s(z), s(s(s(s(z)))))) | (~(z = elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.99 tff(5731,plain,
% 1.72/1.99 (~b(s(z), s(s(s(s(z)))))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[5730, 5491, 1391, 288, 5489, 106, 2647, 287])).
% 1.72/1.99 tff(5732,plain,
% 1.72/1.99 (r(s(z), s(s(s(s(z)))))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[489, 5731])).
% 1.72/1.99 tff(5733,plain,
% 1.72/1.99 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 1.72/1.99 inference(monotonicity,[status(thm)],[289])).
% 1.72/1.99 tff(5734,plain,
% 1.72/1.99 (b(elem!1, s(elem!1))),
% 1.72/1.99 inference(modus_ponens,[status(thm)],[1391, 5733])).
% 1.72/1.99 tff(5735,plain,
% 1.72/1.99 (r(s(elem!1), s(s(s(s(z)))))),
% 1.72/1.99 inference(modus_ponens,[status(thm)],[5732, 5478])).
% 1.72/1.99 tff(5736,plain,
% 1.72/1.99 (~b(elem!1, s(s(s(s(z)))))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[5517, 5489, 288, 287, 5491, 1391])).
% 1.72/1.99 tff(5737,plain,
% 1.72/1.99 (r(elem!1, s(s(s(s(z)))))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[278, 5736, 3522])).
% 1.72/1.99 tff(5738,plain,
% 1.72/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.72/1.99 inference(rewrite,[status(thm)],[])).
% 1.72/1.99 tff(5739,plain,
% 1.72/1.99 (((~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), elem!1))) <=> ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.72/1.99 inference(rewrite,[status(thm)],[])).
% 1.72/1.99 tff(5740,plain,
% 1.72/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 1.72/1.99 inference(monotonicity,[status(thm)],[5739])).
% 1.72/1.99 tff(5741,plain,
% 1.72/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.72/1.99 inference(transitivity,[status(thm)],[5740, 5738])).
% 1.72/1.99 tff(5742,plain,
% 1.72/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), elem!1)))),
% 1.72/1.99 inference(quant_inst,[status(thm)],[])).
% 1.72/1.99 tff(5743,plain,
% 1.72/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z))))))),
% 1.72/1.99 inference(modus_ponens,[status(thm)],[5742, 5741])).
% 1.72/1.99 tff(5744,plain,
% 1.72/1.99 (~r(s(elem!1), elem!1)),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[5743, 37, 5737, 5735])).
% 1.72/1.99 tff(5745,plain,
% 1.72/1.99 (~r(s(z), elem!1)),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[4005, 5744, 288])).
% 1.72/1.99 tff(5746,plain,
% 1.72/1.99 (b(s(z), elem!1)),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[601, 5745, 2478])).
% 1.72/1.99 tff(5747,plain,
% 1.72/1.99 (b(s(elem!1), elem!1)),
% 1.72/1.99 inference(modus_ponens,[status(thm)],[5746, 3568])).
% 1.72/1.99 tff(5748,plain,
% 1.72/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.72/2.00 inference(rewrite,[status(thm)],[])).
% 1.72/2.00 tff(5749,plain,
% 1.72/2.00 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.72/2.00 inference(rewrite,[status(thm)],[])).
% 1.72/2.00 tff(5750,plain,
% 1.72/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1))))),
% 1.72/2.00 inference(monotonicity,[status(thm)],[5749])).
% 1.72/2.00 tff(5751,plain,
% 1.72/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.72/2.00 inference(transitivity,[status(thm)],[5750, 5748])).
% 1.72/2.00 tff(5752,plain,
% 1.72/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.72/2.00 inference(quant_inst,[status(thm)],[])).
% 1.72/2.00 tff(5753,plain,
% 1.72/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1))),
% 1.72/2.00 inference(modus_ponens,[status(thm)],[5752, 5751])).
% 1.72/2.00 tff(5754,plain,
% 1.72/2.00 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[5753, 75, 5747, 5491, 5734])).
% 1.72/2.00 tff(5755,plain,
% 1.72/2.00 (~b(s(z), s(s(s(z))))),
% 1.72/2.00 inference(modus_ponens,[status(thm)],[5754, 5582])).
% 1.72/2.00 tff(5756,plain,
% 1.72/2.00 (r(s(z), s(s(s(z))))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[1263, 5755])).
% 1.72/2.00 tff(5757,plain,
% 1.72/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.72/2.00 inference(rewrite,[status(thm)],[])).
% 1.72/2.00 tff(5758,plain,
% 1.72/2.00 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.72/2.00 inference(rewrite,[status(thm)],[])).
% 1.72/2.00 tff(5759,plain,
% 1.72/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~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(X1, 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(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1))))),
% 1.72/2.00 inference(monotonicity,[status(thm)],[5758])).
% 1.72/2.00 tff(5760,plain,
% 1.72/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~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(X1, 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(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.72/2.00 inference(transitivity,[status(thm)],[5759, 5757])).
% 1.72/2.00 tff(5761,plain,
% 1.72/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.72/2.00 inference(quant_inst,[status(thm)],[])).
% 1.72/2.00 tff(5762,plain,
% 1.72/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1))),
% 1.72/2.00 inference(modus_ponens,[status(thm)],[5761, 5760])).
% 1.72/2.00 tff(5763,plain,
% 1.72/2.00 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[5762, 75, 287, 5747, 5491, 5734])).
% 1.72/2.00 tff(5764,plain,
% 1.72/2.00 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.72/2.00 inference(modus_ponens,[status(thm)],[5763, 3834])).
% 1.72/2.00 tff(5765,plain,
% 1.72/2.00 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[575, 5764])).
% 1.72/2.00 tff(5766,plain,
% 1.72/2.00 ($false),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[1316, 5765, 5756, 5732])).
% 1.72/2.00 tff(5767,plain,((~b(s(s(s(z))), elem!1)) | (~(z = elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.72/2.00 tff(5768,plain,
% 1.72/2.00 (~b(s(s(s(z))), elem!1)),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[5767, 5481, 287, 1391, 288, 5486])).
% 1.72/2.00 tff(5769,plain,
% 1.72/2.00 (r(s(s(s(z))), elem!1)),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[1115, 5768, 4145])).
% 1.72/2.00 tff(5770,plain,
% 1.72/2.00 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(z))), s(z))),
% 1.72/2.00 inference(symmetry,[status(thm)],[5494])).
% 1.72/2.00 tff(5771,plain,
% 1.72/2.00 ((~r(s(s(s(elem!1))), s(elem!1))) <=> (~r(s(s(s(z))), s(z)))),
% 1.72/2.00 inference(monotonicity,[status(thm)],[5770])).
% 1.72/2.00 tff(5772,plain,
% 1.72/2.00 (r(s(elem!1), elem!1)),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[4005, 588, 288])).
% 1.72/2.00 tff(5773,plain,
% 1.72/2.00 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[651, 37, 5772, 4177])).
% 1.72/2.00 tff(5774,plain,
% 1.72/2.00 (~r(s(s(s(z))), s(z))),
% 1.72/2.00 inference(modus_ponens,[status(thm)],[5773, 5771])).
% 1.72/2.00 tff(5775,plain,
% 1.72/2.00 (~r(s(z), s(s(elem!1)))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[3753, 588, 2647])).
% 1.72/2.00 tff(5776,plain,
% 1.72/2.00 (b(s(z), s(s(elem!1)))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[1890, 5775])).
% 1.72/2.00 tff(5777,plain,
% 1.72/2.00 (~r(s(s(z)), s(z))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[596, 588, 106])).
% 1.72/2.00 tff(5778,plain,
% 1.72/2.00 (b(s(s(z)), s(z))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[153, 5777])).
% 1.72/2.00 tff(5779,plain,
% 1.72/2.00 (b(s(s(elem!1)), s(z))),
% 1.72/2.00 inference(modus_ponens,[status(thm)],[5778, 5708])).
% 1.72/2.00 tff(5780,plain,
% 1.72/2.00 (~b(s(s(s(z))), s(z))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[4506, 5779, 16, 2647, 1061, 5776])).
% 1.72/2.00 tff(5781,plain,
% 1.72/2.00 (r(s(s(s(z))), s(z))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[1081, 5780])).
% 1.72/2.00 tff(5782,plain,
% 1.72/2.00 ($false),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[5781, 5774])).
% 1.72/2.00 tff(5783,plain,((~r(s(z), elem!1)) | (~(z = elem!1)) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.72/2.00 tff(5784,plain,
% 1.72/2.00 (~r(s(z), elem!1)),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[5783, 5486, 5493, 288, 5769, 5481])).
% 1.72/2.00 tff(5785,plain,
% 1.72/2.00 (b(s(z), elem!1)),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[601, 5784, 2478])).
% 1.72/2.00 tff(5786,plain,
% 1.72/2.00 (~b(s(z), s(s(s(s(z)))))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[5527, 5785, 1391, 287])).
% 1.72/2.00 tff(5787,plain,
% 1.72/2.00 (r(s(z), s(s(s(s(z)))))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[489, 5786])).
% 1.72/2.00 tff(5788,plain,
% 1.72/2.00 (r(s(elem!1), s(s(s(s(z)))))),
% 1.72/2.00 inference(modus_ponens,[status(thm)],[5787, 5478])).
% 1.72/2.00 tff(5789,plain,
% 1.72/2.00 (b(s(elem!1), elem!1)),
% 1.72/2.00 inference(modus_ponens,[status(thm)],[5785, 3568])).
% 1.72/2.00 tff(5790,plain,
% 1.72/2.00 (r(s(s(s(elem!1))), elem!1)),
% 1.72/2.00 inference(modus_ponens,[status(thm)],[5769, 4176])).
% 1.72/2.00 tff(5791,assumption,(elem!1 = s(s(s(elem!1)))), introduced(assumption)).
% 1.72/2.00 tff(5792,plain,
% 1.72/2.00 (s(s(s(elem!1))) = elem!1),
% 1.72/2.00 inference(symmetry,[status(thm)],[5791])).
% 1.72/2.00 tff(5793,plain,
% 1.72/2.00 (s(s(s(elem!1))) = z),
% 1.72/2.00 inference(transitivity,[status(thm)],[5792, 3962])).
% 1.72/2.00 tff(5794,plain,
% 1.72/2.00 ($false),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[662, 5793])).
% 1.72/2.00 tff(5795,plain,((~(elem!1 = s(s(s(elem!1))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.72/2.00 tff(5796,plain,
% 1.72/2.00 (~(elem!1 = s(s(s(elem!1))))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[5795, 288])).
% 1.72/2.00 tff(5797,assumption,(s(s(elem!1)) = s(s(s(elem!1)))), introduced(assumption)).
% 1.72/2.00 tff(5798,plain,
% 1.72/2.00 (inj_0(s(s(elem!1))) = inj_0(s(s(s(elem!1))))),
% 1.72/2.00 inference(monotonicity,[status(thm)],[5797])).
% 1.72/2.00 tff(5799,plain,
% 1.72/2.00 (s(elem!1) = s(s(s(elem!1)))),
% 1.72/2.00 inference(transitivity,[status(thm)],[229, 5798, 11, 5797])).
% 1.72/2.00 tff(5800,plain,
% 1.72/2.00 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 1.72/2.00 inference(monotonicity,[status(thm)],[5799])).
% 1.72/2.00 tff(5801,plain,
% 1.72/2.00 (elem!1 = s(s(s(elem!1)))),
% 1.72/2.00 inference(transitivity,[status(thm)],[725, 5800, 11, 5797])).
% 1.72/2.00 tff(5802,assumption,(~(elem!1 = s(s(s(elem!1))))), introduced(assumption)).
% 1.72/2.00 tff(5803,plain,
% 1.72/2.00 ($false),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[5802, 5801])).
% 1.72/2.00 tff(5804,plain,((~(s(s(elem!1)) = s(s(s(elem!1))))) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.72/2.00 tff(5805,plain,
% 1.72/2.00 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[5804, 5796])).
% 1.72/2.00 tff(5806,plain,
% 1.72/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(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(elem!1)), s(s(s(elem!1))))))),
% 1.72/2.00 inference(rewrite,[status(thm)],[])).
% 1.72/2.00 tff(5807,plain,
% 1.72/2.00 (((~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(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.72/2.00 inference(rewrite,[status(thm)],[])).
% 1.72/2.00 tff(5808,plain,
% 1.72/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.72/2.00 inference(monotonicity,[status(thm)],[5807])).
% 1.72/2.00 tff(5809,plain,
% 1.72/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.72/2.00 inference(transitivity,[status(thm)],[5808, 5806])).
% 1.72/2.00 tff(5810,plain,
% 1.72/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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))))))),
% 1.72/2.00 inference(quant_inst,[status(thm)],[])).
% 1.72/2.00 tff(5811,plain,
% 1.72/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.72/2.00 inference(modus_ponens,[status(thm)],[5810, 5809])).
% 1.72/2.00 tff(5812,plain,
% 1.72/2.00 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[5811, 37, 5486, 5790])).
% 1.72/2.00 tff(5813,plain,
% 1.72/2.00 (((~![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)))))),
% 1.72/2.00 inference(rewrite,[status(thm)],[])).
% 1.72/2.00 tff(5814,plain,
% 1.72/2.00 ((~![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)))))),
% 1.72/2.00 inference(quant_inst,[status(thm)],[])).
% 1.72/2.00 tff(5815,plain,
% 1.72/2.00 ((~![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))))),
% 1.72/2.00 inference(modus_ponens,[status(thm)],[5814, 5813])).
% 1.72/2.00 tff(5816,plain,
% 1.72/2.00 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[5815, 58, 5812, 5805])).
% 1.72/2.00 tff(5817,plain,
% 1.72/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!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(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 1.72/2.00 inference(rewrite,[status(thm)],[])).
% 1.72/2.00 tff(5818,plain,
% 1.72/2.00 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 1.72/2.00 inference(rewrite,[status(thm)],[])).
% 1.72/2.00 tff(5819,plain,
% 1.72/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(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))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))))),
% 1.72/2.00 inference(monotonicity,[status(thm)],[5818])).
% 1.72/2.00 tff(5820,plain,
% 1.72/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(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))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 1.72/2.00 inference(transitivity,[status(thm)],[5819, 5817])).
% 1.72/2.00 tff(5821,plain,
% 1.72/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 1.72/2.00 inference(quant_inst,[status(thm)],[])).
% 1.72/2.00 tff(5822,plain,
% 1.72/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 1.72/2.00 inference(modus_ponens,[status(thm)],[5821, 5820])).
% 1.72/2.00 tff(5823,plain,
% 1.72/2.00 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[5822, 37, 738, 624])).
% 1.72/2.00 tff(5824,plain,
% 1.72/2.00 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[870, 868])).
% 1.72/2.00 tff(5825,plain,
% 1.72/2.00 (b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[874, 58, 5824, 5823])).
% 1.72/2.00 tff(5826,plain,
% 1.72/2.00 (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[4183, 37, 738, 624])).
% 1.72/2.00 tff(5827,plain,
% 1.72/2.00 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[3083, 58, 868, 5826])).
% 1.72/2.00 tff(5828,plain,
% 1.72/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 1.72/2.00 inference(rewrite,[status(thm)],[])).
% 1.72/2.00 tff(5829,plain,
% 1.72/2.00 (((~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 1.72/2.00 inference(rewrite,[status(thm)],[])).
% 1.72/2.00 tff(5830,plain,
% 1.72/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))))),
% 1.72/2.00 inference(monotonicity,[status(thm)],[5829])).
% 1.72/2.00 tff(5831,plain,
% 1.72/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 1.72/2.01 inference(transitivity,[status(thm)],[5830, 5828])).
% 1.72/2.01 tff(5832,plain,
% 1.72/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.72/2.01 inference(quant_inst,[status(thm)],[])).
% 1.72/2.01 tff(5833,plain,
% 1.72/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))),
% 1.72/2.01 inference(modus_ponens,[status(thm)],[5832, 5831])).
% 1.72/2.01 tff(5834,plain,
% 1.72/2.01 ($false),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[5833, 75, 5071, 5827, 3068, 5825])).
% 1.72/2.01 tff(5835,plain,((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))) | (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.72/2.01 tff(5836,plain,
% 1.72/2.01 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[5835, 5816, 3974, 3959, 5790, 5486])).
% 1.72/2.01 tff(5837,plain,
% 1.72/2.01 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[813, 5836, 3966])).
% 1.72/2.01 tff(5838,plain,
% 1.72/2.01 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[5193, 75, 5837, 5789, 5734])).
% 1.72/2.01 tff(5839,plain,
% 1.72/2.01 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[793, 58, 3961, 5838])).
% 1.72/2.01 tff(5840,plain,
% 1.72/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.72/2.01 inference(rewrite,[status(thm)],[])).
% 1.72/2.01 tff(5841,plain,
% 1.72/2.01 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.72/2.01 inference(rewrite,[status(thm)],[])).
% 1.72/2.01 tff(5842,plain,
% 1.72/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 1.72/2.01 inference(monotonicity,[status(thm)],[5841])).
% 1.72/2.01 tff(5843,plain,
% 1.72/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.72/2.01 inference(transitivity,[status(thm)],[5842, 5840])).
% 1.72/2.01 tff(5844,plain,
% 1.72/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.72/2.01 inference(quant_inst,[status(thm)],[])).
% 1.72/2.01 tff(5845,plain,
% 1.72/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 1.72/2.01 inference(modus_ponens,[status(thm)],[5844, 5843])).
% 1.72/2.01 tff(5846,plain,
% 1.72/2.01 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[5845, 75, 287, 5837, 5789, 5734])).
% 1.72/2.01 tff(5847,plain,
% 1.72/2.01 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[1179, 58, 3989, 5846])).
% 1.72/2.01 tff(5848,plain,
% 1.72/2.01 ($false),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[1198, 5847, 5839, 5788])).
% 1.72/2.01 tff(5849,plain,(b(s(s(z)), elem!1) | (~b(s(s(s(s(z)))), elem!1)) | (~(z = elem!1)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.72/2.01 tff(5850,plain,
% 1.72/2.01 (b(s(s(z)), elem!1)),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[5849, 3838, 288, 1391])).
% 1.72/2.01 tff(5851,plain,
% 1.72/2.01 (b(s(s(elem!1)), elem!1)),
% 1.72/2.01 inference(modus_ponens,[status(thm)],[5850, 3648])).
% 1.72/2.01 tff(5852,plain,
% 1.72/2.01 (b(s(s(z)), elem!1)),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[5849, 287, 288, 1391])).
% 1.72/2.01 tff(5853,plain,
% 1.72/2.01 (b(s(s(elem!1)), elem!1)),
% 1.72/2.01 inference(modus_ponens,[status(thm)],[5852, 3648])).
% 1.72/2.01 tff(5854,plain,
% 1.72/2.01 (~b(elem!1, s(s(s(s(z)))))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[1438, 578, 1391, 287])).
% 1.72/2.01 tff(5855,plain,
% 1.72/2.01 (r(elem!1, s(s(s(s(z)))))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[278, 5854, 3522])).
% 1.72/2.01 tff(5856,plain,
% 1.72/2.01 (b(s(s(elem!1)), z)),
% 1.72/2.01 inference(modus_ponens,[status(thm)],[5852, 5540])).
% 1.72/2.01 tff(5857,plain,
% 1.72/2.01 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(z)))), elem!1)),
% 1.72/2.01 inference(monotonicity,[status(thm)],[288])).
% 1.72/2.01 tff(5858,plain,
% 1.72/2.01 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), z)),
% 1.72/2.01 inference(symmetry,[status(thm)],[5857])).
% 1.72/2.01 tff(5859,plain,
% 1.72/2.01 (b(s(s(s(s(z)))), z)),
% 1.72/2.01 inference(modus_ponens,[status(thm)],[287, 5858])).
% 1.72/2.01 tff(5860,plain,
% 1.72/2.01 (~b(s(z), z)),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[4839, 578, 5859, 5501])).
% 1.72/2.01 tff(5861,plain,
% 1.72/2.01 (r(s(z), z)),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[169, 5860])).
% 1.72/2.01 tff(5862,plain,
% 1.72/2.01 (~b(s(s(s(s(z)))), s(elem!1))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[5694, 5491, 1391, 588, 3195, 5493, 5489, 578, 288])).
% 1.72/2.01 tff(5863,plain,
% 1.72/2.01 (r(s(s(s(s(z)))), s(elem!1))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[4263, 58, 5862, 4260])).
% 1.72/2.01 tff(5864,plain,
% 1.72/2.01 (b(s(z), s(s(z))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.72/2.01 inference(monotonicity,[status(thm)],[289, 290])).
% 1.72/2.01 tff(5865,plain,
% 1.72/2.01 (b(s(elem!1), s(s(elem!1))) <=> b(s(z), s(s(z)))),
% 1.72/2.01 inference(symmetry,[status(thm)],[5864])).
% 1.72/2.01 tff(5866,plain,
% 1.72/2.01 (b(s(z), s(s(z)))),
% 1.72/2.01 inference(modus_ponens,[status(thm)],[3581, 5865])).
% 1.72/2.01 tff(5867,plain,
% 1.72/2.01 (r(s(s(z)), s(z)) <=> r(s(s(z)), s(elem!1))),
% 1.72/2.01 inference(monotonicity,[status(thm)],[289])).
% 1.72/2.01 tff(5868,plain,
% 1.72/2.01 (r(s(s(z)), s(elem!1)) <=> r(s(s(z)), s(z))),
% 1.72/2.01 inference(symmetry,[status(thm)],[5867])).
% 1.72/2.01 tff(5869,plain,
% 1.72/2.01 (r(s(s(z)), s(elem!1)) <=> r(s(s(elem!1)), s(elem!1))),
% 1.72/2.01 inference(monotonicity,[status(thm)],[290])).
% 1.72/2.01 tff(5870,plain,
% 1.72/2.01 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(z)), s(elem!1))),
% 1.72/2.01 inference(symmetry,[status(thm)],[5869])).
% 1.72/2.01 tff(5871,plain,
% 1.72/2.01 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(z)), s(z))),
% 1.72/2.01 inference(transitivity,[status(thm)],[5870, 5868])).
% 1.72/2.01 tff(5872,plain,
% 1.72/2.01 ((~r(s(s(elem!1)), s(elem!1))) <=> (~r(s(s(z)), s(z)))),
% 1.72/2.01 inference(monotonicity,[status(thm)],[5871])).
% 1.72/2.01 tff(5873,assumption,(r(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 1.72/2.01 tff(5874,plain,
% 1.72/2.01 (((~![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(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.72/2.01 inference(rewrite,[status(thm)],[])).
% 1.72/2.01 tff(5875,plain,
% 1.72/2.01 (((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.72/2.01 inference(rewrite,[status(thm)],[])).
% 1.72/2.01 tff(5876,plain,
% 1.72/2.01 (((~![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(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))))),
% 1.72/2.01 inference(monotonicity,[status(thm)],[5875])).
% 1.72/2.01 tff(5877,plain,
% 1.72/2.01 (((~![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(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.72/2.01 inference(transitivity,[status(thm)],[5876, 5874])).
% 1.72/2.01 tff(5878,plain,
% 1.72/2.01 ((~![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(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.72/2.01 inference(quant_inst,[status(thm)],[])).
% 1.72/2.01 tff(5879,plain,
% 1.72/2.01 ((~![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(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.72/2.01 inference(modus_ponens,[status(thm)],[5878, 5877])).
% 1.72/2.01 tff(5880,plain,
% 1.72/2.01 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[5879, 37, 4249, 5873])).
% 1.72/2.01 tff(5881,plain,
% 1.72/2.01 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[5700, 1011])).
% 1.72/2.01 tff(5882,plain,
% 1.72/2.01 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[3876, 58, 5881, 5880])).
% 1.72/2.01 tff(5883,plain,
% 1.72/2.01 (((~![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(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.72/2.01 inference(rewrite,[status(thm)],[])).
% 1.72/2.01 tff(5884,plain,
% 1.72/2.01 (((~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.72/2.01 inference(rewrite,[status(thm)],[])).
% 1.72/2.01 tff(5885,plain,
% 1.72/2.01 (((~![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(z)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))))),
% 1.72/2.01 inference(monotonicity,[status(thm)],[5884])).
% 1.72/2.01 tff(5886,plain,
% 1.72/2.01 (((~![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(z)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.72/2.01 inference(transitivity,[status(thm)],[5885, 5883])).
% 1.72/2.01 tff(5887,plain,
% 1.72/2.01 ((~![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(z)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.72/2.01 inference(quant_inst,[status(thm)],[])).
% 1.72/2.01 tff(5888,plain,
% 1.72/2.01 ((~![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(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.72/2.01 inference(modus_ponens,[status(thm)],[5887, 5886])).
% 1.72/2.01 tff(5889,plain,
% 1.72/2.01 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[5888, 37, 4249, 5873])).
% 1.72/2.01 tff(5890,plain,
% 1.72/2.01 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[1660, 5889, 1011])).
% 1.72/2.01 tff(5891,plain,
% 1.72/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.72/2.01 inference(rewrite,[status(thm)],[])).
% 1.72/2.01 tff(5892,plain,
% 1.72/2.01 (((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.72/2.01 inference(rewrite,[status(thm)],[])).
% 1.72/2.01 tff(5893,plain,
% 1.72/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))))),
% 1.72/2.01 inference(monotonicity,[status(thm)],[5892])).
% 1.72/2.01 tff(5894,plain,
% 1.72/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.72/2.01 inference(transitivity,[status(thm)],[5893, 5891])).
% 1.72/2.01 tff(5895,plain,
% 1.72/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.72/2.01 inference(quant_inst,[status(thm)],[])).
% 1.72/2.01 tff(5896,plain,
% 1.72/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 1.72/2.01 inference(modus_ponens,[status(thm)],[5895, 5894])).
% 1.72/2.01 tff(5897,plain,
% 1.72/2.01 ($false),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[5896, 75, 5890, 3581, 5882, 3862])).
% 1.72/2.01 tff(5898,plain,((~r(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (s(s(elem!1)) = s(s(s(s(z))))) | (~r(s(s(s(s(z)))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.72/2.01 tff(5899,plain,
% 1.72/2.01 (~r(s(s(elem!1)), s(elem!1))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[5898, 3581, 3862, 5479, 4249])).
% 1.72/2.01 tff(5900,plain,
% 1.72/2.01 (~r(s(s(z)), s(z))),
% 1.72/2.01 inference(modus_ponens,[status(thm)],[5899, 5872])).
% 1.72/2.01 tff(5901,plain,
% 1.72/2.01 (b(s(s(z)), s(z))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[153, 5900])).
% 1.72/2.01 tff(5902,plain,
% 1.72/2.01 (r(s(s(elem!1)), s(z)) <=> r(s(s(elem!1)), s(elem!1))),
% 1.72/2.01 inference(monotonicity,[status(thm)],[289])).
% 1.72/2.01 tff(5903,plain,
% 1.72/2.01 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(z))),
% 1.72/2.01 inference(symmetry,[status(thm)],[5902])).
% 1.72/2.01 tff(5904,plain,
% 1.72/2.01 ((~r(s(s(elem!1)), s(elem!1))) <=> (~r(s(s(elem!1)), s(z)))),
% 1.72/2.01 inference(monotonicity,[status(thm)],[5903])).
% 1.72/2.01 tff(5905,plain,
% 1.72/2.01 (~r(s(s(elem!1)), s(z))),
% 1.72/2.01 inference(modus_ponens,[status(thm)],[5899, 5904])).
% 1.72/2.01 tff(5906,plain,
% 1.72/2.01 (b(s(s(elem!1)), s(z))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[561, 5905])).
% 1.72/2.01 tff(5907,plain,
% 1.72/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))))),
% 1.72/2.01 inference(rewrite,[status(thm)],[])).
% 1.72/2.01 tff(5908,plain,
% 1.72/2.01 (((~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))))),
% 1.72/2.02 inference(rewrite,[status(thm)],[])).
% 1.72/2.02 tff(5909,plain,
% 1.72/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z)))))),
% 1.72/2.02 inference(monotonicity,[status(thm)],[5908])).
% 1.72/2.02 tff(5910,plain,
% 1.72/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))))),
% 1.72/2.02 inference(transitivity,[status(thm)],[5909, 5907])).
% 1.72/2.02 tff(5911,plain,
% 1.72/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))),
% 1.72/2.02 inference(quant_inst,[status(thm)],[])).
% 1.72/2.02 tff(5912,plain,
% 1.72/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z)))),
% 1.72/2.02 inference(modus_ponens,[status(thm)],[5911, 5910])).
% 1.72/2.02 tff(5913,plain,
% 1.72/2.02 ($false),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[5912, 75, 1457, 1391, 309, 402, 707])).
% 1.72/2.02 tff(5914,plain,((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.72/2.02 tff(5915,plain,
% 1.72/2.02 ($false),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[5914, 5906, 5901, 1391, 707, 5866])).
% 1.72/2.02 tff(5916,plain,((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~(z = elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.72/2.02 tff(5917,plain,
% 1.72/2.02 (~b(s(elem!1), s(s(elem!1)))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[5916, 5863, 707, 288, 5531, 1391])).
% 1.72/2.02 tff(5918,plain,
% 1.72/2.02 (~b(s(z), s(s(elem!1)))),
% 1.72/2.02 inference(modus_ponens,[status(thm)],[5917, 4271])).
% 1.72/2.02 tff(5919,plain,
% 1.72/2.02 (r(s(z), s(s(elem!1)))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[1890, 5918])).
% 1.72/2.02 tff(5920,plain,
% 1.72/2.02 (~r(z, s(s(elem!1)))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[5301, 5919, 1561])).
% 1.72/2.02 tff(5921,plain,
% 1.72/2.02 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[5576, 5920, 5489, 1892])).
% 1.72/2.02 tff(5922,plain,
% 1.72/2.02 (r(s(s(s(z))), s(s(elem!1)))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[62, 5921, 5493])).
% 1.72/2.02 tff(5923,plain,
% 1.72/2.02 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.72/2.02 inference(modus_ponens,[status(thm)],[5922, 5537])).
% 1.72/2.02 tff(5924,plain,
% 1.72/2.02 (r(s(elem!1), s(s(elem!1)))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[1851, 5917, 3438])).
% 1.72/2.02 tff(5925,plain,
% 1.72/2.02 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[5160, 37, 5924, 5923])).
% 1.72/2.02 tff(5926,plain,
% 1.72/2.02 (~r(s(s(s(z))), s(z))),
% 1.72/2.02 inference(modus_ponens,[status(thm)],[5925, 5771])).
% 1.72/2.02 tff(5927,plain,
% 1.72/2.02 (b(s(s(s(z))), s(z))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[1081, 5926])).
% 1.72/2.02 tff(5928,plain,
% 1.72/2.02 (~b(s(z), s(s(elem!1)))),
% 1.72/2.02 inference(modus_ponens,[status(thm)],[1846, 4271])).
% 1.72/2.02 tff(5929,plain,
% 1.72/2.02 (r(s(z), s(s(elem!1)))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[1890, 5928])).
% 1.72/2.02 tff(5930,plain,
% 1.72/2.02 (~r(z, s(s(elem!1)))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[5301, 5929, 1561])).
% 1.72/2.02 tff(5931,plain,
% 1.72/2.02 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[5576, 5930, 1083, 1892])).
% 1.72/2.02 tff(5932,plain,
% 1.72/2.02 (r(s(s(s(z))), s(s(elem!1)))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[62, 5931, 16])).
% 1.72/2.02 tff(5933,plain,
% 1.72/2.02 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.72/2.02 inference(modus_ponens,[status(thm)],[5932, 5537])).
% 1.72/2.02 tff(5934,plain,
% 1.72/2.02 (r(s(elem!1), s(s(elem!1)))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[1851, 1846, 3438])).
% 1.72/2.02 tff(5935,plain,
% 1.72/2.02 ($false),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[5638, 37, 5934, 5090, 5933])).
% 1.72/2.02 tff(5936,plain,(b(s(elem!1), s(s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~(z = elem!1)) | (s(s(s(z))) = s(s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.72/2.02 tff(5937,plain,
% 1.72/2.02 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[5936, 5917, 288, 5493, 5489, 1892, 1561])).
% 1.72/2.02 tff(5938,plain,
% 1.72/2.02 (~r(s(z), s(s(s(z))))),
% 1.72/2.02 inference(modus_ponens,[status(thm)],[5937, 5632])).
% 1.72/2.02 tff(5939,plain,
% 1.72/2.02 (b(s(z), s(s(s(z))))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[1263, 5938])).
% 1.72/2.02 tff(5940,plain,
% 1.72/2.02 ($false),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[1091, 5939, 5927, 5501, 5489])).
% 1.72/2.02 tff(5941,plain,((~b(s(s(s(z))), elem!1)) | (~(z = elem!1)) | (~b(s(s(elem!1)), z)) | (~r(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.72/2.02 tff(5942,plain,
% 1.72/2.02 (~b(s(s(s(z))), elem!1)),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[5941, 5861, 5856, 288, 5853, 1391, 5529, 5855, 578])).
% 1.72/2.02 tff(5943,plain,
% 1.72/2.02 (r(s(s(s(z))), elem!1)),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[1115, 5942, 4145])).
% 1.72/2.02 tff(5944,plain,
% 1.72/2.02 (r(s(s(s(elem!1))), elem!1)),
% 1.72/2.02 inference(modus_ponens,[status(thm)],[5943, 4176])).
% 1.72/2.02 tff(5945,plain,
% 1.72/2.02 (r(s(elem!1), elem!1)),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[4005, 5529, 288])).
% 1.72/2.02 tff(5946,plain,
% 1.72/2.02 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[633, 37, 5945, 5944])).
% 1.72/2.02 tff(5947,plain,
% 1.72/2.02 (~r(s(z), s(s(s(z))))),
% 1.72/2.02 inference(modus_ponens,[status(thm)],[5946, 5632])).
% 1.72/2.02 tff(5948,plain,
% 1.72/2.02 (b(s(z), s(s(s(z))))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[1263, 5947])).
% 1.72/2.02 tff(5949,plain,
% 1.72/2.02 (b(s(elem!1), s(s(s(elem!1))))),
% 1.72/2.02 inference(modus_ponens,[status(thm)],[5948, 3831])).
% 1.72/2.02 tff(5950,plain,
% 1.72/2.02 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.72/2.02 inference(monotonicity,[status(thm)],[3417, 289])).
% 1.72/2.02 tff(5951,plain,
% 1.72/2.02 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[651, 37, 5945, 5944])).
% 1.72/2.02 tff(5952,plain,
% 1.72/2.02 (~r(s(s(s(z))), s(z))),
% 1.72/2.02 inference(modus_ponens,[status(thm)],[5951, 5771])).
% 1.72/2.02 tff(5953,plain,
% 1.72/2.02 (b(s(s(s(z))), s(z))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[1081, 5952])).
% 1.72/2.02 tff(5954,plain,
% 1.72/2.02 (b(s(s(s(elem!1))), s(elem!1))),
% 1.72/2.02 inference(modus_ponens,[status(thm)],[5953, 5950])).
% 1.72/2.02 tff(5955,plain,
% 1.72/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.72/2.02 inference(rewrite,[status(thm)],[])).
% 1.72/2.02 tff(5956,plain,
% 1.72/2.02 (((~b(s(s(s(elem!1))), s(elem!1))) | (~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(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))))))),
% 1.72/2.02 inference(rewrite,[status(thm)],[])).
% 1.72/2.02 tff(5957,plain,
% 1.72/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.72/2.02 inference(monotonicity,[status(thm)],[5956])).
% 1.72/2.02 tff(5958,plain,
% 1.72/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.72/2.02 inference(transitivity,[status(thm)],[5957, 5955])).
% 1.72/2.02 tff(5959,plain,
% 1.72/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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))))))),
% 1.72/2.02 inference(quant_inst,[status(thm)],[])).
% 1.72/2.02 tff(5960,plain,
% 1.72/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.72/2.02 inference(modus_ponens,[status(thm)],[5959, 5958])).
% 1.72/2.02 tff(5961,plain,
% 1.72/2.02 (~b(elem!1, s(s(s(elem!1))))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[5960, 75, 5734, 5949, 5954])).
% 1.72/2.02 tff(5962,assumption,(~b(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 1.72/2.02 tff(5963,plain,
% 1.72/2.02 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1)))))),
% 1.72/2.02 inference(rewrite,[status(thm)],[])).
% 1.72/2.02 tff(5964,plain,
% 1.72/2.02 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1)))))),
% 1.72/2.02 inference(quant_inst,[status(thm)],[])).
% 1.72/2.02 tff(5965,plain,
% 1.72/2.02 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1))))),
% 1.72/2.02 inference(modus_ponens,[status(thm)],[5964, 5963])).
% 1.72/2.02 tff(5966,plain,
% 1.72/2.02 ($false),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[5965, 58, 5962, 5306, 5802])).
% 1.72/2.02 tff(5967,plain,(r(elem!1, s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.72/2.02 tff(5968,plain,
% 1.72/2.02 (r(elem!1, s(s(s(elem!1))))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[5967, 5961, 5796])).
% 1.72/2.02 tff(5969,plain,
% 1.72/2.02 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[5598, 37, 3195, 5311])).
% 1.72/2.02 tff(5970,plain,
% 1.72/2.02 ($false),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[5969, 5592])).
% 1.72/2.02 tff(5971,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~(z = elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.72/2.02 tff(5972,plain,
% 1.72/2.02 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[5971, 5968, 288, 5855])).
% 1.72/2.02 tff(5973,plain,
% 1.72/2.02 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[575, 5972])).
% 1.72/2.02 tff(5974,plain,
% 1.72/2.02 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.72/2.02 inference(modus_ponens,[status(thm)],[5973, 3832])).
% 1.72/2.02 tff(5975,assumption,(b(s(s(s(elem!1))), s(s(s(s(z)))))), introduced(assumption)).
% 1.72/2.02 tff(5976,plain,
% 1.72/2.02 ($false),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[5653, 75, 5975, 3862, 920, 4272])).
% 1.72/2.02 tff(5977,plain,((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.72/2.02 tff(5978,plain,
% 1.72/2.02 (~b(s(s(s(s(z)))), s(elem!1))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[5977, 5974, 5949, 5531])).
% 1.72/2.02 tff(5979,plain,
% 1.72/2.02 (r(s(s(s(s(z)))), s(elem!1))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[4263, 58, 5978, 4260])).
% 1.72/2.02 tff(5980,plain,
% 1.72/2.02 (~b(s(elem!1), s(s(elem!1)))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[5916, 5979, 5853, 288, 5531, 1391])).
% 1.72/2.02 tff(5981,plain,
% 1.72/2.02 (~b(s(z), s(s(elem!1)))),
% 1.72/2.02 inference(modus_ponens,[status(thm)],[5980, 4271])).
% 1.72/2.02 tff(5982,plain,
% 1.72/2.02 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 1.72/2.02 inference(monotonicity,[status(thm)],[288])).
% 1.72/2.02 tff(5983,plain,
% 1.72/2.02 (r(elem!1, s(s(elem!1))) <=> r(z, s(s(elem!1)))),
% 1.72/2.02 inference(symmetry,[status(thm)],[5982])).
% 1.72/2.02 tff(5984,plain,
% 1.72/2.02 (r(s(elem!1), s(s(elem!1)))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[1851, 5980, 3438])).
% 1.72/2.02 tff(5985,plain,
% 1.72/2.02 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[870, 3974])).
% 1.72/2.02 tff(5986,plain,
% 1.72/2.02 (b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[874, 58, 4907, 5823])).
% 1.72/2.02 tff(5987,plain,
% 1.72/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), 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), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.72/2.02 inference(rewrite,[status(thm)],[])).
% 1.72/2.02 tff(5988,plain,
% 1.72/2.02 (((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.72/2.02 inference(rewrite,[status(thm)],[])).
% 1.72/2.02 tff(5989,plain,
% 1.72/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(elem!1))))))),
% 1.72/2.02 inference(monotonicity,[status(thm)],[5988])).
% 1.72/2.02 tff(5990,plain,
% 1.72/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.72/2.02 inference(transitivity,[status(thm)],[5989, 5987])).
% 1.72/2.02 tff(5991,plain,
% 1.72/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.72/2.02 inference(quant_inst,[status(thm)],[])).
% 1.72/2.02 tff(5992,plain,
% 1.72/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), s(s(elem!1))))),
% 1.72/2.02 inference(modus_ponens,[status(thm)],[5991, 5990])).
% 1.72/2.02 tff(5993,plain,
% 1.72/2.02 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[5992, 37, 738, 1918, 752])).
% 1.72/2.02 tff(5994,plain,
% 1.72/2.02 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.72/2.02 inference(unit_resolution,[status(thm)],[3010, 58, 3064, 5993])).
% 1.72/2.02 tff(5995,plain,
% 1.72/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.72/2.02 inference(rewrite,[status(thm)],[])).
% 1.72/2.02 tff(5996,plain,
% 1.72/2.02 (((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.72/2.02 inference(rewrite,[status(thm)],[])).
% 1.72/2.02 tff(5997,plain,
% 1.72/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 1.72/2.02 inference(monotonicity,[status(thm)],[5996])).
% 1.72/2.02 tff(5998,plain,
% 1.72/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.72/2.02 inference(transitivity,[status(thm)],[5997, 5995])).
% 1.72/2.02 tff(5999,plain,
% 1.72/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 1.84/2.03 inference(quant_inst,[status(thm)],[])).
% 1.84/2.03 tff(6000,plain,
% 1.84/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 1.84/2.03 inference(modus_ponens,[status(thm)],[5999, 5998])).
% 1.84/2.03 tff(6001,plain,
% 1.84/2.03 ($false),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[6000, 75, 794, 4190, 5994, 5986])).
% 1.84/2.03 tff(6002,plain,((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.03 tff(6003,plain,
% 1.84/2.03 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[6002, 5984, 5985, 3954, 3961, 5944, 5945, 5954])).
% 1.84/2.03 tff(6004,plain,
% 1.84/2.03 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[813, 6003, 3966])).
% 1.84/2.03 tff(6005,plain,
% 1.84/2.03 ((s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 1.84/2.03 inference(symmetry,[status(thm)],[3955])).
% 1.84/2.03 tff(6006,plain,
% 1.84/2.03 ((~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1))))),
% 1.84/2.03 inference(monotonicity,[status(thm)],[6005])).
% 1.84/2.03 tff(6007,plain,
% 1.84/2.03 (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 1.84/2.03 inference(modus_ponens,[status(thm)],[3067, 6006])).
% 1.84/2.03 tff(6008,plain,
% 1.84/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.84/2.03 inference(rewrite,[status(thm)],[])).
% 1.84/2.03 tff(6009,plain,
% 1.84/2.03 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.84/2.03 inference(rewrite,[status(thm)],[])).
% 1.84/2.03 tff(6010,plain,
% 1.84/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 1.84/2.03 inference(monotonicity,[status(thm)],[6009])).
% 1.84/2.03 tff(6011,plain,
% 1.84/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.84/2.03 inference(transitivity,[status(thm)],[6010, 6008])).
% 1.84/2.03 tff(6012,plain,
% 1.84/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.84/2.03 inference(quant_inst,[status(thm)],[])).
% 1.84/2.03 tff(6013,plain,
% 1.84/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 1.84/2.03 inference(modus_ponens,[status(thm)],[6012, 6011])).
% 1.84/2.03 tff(6014,plain,
% 1.84/2.03 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[6013, 75, 1620, 1168, 707])).
% 1.84/2.03 tff(6015,plain,
% 1.84/2.03 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) | r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) | r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.84/2.03 inference(rewrite,[status(thm)],[])).
% 1.84/2.03 tff(6016,plain,
% 1.84/2.03 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) | r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.84/2.03 inference(quant_inst,[status(thm)],[])).
% 1.84/2.03 tff(6017,plain,
% 1.84/2.03 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) | r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.84/2.03 inference(modus_ponens,[status(thm)],[6016, 6015])).
% 1.84/2.03 tff(6018,plain,
% 1.84/2.03 ((s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[6017, 58, 6014])).
% 1.84/2.03 tff(6019,plain,
% 1.84/2.03 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[6018, 6007])).
% 1.84/2.03 tff(6020,plain,
% 1.84/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.84/2.03 inference(rewrite,[status(thm)],[])).
% 1.84/2.03 tff(6021,plain,
% 1.84/2.03 (((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.84/2.03 inference(rewrite,[status(thm)],[])).
% 1.84/2.03 tff(6022,plain,
% 1.84/2.03 (((~![X0: $i, 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(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 1.84/2.03 inference(monotonicity,[status(thm)],[6021])).
% 1.84/2.03 tff(6023,plain,
% 1.84/2.03 (((~![X0: $i, 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(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.84/2.03 inference(transitivity,[status(thm)],[6022, 6020])).
% 1.84/2.03 tff(6024,plain,
% 1.84/2.03 ((~![X0: $i, 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(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.84/2.03 inference(quant_inst,[status(thm)],[])).
% 1.84/2.03 tff(6025,plain,
% 1.84/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.84/2.03 inference(modus_ponens,[status(thm)],[6024, 6023])).
% 1.84/2.03 tff(6026,plain,
% 1.84/2.03 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[6025, 37, 1918, 6019])).
% 1.84/2.03 tff(6027,plain,
% 1.84/2.03 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[3010, 58, 3064, 6026])).
% 1.84/2.03 tff(6028,plain,
% 1.84/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.84/2.03 inference(rewrite,[status(thm)],[])).
% 1.84/2.03 tff(6029,plain,
% 1.84/2.03 (((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.84/2.03 inference(rewrite,[status(thm)],[])).
% 1.84/2.03 tff(6030,plain,
% 1.84/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 1.84/2.03 inference(monotonicity,[status(thm)],[6029])).
% 1.84/2.03 tff(6031,plain,
% 1.84/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 1.84/2.03 inference(transitivity,[status(thm)],[6030, 6028])).
% 1.84/2.03 tff(6032,plain,
% 1.84/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 1.84/2.03 inference(quant_inst,[status(thm)],[])).
% 1.84/2.03 tff(6033,plain,
% 1.84/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 1.84/2.03 inference(modus_ponens,[status(thm)],[6032, 6031])).
% 1.84/2.03 tff(6034,plain,
% 1.84/2.03 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[6033, 37, 1918, 6019])).
% 1.84/2.03 tff(6035,plain,
% 1.84/2.03 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[793, 58, 790, 6034])).
% 1.84/2.03 tff(6036,plain,
% 1.84/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.84/2.03 inference(rewrite,[status(thm)],[])).
% 1.84/2.03 tff(6037,plain,
% 1.84/2.03 (((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.84/2.03 inference(rewrite,[status(thm)],[])).
% 1.84/2.03 tff(6038,plain,
% 1.84/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 1.84/2.03 inference(monotonicity,[status(thm)],[6037])).
% 1.84/2.03 tff(6039,plain,
% 1.84/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.84/2.03 inference(transitivity,[status(thm)],[6038, 6036])).
% 1.84/2.03 tff(6040,plain,
% 1.84/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 1.84/2.03 inference(quant_inst,[status(thm)],[])).
% 1.84/2.03 tff(6041,plain,
% 1.84/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 1.84/2.03 inference(modus_ponens,[status(thm)],[6040, 6039])).
% 1.84/2.03 tff(6042,plain,
% 1.84/2.03 ($false),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[6041, 75, 1168, 6035, 2609, 6027])).
% 1.84/2.03 tff(6043,plain,((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(elem!1))) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (~r(s(elem!1), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.03 tff(6044,plain,
% 1.84/2.03 (~b(elem!1, s(s(elem!1)))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[6043, 6004, 3961, 3954, 5734, 3959, 5984, 5853])).
% 1.84/2.03 tff(6045,plain,
% 1.84/2.03 (r(elem!1, s(s(elem!1)))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[1617, 6044, 3432])).
% 1.84/2.03 tff(6046,plain,
% 1.84/2.03 (r(z, s(s(elem!1)))),
% 1.84/2.03 inference(modus_ponens,[status(thm)],[6045, 5983])).
% 1.84/2.03 tff(6047,plain,
% 1.84/2.03 (~r(s(z), s(s(elem!1)))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[5301, 6046, 5861])).
% 1.84/2.03 tff(6048,plain,
% 1.84/2.03 (b(s(z), s(s(elem!1)))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[1890, 6047])).
% 1.84/2.03 tff(6049,plain,
% 1.84/2.03 ($false),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[6048, 5981])).
% 1.84/2.03 tff(6050,plain,((~b(s(z), s(s(s(s(z)))))) | (~(z = elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.03 tff(6051,plain,
% 1.84/2.03 (~b(s(z), s(s(s(s(z)))))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[6050, 288, 1391, 3838])).
% 1.84/2.03 tff(6052,plain,
% 1.84/2.03 (r(s(z), s(s(s(s(z)))))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[489, 6051])).
% 1.84/2.03 tff(6053,plain,
% 1.84/2.03 (r(s(elem!1), s(s(s(s(z)))))),
% 1.84/2.03 inference(modus_ponens,[status(thm)],[6052, 5478])).
% 1.84/2.03 tff(6054,plain,
% 1.84/2.03 (r(s(z), z) <=> r(s(elem!1), elem!1)),
% 1.84/2.03 inference(transitivity,[status(thm)],[5532, 4002])).
% 1.84/2.03 tff(6055,plain,
% 1.84/2.03 (b(s(s(elem!1)), z)),
% 1.84/2.03 inference(modus_ponens,[status(thm)],[5850, 5540])).
% 1.84/2.03 tff(6056,plain,
% 1.84/2.03 (b(s(z), z) <=> b(s(z), elem!1)),
% 1.84/2.03 inference(monotonicity,[status(thm)],[288])).
% 1.84/2.03 tff(6057,plain,
% 1.84/2.03 (b(s(z), z) <=> b(s(elem!1), elem!1)),
% 1.84/2.03 inference(transitivity,[status(thm)],[6056, 3568])).
% 1.84/2.03 tff(6058,plain,
% 1.84/2.03 (b(s(elem!1), elem!1)),
% 1.84/2.03 inference(modus_ponens,[status(thm)],[371, 6057])).
% 1.84/2.03 tff(6059,plain,
% 1.84/2.03 (~b(s(s(elem!1)), s(z))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[4754, 371, 372, 1892])).
% 1.84/2.03 tff(6060,plain,
% 1.84/2.03 (r(s(s(elem!1)), s(z))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[561, 6059])).
% 1.84/2.03 tff(6061,plain,
% 1.84/2.03 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[1655, 6060, 468])).
% 1.84/2.03 tff(6062,plain,
% 1.84/2.03 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[1660, 6061, 5479])).
% 1.84/2.03 tff(6063,plain,
% 1.84/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.84/2.03 inference(rewrite,[status(thm)],[])).
% 1.84/2.03 tff(6064,plain,
% 1.84/2.03 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.84/2.03 inference(rewrite,[status(thm)],[])).
% 1.84/2.03 tff(6065,plain,
% 1.84/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1)))))),
% 1.84/2.03 inference(monotonicity,[status(thm)],[6064])).
% 1.84/2.03 tff(6066,plain,
% 1.84/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))),
% 1.84/2.03 inference(transitivity,[status(thm)],[6065, 6063])).
% 1.84/2.03 tff(6067,plain,
% 1.84/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.84/2.03 inference(quant_inst,[status(thm)],[])).
% 1.84/2.03 tff(6068,plain,
% 1.84/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1)))),
% 1.84/2.03 inference(modus_ponens,[status(thm)],[6067, 6066])).
% 1.84/2.03 tff(6069,plain,
% 1.84/2.03 ($false),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[6068, 75, 6062, 287, 6058, 707, 2609])).
% 1.84/2.03 tff(6070,plain,((~b(s(z), z)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~(z = elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.03 tff(6071,plain,
% 1.84/2.03 (~b(s(z), z)),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[6070, 3838, 5851, 5734, 288, 6052, 5501, 6055])).
% 1.84/2.03 tff(6072,plain,
% 1.84/2.03 (r(s(z), z)),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[169, 6071])).
% 1.84/2.03 tff(6073,plain,
% 1.84/2.03 (r(s(elem!1), elem!1)),
% 1.84/2.03 inference(modus_ponens,[status(thm)],[6072, 6054])).
% 1.84/2.03 tff(6074,plain,
% 1.84/2.03 ($false),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[5743, 37, 3195, 752, 1167])).
% 1.84/2.03 tff(6075,plain,((~r(elem!1, s(s(s(s(z)))))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.03 tff(6076,plain,
% 1.84/2.03 (~r(elem!1, s(s(s(s(z)))))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[6075, 6073, 6053])).
% 1.84/2.03 tff(6077,plain,
% 1.84/2.03 (b(elem!1, s(s(s(s(z)))))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[278, 6076, 3522])).
% 1.84/2.03 tff(6078,plain,
% 1.84/2.03 (~b(s(s(s(elem!1))), elem!1)),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[4243, 6077, 288, 5479, 3838, 5851])).
% 1.84/2.03 tff(6079,plain,
% 1.84/2.03 (~b(s(z), s(s(s(s(z)))))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[6050, 288, 1391, 287])).
% 1.84/2.03 tff(6080,plain,
% 1.84/2.03 (r(s(z), s(s(s(s(z)))))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[489, 6079])).
% 1.84/2.03 tff(6081,plain,
% 1.84/2.03 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[4155, 75, 286, 287, 5853])).
% 1.84/2.03 tff(6082,plain,
% 1.84/2.03 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[1660, 6081, 5479])).
% 1.84/2.03 tff(6083,plain,
% 1.84/2.03 (r(s(s(z)), s(s(s(s(z)))))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[3576, 6082, 3839])).
% 1.84/2.03 tff(6084,plain,
% 1.84/2.03 (~r(s(s(z)), s(z))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[476, 6083, 6080])).
% 1.84/2.03 tff(6085,plain,
% 1.84/2.03 (~b(s(z), z)),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[6070, 287, 5853, 5734, 288, 6080, 5501, 5856])).
% 1.84/2.03 tff(6086,plain,
% 1.84/2.03 (r(s(z), z)),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[169, 6085])).
% 1.84/2.03 tff(6087,plain,
% 1.84/2.03 (r(s(elem!1), elem!1)),
% 1.84/2.03 inference(modus_ponens,[status(thm)],[6086, 6054])).
% 1.84/2.03 tff(6088,plain,
% 1.84/2.03 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[651, 37, 6087, 624])).
% 1.84/2.03 tff(6089,plain,
% 1.84/2.03 (~r(s(s(s(z))), s(z))),
% 1.84/2.03 inference(modus_ponens,[status(thm)],[6088, 5771])).
% 1.84/2.04 tff(6090,plain,
% 1.84/2.04 (b(s(s(s(z))), s(z))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[1081, 6089])).
% 1.84/2.04 tff(6091,plain,
% 1.84/2.04 (b(s(s(s(elem!1))), s(elem!1))),
% 1.84/2.04 inference(modus_ponens,[status(thm)],[6090, 5950])).
% 1.84/2.04 tff(6092,plain,
% 1.84/2.04 (((~![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(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(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(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.84/2.04 inference(rewrite,[status(thm)],[])).
% 1.84/2.04 tff(6093,plain,
% 1.84/2.04 (((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1)))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.84/2.04 inference(rewrite,[status(thm)],[])).
% 1.84/2.04 tff(6094,plain,
% 1.84/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(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(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 1.84/2.04 inference(monotonicity,[status(thm)],[6093])).
% 1.84/2.04 tff(6095,plain,
% 1.84/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(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(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.84/2.04 inference(transitivity,[status(thm)],[6094, 6092])).
% 1.84/2.04 tff(6096,plain,
% 1.84/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 1.84/2.04 inference(quant_inst,[status(thm)],[])).
% 1.84/2.04 tff(6097,plain,
% 1.84/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 1.84/2.04 inference(modus_ponens,[status(thm)],[6096, 6095])).
% 1.84/2.04 tff(6098,plain,
% 1.84/2.04 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[6097, 37, 5509, 3990])).
% 1.84/2.04 tff(6099,plain,
% 1.84/2.04 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[3010, 58, 3954, 6098])).
% 1.84/2.04 tff(6100,plain,
% 1.84/2.04 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[1198, 3990, 5509])).
% 1.84/2.04 tff(6101,plain,
% 1.84/2.04 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[793, 58, 3961, 6100])).
% 1.84/2.04 tff(6102,plain,
% 1.84/2.04 ($false),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[6041, 75, 1168, 6101, 5734, 6099])).
% 1.84/2.04 tff(6103,plain,((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~(z = elem!1)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.04 tff(6104,plain,
% 1.84/2.04 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[6103, 286, 287, 288, 1391])).
% 1.84/2.04 tff(6105,plain,
% 1.84/2.04 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[813, 6104, 3966])).
% 1.84/2.04 tff(6106,plain,
% 1.84/2.04 (~r(s(elem!1), s(s(elem!1)))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[6002, 6105, 5985, 3954, 3961, 624, 6087, 6091])).
% 1.84/2.04 tff(6107,plain,
% 1.84/2.04 (~r(s(z), s(s(z)))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[3414, 6106, 288])).
% 1.84/2.04 tff(6108,plain,
% 1.84/2.04 (b(s(z), s(s(z)))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[416, 6107])).
% 1.84/2.04 tff(6109,plain,
% 1.84/2.04 (~r(s(s(elem!1)), s(z))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[1655, 6082, 6080])).
% 1.84/2.04 tff(6110,plain,
% 1.84/2.04 (b(s(s(elem!1)), s(z))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[561, 6109])).
% 1.84/2.04 tff(6111,plain,
% 1.84/2.04 (~b(s(s(z)), s(z))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[5914, 6110, 1391, 5853, 6108])).
% 1.84/2.04 tff(6112,plain,
% 1.84/2.04 ($false),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[153, 6111, 6084])).
% 1.84/2.04 tff(6113,plain,((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~(z = elem!1)) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.04 tff(6114,plain,
% 1.84/2.04 (~r(s(s(s(elem!1))), elem!1)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[6113, 6077, 3838, 288, 1391])).
% 1.84/2.04 tff(6115,plain,
% 1.84/2.04 ($false),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[3370, 6114, 6078, 5477])).
% 1.84/2.04 tff(6116,plain,((~(z = elem!1)) | (~b(elem!1, s(z))) | r(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.84/2.04 tff(6117,plain,
% 1.84/2.04 (~(z = elem!1)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[6116, 5472, 12])).
% 1.84/2.04 tff(6118,plain,
% 1.84/2.04 (~(s(s(elem!1)) = s(s(z)))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[237, 6117])).
% 1.84/2.04 tff(6119,plain,
% 1.84/2.04 (~(elem!1 = s(s(elem!1)))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[4475, 4464, 6118])).
% 1.84/2.04 tff(6120,plain,
% 1.84/2.04 (~(s(s(elem!1)) = elem!1)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[2555, 6119])).
% 1.84/2.04 tff(6121,plain,
% 1.84/2.04 (r(s(s(elem!1)), elem!1)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[2673, 6120, 1])).
% 1.84/2.04 tff(6122,plain,
% 1.84/2.04 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(z)), elem!1)),
% 1.84/2.04 inference(monotonicity,[status(thm)],[3285])).
% 1.84/2.04 tff(6123,plain,
% 1.84/2.04 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(s(z)))))),
% 1.84/2.04 inference(symmetry,[status(thm)],[6122])).
% 1.84/2.04 tff(6124,plain,
% 1.84/2.04 ((~b(s(s(z)), elem!1)) <=> (~b(s(s(z)), s(s(s(s(z))))))),
% 1.84/2.04 inference(monotonicity,[status(thm)],[6123])).
% 1.84/2.04 tff(6125,plain,
% 1.84/2.04 (b(z, elem!1)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[298, 6117, 13])).
% 1.84/2.04 tff(6126,plain,
% 1.84/2.04 (b(s(z), elem!1)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[3669, 3656, 3285])).
% 1.84/2.04 tff(6127,plain,
% 1.84/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)))),
% 1.84/2.04 inference(rewrite,[status(thm)],[])).
% 1.84/2.04 tff(6128,plain,
% 1.84/2.04 (((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)))),
% 1.84/2.04 inference(rewrite,[status(thm)],[])).
% 1.84/2.04 tff(6129,plain,
% 1.84/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1))))),
% 1.84/2.04 inference(monotonicity,[status(thm)],[6128])).
% 1.84/2.04 tff(6130,plain,
% 1.84/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)))),
% 1.84/2.04 inference(transitivity,[status(thm)],[6129, 6127])).
% 1.84/2.04 tff(6131,plain,
% 1.84/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 1.84/2.04 inference(quant_inst,[status(thm)],[])).
% 1.84/2.04 tff(6132,plain,
% 1.84/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1))),
% 1.84/2.04 inference(modus_ponens,[status(thm)],[6131, 6130])).
% 1.84/2.04 tff(6133,plain,
% 1.84/2.04 (~b(s(s(z)), z)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[6132, 75, 1518, 107, 1391, 964])).
% 1.84/2.04 tff(6134,plain,
% 1.84/2.04 (b(s(s(s(s(z)))), s(z)) <=> b(elem!1, s(z))),
% 1.84/2.04 inference(monotonicity,[status(thm)],[3285])).
% 1.84/2.04 tff(6135,plain,
% 1.84/2.04 (b(elem!1, s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 1.84/2.04 inference(symmetry,[status(thm)],[6134])).
% 1.84/2.04 tff(6136,plain,
% 1.84/2.04 (b(s(s(s(s(z)))), s(z))),
% 1.84/2.04 inference(modus_ponens,[status(thm)],[1391, 6135])).
% 1.84/2.04 tff(6137,plain,
% 1.84/2.04 (b(s(s(z)), s(s(s(s(z)))))),
% 1.84/2.04 inference(modus_ponens,[status(thm)],[964, 6123])).
% 1.84/2.04 tff(6138,plain,
% 1.84/2.04 ($false),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[428, 6137])).
% 1.84/2.04 tff(6139,plain,((~(s(s(s(s(z)))) = elem!1)) | b(s(s(z)), s(s(s(s(z))))) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.04 tff(6140,plain,
% 1.84/2.04 (b(s(s(z)), s(s(s(s(z)))))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[6139, 964, 3285])).
% 1.84/2.04 tff(6141,plain,
% 1.84/2.04 (~b(s(s(z)), s(z))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[3906, 6140, 6136, 578])).
% 1.84/2.04 tff(6142,plain,
% 1.84/2.04 (r(s(s(z)), s(z))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[153, 6141])).
% 1.84/2.04 tff(6143,plain,
% 1.84/2.04 (b(z, s(s(s(s(z))))) <=> b(z, elem!1)),
% 1.84/2.04 inference(monotonicity,[status(thm)],[3285])).
% 1.84/2.04 tff(6144,plain,
% 1.84/2.04 (b(z, elem!1) <=> b(z, s(s(s(s(z)))))),
% 1.84/2.04 inference(symmetry,[status(thm)],[6143])).
% 1.84/2.04 tff(6145,plain,
% 1.84/2.04 (b(z, s(s(s(s(z)))))),
% 1.84/2.04 inference(modus_ponens,[status(thm)],[1518, 6144])).
% 1.84/2.04 tff(6146,plain,
% 1.84/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))))),
% 1.84/2.04 inference(rewrite,[status(thm)],[])).
% 1.84/2.04 tff(6147,plain,
% 1.84/2.04 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(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(z)))))))),
% 1.84/2.04 inference(rewrite,[status(thm)],[])).
% 1.84/2.04 tff(6148,plain,
% 1.84/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(s(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)))))) | (~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(X1, 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(z))))))))),
% 1.84/2.04 inference(monotonicity,[status(thm)],[6147])).
% 1.84/2.04 tff(6149,plain,
% 1.84/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(s(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)))))) | (~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(X1, 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(z)))))))),
% 1.84/2.04 inference(transitivity,[status(thm)],[6148, 6146])).
% 1.84/2.04 tff(6150,plain,
% 1.84/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(s(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)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))),
% 1.84/2.04 inference(quant_inst,[status(thm)],[])).
% 1.84/2.04 tff(6151,plain,
% 1.84/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 1.84/2.04 inference(modus_ponens,[status(thm)],[6150, 6149])).
% 1.84/2.04 tff(6152,plain,
% 1.84/2.04 ($false),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[6151, 75, 372, 578, 982, 1582])).
% 1.84/2.04 tff(6153,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.04 tff(6154,plain,
% 1.84/2.04 (~b(z, s(z))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[6153, 578, 6136, 6145])).
% 1.84/2.04 tff(6155,plain,
% 1.84/2.04 (r(z, s(z))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[187, 6154])).
% 1.84/2.04 tff(6156,plain,
% 1.84/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 1.84/2.04 inference(rewrite,[status(thm)],[])).
% 1.84/2.04 tff(6157,plain,
% 1.84/2.04 (((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z))) <=> ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 1.84/2.04 inference(rewrite,[status(thm)],[])).
% 1.84/2.04 tff(6158,plain,
% 1.84/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))))),
% 1.84/2.04 inference(monotonicity,[status(thm)],[6157])).
% 1.84/2.04 tff(6159,plain,
% 1.84/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 1.84/2.04 inference(transitivity,[status(thm)],[6158, 6156])).
% 1.84/2.04 tff(6160,plain,
% 1.84/2.04 ((~![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)))),
% 1.84/2.04 inference(quant_inst,[status(thm)],[])).
% 1.84/2.04 tff(6161,plain,
% 1.84/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))),
% 1.84/2.04 inference(modus_ponens,[status(thm)],[6160, 6159])).
% 1.84/2.04 tff(6162,plain,
% 1.84/2.04 (~r(s(s(z)), z)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[6161, 37, 6155, 6142])).
% 1.84/2.04 tff(6163,plain,
% 1.84/2.04 ($false),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[202, 6162, 6133])).
% 1.84/2.04 tff(6164,plain,((~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~(s(s(s(s(z)))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.04 tff(6165,plain,
% 1.84/2.04 (~b(s(s(z)), elem!1)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[6164, 6126, 6125, 5472, 3657, 3285])).
% 1.84/2.04 tff(6166,plain,
% 1.84/2.04 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.84/2.04 inference(modus_ponens,[status(thm)],[6165, 6124])).
% 1.84/2.04 tff(6167,plain,
% 1.84/2.04 (b(z, s(s(s(s(z)))))),
% 1.84/2.04 inference(modus_ponens,[status(thm)],[6125, 6144])).
% 1.84/2.04 tff(6168,plain,
% 1.84/2.04 (b(s(s(s(s(z)))), s(z))),
% 1.84/2.04 inference(modus_ponens,[status(thm)],[5472, 6135])).
% 1.84/2.04 tff(6169,plain,
% 1.84/2.04 (~b(z, s(z))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[6153, 3657, 6168, 6167])).
% 1.84/2.04 tff(6170,plain,
% 1.84/2.04 (r(z, s(z))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[187, 6169])).
% 1.84/2.04 tff(6171,plain,
% 1.84/2.04 (~b(s(s(elem!1)), s(z))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[1638, 107, 1391, 1620])).
% 1.84/2.04 tff(6172,plain,
% 1.84/2.04 (r(s(s(elem!1)), s(z))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[561, 6171])).
% 1.84/2.04 tff(6173,plain,
% 1.84/2.04 (~r(z, s(z))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[4577, 6172, 1518, 1620])).
% 1.84/2.04 tff(6174,plain,
% 1.84/2.04 (b(z, s(z))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[187, 6173])).
% 1.84/2.04 tff(6175,plain,
% 1.84/2.04 ($false),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[1790, 75, 1518, 6174, 107, 1391])).
% 1.84/2.04 tff(6176,plain,((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.04 tff(6177,plain,
% 1.84/2.04 (~b(elem!1, s(s(elem!1)))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[6176, 6126, 5472, 6125])).
% 1.84/2.04 tff(6178,plain,
% 1.84/2.04 (r(elem!1, s(s(elem!1)))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[1617, 6177, 6119])).
% 1.84/2.04 tff(6179,plain,
% 1.84/2.04 (~(s(z) = elem!1)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[1393, 5472])).
% 1.84/2.04 tff(6180,plain,
% 1.84/2.04 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, elem!1)),
% 1.84/2.04 inference(monotonicity,[status(thm)],[3285])).
% 1.84/2.04 tff(6181,plain,
% 1.84/2.04 (b(elem!1, elem!1) <=> b(elem!1, s(s(s(s(z)))))),
% 1.84/2.04 inference(symmetry,[status(thm)],[6180])).
% 1.84/2.04 tff(6182,plain,
% 1.84/2.04 ((~b(elem!1, elem!1)) <=> (~b(elem!1, s(s(s(s(z))))))),
% 1.84/2.04 inference(monotonicity,[status(thm)],[6181])).
% 1.84/2.04 tff(6183,plain,
% 1.84/2.04 (~b(elem!1, s(s(s(s(z)))))),
% 1.84/2.04 inference(modus_ponens,[status(thm)],[1389, 6182])).
% 1.84/2.04 tff(6184,plain,
% 1.84/2.04 (~(elem!1 = z)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[304, 6117])).
% 1.84/2.04 tff(6185,plain,
% 1.84/2.04 (~b(z, s(z))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[6153, 3657, 6136, 6145])).
% 1.84/2.04 tff(6186,plain,
% 1.84/2.04 (r(z, s(z))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[187, 6185])).
% 1.84/2.04 tff(6187,plain,
% 1.84/2.04 (~b(elem!1, s(s(elem!1)))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[6176, 6126, 1391, 1518])).
% 1.84/2.04 tff(6188,plain,
% 1.84/2.04 (r(elem!1, s(s(elem!1)))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[1617, 6187, 4476])).
% 1.84/2.04 tff(6189,plain,
% 1.84/2.04 ($false),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[1818, 37, 494, 506, 2698])).
% 1.84/2.04 tff(6190,plain,((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.04 tff(6191,plain,
% 1.84/2.04 (~r(s(s(elem!1)), s(z))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[6190, 2698, 6186])).
% 1.84/2.04 tff(6192,plain,
% 1.84/2.04 (b(s(s(elem!1)), s(z))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[561, 6191])).
% 1.84/2.04 tff(6193,assumption,(~b(elem!1, s(s(s(s(z)))))), introduced(assumption)).
% 1.84/2.04 tff(6194,plain,
% 1.84/2.04 (~r(elem!1, s(s(s(s(z)))))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[3811, 1647, 1490])).
% 1.84/2.04 tff(6195,plain,
% 1.84/2.04 (elem!1 = s(s(s(s(z))))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[278, 6194, 6193])).
% 1.84/2.04 tff(6196,plain,
% 1.84/2.04 (b(elem!1, s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 1.84/2.04 inference(monotonicity,[status(thm)],[6195])).
% 1.84/2.04 tff(6197,plain,
% 1.84/2.04 (b(s(s(s(s(z)))), s(z))),
% 1.84/2.04 inference(modus_ponens,[status(thm)],[1391, 6196])).
% 1.84/2.04 tff(6198,plain,
% 1.84/2.04 (s(elem!1) = s(s(s(s(s(z)))))),
% 1.84/2.04 inference(monotonicity,[status(thm)],[6195])).
% 1.84/2.04 tff(6199,plain,
% 1.84/2.04 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 1.84/2.04 inference(monotonicity,[status(thm)],[6198])).
% 1.84/2.04 tff(6200,plain,
% 1.84/2.04 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 1.84/2.04 inference(symmetry,[status(thm)],[6199])).
% 1.84/2.04 tff(6201,plain,
% 1.84/2.04 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.84/2.04 inference(monotonicity,[status(thm)],[6200])).
% 1.84/2.05 tff(6202,plain,
% 1.84/2.05 (r(s(s(elem!1)), s(s(s(s(z))))) <=> r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.84/2.05 inference(symmetry,[status(thm)],[6201])).
% 1.84/2.05 tff(6203,plain,
% 1.84/2.05 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.84/2.05 inference(modus_ponens,[status(thm)],[1647, 6202])).
% 1.84/2.05 tff(6204,plain,
% 1.84/2.05 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[4541, 3262])).
% 1.84/2.05 tff(6205,plain,
% 1.84/2.05 (s(s(s(s(z)))) = elem!1),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[273, 6195])).
% 1.84/2.05 tff(6206,plain,
% 1.84/2.05 (~r(s(z), elem!1)),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[3664, 6205, 3656])).
% 1.84/2.05 tff(6207,plain,
% 1.84/2.05 (b(s(z), elem!1)),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[601, 6206, 108])).
% 1.84/2.05 tff(6208,plain,
% 1.84/2.05 (r(s(s(s(s(s(s(z)))))), s(s(z))) <=> r(s(s(elem!1)), s(s(z)))),
% 1.84/2.05 inference(monotonicity,[status(thm)],[6200])).
% 1.84/2.05 tff(6209,plain,
% 1.84/2.05 ((~r(s(s(s(s(s(s(z)))))), s(s(z)))) <=> (~r(s(s(elem!1)), s(s(z))))),
% 1.84/2.05 inference(monotonicity,[status(thm)],[6208])).
% 1.84/2.05 tff(6210,plain,
% 1.84/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 1.84/2.05 inference(rewrite,[status(thm)],[])).
% 1.84/2.05 tff(6211,plain,
% 1.84/2.05 (((~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(z)))))) | (~r(s(s(s(s(s(s(z)))))), 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(s(s(s(s(z)))))), s(s(z)))))),
% 1.84/2.05 inference(rewrite,[status(thm)],[])).
% 1.84/2.05 tff(6212,plain,
% 1.84/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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(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(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z))))))),
% 1.84/2.05 inference(monotonicity,[status(thm)],[6211])).
% 1.84/2.05 tff(6213,plain,
% 1.84/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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(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(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 1.84/2.05 inference(transitivity,[status(thm)],[6212, 6210])).
% 1.84/2.05 tff(6214,plain,
% 1.84/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 1.84/2.05 inference(quant_inst,[status(thm)],[])).
% 1.84/2.05 tff(6215,plain,
% 1.84/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z))))),
% 1.84/2.05 inference(modus_ponens,[status(thm)],[6214, 6213])).
% 1.84/2.05 tff(6216,plain,
% 1.84/2.05 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[6215, 37, 467, 6203])).
% 1.84/2.05 tff(6217,plain,
% 1.84/2.05 (~r(s(s(elem!1)), s(s(z)))),
% 1.84/2.05 inference(modus_ponens,[status(thm)],[6216, 6209])).
% 1.84/2.05 tff(6218,plain,
% 1.84/2.05 (b(s(s(elem!1)), s(s(z)))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[1476, 6217, 266])).
% 1.84/2.05 tff(6219,plain,
% 1.84/2.05 (~b(s(s(z)), s(z))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[1465, 6218, 1391, 6207, 1457])).
% 1.84/2.05 tff(6220,plain,
% 1.84/2.05 (r(s(s(z)), s(z))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[153, 6219])).
% 1.84/2.05 tff(6221,plain,
% 1.84/2.05 (b(s(s(s(s(s(s(z)))))), s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 1.84/2.05 inference(monotonicity,[status(thm)],[6200])).
% 1.84/2.05 tff(6222,plain,
% 1.84/2.05 (b(s(s(elem!1)), s(s(z))) <=> b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.84/2.05 inference(symmetry,[status(thm)],[6221])).
% 1.84/2.05 tff(6223,plain,
% 1.84/2.05 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.84/2.05 inference(modus_ponens,[status(thm)],[6218, 6222])).
% 1.84/2.05 tff(6224,plain,
% 1.84/2.05 (~r(s(s(z)), z)),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[6161, 37, 506, 6220])).
% 1.84/2.05 tff(6225,plain,
% 1.84/2.05 (b(s(s(z)), z)),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[202, 6224])).
% 1.84/2.05 tff(6226,plain,
% 1.84/2.05 (~r(z, s(s(z)))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[537, 37, 506, 6220])).
% 1.84/2.05 tff(6227,plain,
% 1.84/2.05 (b(z, s(s(z)))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[351, 6226])).
% 1.84/2.05 tff(6228,assumption,(b(s(s(s(s(s(s(z)))))), s(s(z)))), introduced(assumption)).
% 1.84/2.05 tff(6229,plain,
% 1.84/2.05 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.84/2.05 inference(monotonicity,[status(thm)],[4466])).
% 1.84/2.05 tff(6230,plain,
% 1.84/2.05 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[4613, 1308, 270, 4601])).
% 1.84/2.05 tff(6231,plain,
% 1.84/2.05 (b(s(s(s(z))), s(s(elem!1)))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[62, 6230, 16])).
% 1.84/2.05 tff(6232,plain,
% 1.84/2.05 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.84/2.05 inference(modus_ponens,[status(thm)],[6231, 6229])).
% 1.84/2.05 tff(6233,plain,
% 1.84/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.84/2.05 inference(rewrite,[status(thm)],[])).
% 1.84/2.05 tff(6234,plain,
% 1.84/2.05 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.84/2.05 inference(rewrite,[status(thm)],[])).
% 1.84/2.05 tff(6235,plain,
% 1.84/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.84/2.05 inference(monotonicity,[status(thm)],[6234])).
% 1.84/2.05 tff(6236,plain,
% 1.84/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.84/2.05 inference(transitivity,[status(thm)],[6235, 6233])).
% 1.84/2.05 tff(6237,plain,
% 1.84/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.84/2.05 inference(quant_inst,[status(thm)],[])).
% 1.84/2.05 tff(6238,plain,
% 1.84/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.84/2.05 inference(modus_ponens,[status(thm)],[6237, 6236])).
% 1.84/2.05 tff(6239,plain,
% 1.84/2.05 (~r(s(s(s(z))), s(s(z)))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[6238, 37, 115, 1308, 467])).
% 1.84/2.05 tff(6240,plain,
% 1.84/2.05 ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z)))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[2173, 58, 6239])).
% 1.84/2.05 tff(6241,plain,
% 1.84/2.05 (b(s(s(s(z))), s(s(z)))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[6240, 2150])).
% 1.84/2.05 tff(6242,plain,
% 1.84/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 1.84/2.05 inference(rewrite,[status(thm)],[])).
% 1.84/2.05 tff(6243,plain,
% 1.84/2.05 (((~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), 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(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 1.84/2.05 inference(rewrite,[status(thm)],[])).
% 1.84/2.05 tff(6244,plain,
% 1.84/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), 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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))))),
% 1.84/2.05 inference(monotonicity,[status(thm)],[6243])).
% 1.84/2.05 tff(6245,plain,
% 1.84/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), 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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 1.84/2.05 inference(transitivity,[status(thm)],[6244, 6242])).
% 1.84/2.05 tff(6246,plain,
% 1.84/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), 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)))))))))),
% 1.84/2.05 inference(quant_inst,[status(thm)],[])).
% 1.84/2.05 tff(6247,plain,
% 1.84/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))),
% 1.84/2.05 inference(modus_ponens,[status(thm)],[6246, 6245])).
% 1.84/2.05 tff(6248,plain,
% 1.84/2.05 ($false),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[6247, 75, 370, 401, 6241, 6232, 6228])).
% 1.84/2.05 tff(6249,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~(elem!1 = s(s(s(s(z)))))) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.05 tff(6250,plain,
% 1.84/2.05 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[6249, 6227, 6225, 6223, 6220, 467, 6195, 6204, 6203])).
% 1.84/2.05 tff(6251,plain,
% 1.84/2.05 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[575, 6250])).
% 1.84/2.05 tff(6252,plain,
% 1.84/2.05 (~b(s(s(s(z))), s(z))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[991, 6251, 3657, 6197])).
% 1.84/2.05 tff(6253,plain,
% 1.84/2.05 (r(s(s(s(z))), s(z))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[1081, 6252])).
% 1.84/2.05 tff(6254,plain,
% 1.84/2.05 (((~![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(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 1.84/2.05 inference(rewrite,[status(thm)],[])).
% 1.84/2.05 tff(6255,plain,
% 1.84/2.05 (((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 1.84/2.05 inference(rewrite,[status(thm)],[])).
% 1.84/2.05 tff(6256,plain,
% 1.84/2.05 (((~![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(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z))))),
% 1.84/2.05 inference(monotonicity,[status(thm)],[6255])).
% 1.84/2.05 tff(6257,plain,
% 1.84/2.05 (((~![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(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 1.84/2.05 inference(transitivity,[status(thm)],[6256, 6254])).
% 1.84/2.05 tff(6258,plain,
% 1.84/2.05 ((~![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(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)))),
% 1.84/2.05 inference(quant_inst,[status(thm)],[])).
% 1.84/2.05 tff(6259,plain,
% 1.84/2.05 ((~![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(s(s(z))), s(z))) | (~r(s(s(s(z))), z))),
% 1.84/2.05 inference(modus_ponens,[status(thm)],[6258, 6257])).
% 1.84/2.05 tff(6260,plain,
% 1.84/2.05 (~r(s(s(s(z))), z)),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[6259, 37, 506, 6253])).
% 1.84/2.05 tff(6261,plain,
% 1.84/2.05 (s(s(s(s(z)))) = elem!1),
% 1.84/2.05 inference(symmetry,[status(thm)],[6195])).
% 1.84/2.05 tff(6262,plain,
% 1.84/2.05 (b(z, s(s(s(s(z))))) <=> b(z, elem!1)),
% 1.84/2.05 inference(monotonicity,[status(thm)],[6261])).
% 1.84/2.05 tff(6263,plain,
% 1.84/2.05 (b(z, elem!1) <=> b(z, s(s(s(s(z)))))),
% 1.84/2.05 inference(symmetry,[status(thm)],[6262])).
% 1.84/2.05 tff(6264,plain,
% 1.84/2.05 (b(z, s(s(s(s(z)))))),
% 1.84/2.05 inference(modus_ponens,[status(thm)],[1518, 6263])).
% 1.84/2.05 tff(6265,plain,
% 1.84/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.84/2.05 inference(rewrite,[status(thm)],[])).
% 1.84/2.05 tff(6266,plain,
% 1.84/2.05 (((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.84/2.05 inference(rewrite,[status(thm)],[])).
% 1.84/2.05 tff(6267,plain,
% 1.84/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 1.84/2.06 inference(monotonicity,[status(thm)],[6266])).
% 1.84/2.06 tff(6268,plain,
% 1.84/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.84/2.06 inference(transitivity,[status(thm)],[6267, 6265])).
% 1.84/2.06 tff(6269,plain,
% 1.84/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 1.84/2.06 inference(quant_inst,[status(thm)],[])).
% 1.84/2.06 tff(6270,plain,
% 1.84/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[6269, 6268])).
% 1.84/2.06 tff(6271,plain,
% 1.84/2.06 (~b(s(s(s(z))), z)),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[6270, 75, 3657, 6251, 6197, 6264])).
% 1.84/2.06 tff(6272,plain,
% 1.84/2.06 ($false),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[1334, 58, 221, 6271, 6260])).
% 1.84/2.06 tff(6273,plain,((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (s(s(elem!1)) = s(s(z))) | (~b(z, elem!1)) | (s(z) = elem!1) | r(s(z), s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.06 tff(6274,plain,
% 1.84/2.06 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[6273, 6192, 1391, 266, 1518, 4487, 6183, 2478, 3656, 6188, 6186])).
% 1.84/2.06 tff(6275,plain,
% 1.84/2.06 (b(s(s(z)), s(s(s(s(z)))))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[465, 6274])).
% 1.84/2.06 tff(6276,plain,
% 1.84/2.06 (~b(s(s(z)), s(z))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[3906, 6275, 6136, 3657])).
% 1.84/2.06 tff(6277,plain,
% 1.84/2.06 (r(s(s(z)), s(z))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[153, 6276])).
% 1.84/2.06 tff(6278,plain,
% 1.84/2.06 (~r(s(s(z)), z)),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[6161, 37, 6186, 6277])).
% 1.84/2.06 tff(6279,plain,
% 1.84/2.06 (b(s(s(z)), z)),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[202, 6278])).
% 1.84/2.06 tff(6280,plain,
% 1.84/2.06 (~r(z, s(s(z)))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[537, 37, 6186, 6277])).
% 1.84/2.06 tff(6281,plain,
% 1.84/2.06 (b(z, s(s(z)))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[351, 6280])).
% 1.84/2.06 tff(6282,plain,
% 1.84/2.06 (~r(elem!1, z)),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[4774, 2698, 2647])).
% 1.84/2.06 tff(6283,plain,
% 1.84/2.06 (b(elem!1, z)),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[387, 6282, 353])).
% 1.84/2.06 tff(6284,plain,
% 1.84/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z)))),
% 1.84/2.06 inference(rewrite,[status(thm)],[])).
% 1.84/2.06 tff(6285,plain,
% 1.84/2.06 (((~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z)))),
% 1.84/2.06 inference(rewrite,[status(thm)],[])).
% 1.84/2.06 tff(6286,plain,
% 1.84/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)), z)) | (~b(z, s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z))))),
% 1.84/2.06 inference(monotonicity,[status(thm)],[6285])).
% 1.84/2.06 tff(6287,plain,
% 1.84/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)), z)) | (~b(z, s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z)))),
% 1.84/2.06 inference(transitivity,[status(thm)],[6286, 6284])).
% 1.84/2.06 tff(6288,plain,
% 1.84/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 1.84/2.06 inference(quant_inst,[status(thm)],[])).
% 1.84/2.06 tff(6289,plain,
% 1.84/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z))),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[6288, 6287])).
% 1.84/2.06 tff(6290,plain,
% 1.84/2.06 (~b(s(s(z)), elem!1)),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[6289, 75, 6283, 6281, 6279])).
% 1.84/2.06 tff(6291,plain,
% 1.84/2.06 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[6290, 6124])).
% 1.84/2.06 tff(6292,plain,
% 1.84/2.06 ($false),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[6275, 6291])).
% 1.84/2.06 tff(6293,plain,((~r(s(s(elem!1)), z)) | (~(s(s(s(s(z)))) = elem!1)) | (~b(elem!1, s(z))) | (s(s(elem!1)) = s(s(z))) | (~b(z, elem!1)) | r(s(z), s(s(s(s(z))))) | (elem!1 = z) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.06 tff(6294,plain,
% 1.84/2.06 (~r(s(s(elem!1)), z)),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[6293, 3656, 5472, 6118, 6125, 3285, 6184, 2647])).
% 1.84/2.06 tff(6295,plain,
% 1.84/2.06 (b(s(s(elem!1)), z)),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[2696, 6294])).
% 1.84/2.06 tff(6296,plain,
% 1.84/2.06 (r(elem!1, s(s(s(s(z))))) <=> r(elem!1, elem!1)),
% 1.84/2.06 inference(monotonicity,[status(thm)],[3285])).
% 1.84/2.06 tff(6297,plain,
% 1.84/2.06 (r(elem!1, elem!1) <=> r(elem!1, s(s(s(s(z)))))),
% 1.84/2.06 inference(symmetry,[status(thm)],[6296])).
% 1.84/2.06 tff(6298,plain,
% 1.84/2.06 ((~r(elem!1, elem!1)) <=> (~r(elem!1, s(s(s(s(z))))))),
% 1.84/2.06 inference(monotonicity,[status(thm)],[6297])).
% 1.84/2.06 tff(6299,plain,
% 1.84/2.06 (^[X: $i] : refl((~r(X, X)) <=> (~r(X, X)))),
% 1.84/2.06 inference(bind,[status(th)],[])).
% 1.84/2.06 tff(6300,plain,
% 1.84/2.06 (![X: $i] : (~r(X, X)) <=> ![X: $i] : (~r(X, X))),
% 1.84/2.06 inference(quant_intro,[status(thm)],[6299])).
% 1.84/2.06 tff(6301,plain,
% 1.84/2.06 (![X: $i] : (~r(X, X)) <=> ![X: $i] : (~r(X, X))),
% 1.84/2.06 inference(rewrite,[status(thm)],[])).
% 1.84/2.06 tff(6302,axiom,(![X: $i] : (~r(X, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ri')).
% 1.84/2.06 tff(6303,plain,
% 1.84/2.06 (![X: $i] : (~r(X, X))),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[6302, 6301])).
% 1.84/2.06 tff(6304,plain,(
% 1.84/2.06 ![X: $i] : (~r(X, X))),
% 1.84/2.06 inference(skolemize,[status(sab)],[6303])).
% 1.84/2.06 tff(6305,plain,
% 1.84/2.06 (![X: $i] : (~r(X, X))),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[6304, 6300])).
% 1.84/2.06 tff(6306,plain,
% 1.84/2.06 ((~![X: $i] : (~r(X, X))) | (~r(elem!1, elem!1))),
% 1.84/2.06 inference(quant_inst,[status(thm)],[])).
% 1.84/2.06 tff(6307,plain,
% 1.84/2.06 (~r(elem!1, elem!1)),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[6306, 6305])).
% 1.84/2.06 tff(6308,plain,
% 1.84/2.06 (~r(elem!1, s(s(s(s(z)))))),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[6307, 6298])).
% 1.84/2.06 tff(6309,plain,
% 1.84/2.06 (~b(z, s(z))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[6153, 578, 6168, 6167])).
% 1.84/2.06 tff(6310,plain,
% 1.84/2.06 (r(z, s(z))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[187, 6309])).
% 1.84/2.06 tff(6311,plain,
% 1.84/2.06 (~r(z, s(s(elem!1)))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[1830, 37, 494, 6310])).
% 1.84/2.06 tff(6312,assumption,(~b(z, s(s(elem!1)))), introduced(assumption)).
% 1.84/2.06 tff(6313,plain,
% 1.84/2.06 ($false),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[1834, 58, 6312, 5566, 5250])).
% 1.84/2.06 tff(6314,plain,(b(z, s(s(elem!1))) | r(z, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.06 tff(6315,plain,
% 1.84/2.06 (b(z, s(s(elem!1)))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[6314, 6311])).
% 1.84/2.06 tff(6316,assumption,(s(s(z)) = s(s(elem!1))), introduced(assumption)).
% 1.84/2.06 tff(6317,plain,
% 1.84/2.06 (s(s(elem!1)) = s(s(z))),
% 1.84/2.06 inference(symmetry,[status(thm)],[6316])).
% 1.84/2.06 tff(6318,plain,
% 1.84/2.06 ($false),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[266, 6317])).
% 1.84/2.06 tff(6319,plain,((~(s(s(z)) = s(s(elem!1)))) | (s(s(elem!1)) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.06 tff(6320,plain,
% 1.84/2.06 (~(s(s(z)) = s(s(elem!1)))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[6319, 6118])).
% 1.84/2.06 tff(6321,plain,
% 1.84/2.06 (elem!1 = s(s(s(s(z))))),
% 1.84/2.06 inference(symmetry,[status(thm)],[3285])).
% 1.84/2.06 tff(6322,plain,
% 1.84/2.06 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(s(s(z)))))),
% 1.84/2.06 inference(monotonicity,[status(thm)],[6321])).
% 1.84/2.06 tff(6323,plain,
% 1.84/2.06 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(z)) = elem!1)),
% 1.84/2.06 inference(symmetry,[status(thm)],[6322])).
% 1.84/2.06 tff(6324,plain,
% 1.84/2.06 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(z)) = elem!1))),
% 1.84/2.06 inference(monotonicity,[status(thm)],[6323])).
% 1.84/2.06 tff(6325,plain,
% 1.84/2.06 (~(s(s(z)) = elem!1)),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[459, 6324])).
% 1.84/2.06 tff(6326,plain,
% 1.84/2.06 (r(s(s(z)), elem!1)),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[104, 99, 6325])).
% 1.84/2.06 tff(6327,plain,
% 1.84/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), 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)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 1.84/2.06 inference(rewrite,[status(thm)],[])).
% 1.84/2.06 tff(6328,plain,
% 1.84/2.06 (((~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)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 1.84/2.06 inference(rewrite,[status(thm)],[])).
% 1.84/2.06 tff(6329,plain,
% 1.84/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), elem!1))))),
% 1.84/2.06 inference(monotonicity,[status(thm)],[6328])).
% 1.84/2.06 tff(6330,plain,
% 1.84/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 1.84/2.06 inference(transitivity,[status(thm)],[6329, 6327])).
% 1.84/2.06 tff(6331,plain,
% 1.84/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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)))))),
% 1.84/2.06 inference(quant_inst,[status(thm)],[])).
% 1.84/2.06 tff(6332,plain,
% 1.84/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), elem!1))),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[6331, 6330])).
% 1.84/2.06 tff(6333,plain,
% 1.84/2.06 (~r(s(s(z)), s(s(elem!1)))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[6332, 37, 494, 6326, 2647])).
% 1.84/2.06 tff(6334,plain,
% 1.84/2.06 (((~![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))))),
% 1.84/2.06 inference(rewrite,[status(thm)],[])).
% 1.84/2.06 tff(6335,plain,
% 1.84/2.06 ((~![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))))),
% 1.84/2.06 inference(quant_inst,[status(thm)],[])).
% 1.84/2.06 tff(6336,plain,
% 1.84/2.06 ((~![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)))),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[6335, 6334])).
% 1.84/2.06 tff(6337,plain,
% 1.84/2.06 (b(s(s(z)), s(s(elem!1)))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[6336, 58, 6333, 6320])).
% 1.84/2.06 tff(6338,plain,
% 1.84/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(elem!1)))))),
% 1.84/2.06 inference(rewrite,[status(thm)],[])).
% 1.84/2.06 tff(6339,plain,
% 1.84/2.06 (((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.84/2.06 inference(rewrite,[status(thm)],[])).
% 1.84/2.06 tff(6340,plain,
% 1.84/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(elem!1))))))),
% 1.84/2.06 inference(monotonicity,[status(thm)],[6339])).
% 1.84/2.06 tff(6341,plain,
% 1.84/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(elem!1)))))),
% 1.84/2.06 inference(transitivity,[status(thm)],[6340, 6338])).
% 1.84/2.06 tff(6342,plain,
% 1.84/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)))),
% 1.84/2.06 inference(quant_inst,[status(thm)],[])).
% 1.84/2.06 tff(6343,plain,
% 1.84/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(elem!1))))),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[6342, 6341])).
% 1.84/2.06 tff(6344,plain,
% 1.84/2.06 (~b(s(s(z)), z)),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[6343, 75, 6337, 6315, 1892])).
% 1.84/2.06 tff(6345,plain,
% 1.84/2.06 (r(s(s(z)), z)),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[202, 6344])).
% 1.84/2.06 tff(6346,plain,
% 1.84/2.06 (~(elem!1 = s(s(z)))),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[6325, 308])).
% 1.84/2.06 tff(6347,plain,
% 1.84/2.06 (~b(s(z), z)),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[1526, 107, 5472, 6125])).
% 1.84/2.06 tff(6348,plain,
% 1.84/2.06 (r(s(z), z)),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[169, 6347])).
% 1.84/2.06 tff(6349,plain,
% 1.84/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 1.84/2.06 inference(rewrite,[status(thm)],[])).
% 1.84/2.06 tff(6350,plain,
% 1.84/2.06 (((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 1.84/2.06 inference(rewrite,[status(thm)],[])).
% 1.84/2.06 tff(6351,plain,
% 1.84/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))))),
% 1.84/2.06 inference(monotonicity,[status(thm)],[6350])).
% 1.84/2.06 tff(6352,plain,
% 1.84/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 1.84/2.06 inference(transitivity,[status(thm)],[6351, 6349])).
% 1.84/2.06 tff(6353,plain,
% 1.84/2.06 ((~![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))))),
% 1.84/2.06 inference(quant_inst,[status(thm)],[])).
% 1.84/2.06 tff(6354,plain,
% 1.84/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[6353, 6352])).
% 1.84/2.06 tff(6355,plain,
% 1.84/2.06 (~r(s(s(z)), s(z))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[6354, 37, 6348, 6345])).
% 1.84/2.06 tff(6356,plain,
% 1.84/2.06 (b(s(s(z)), s(z))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[153, 6355])).
% 1.84/2.06 tff(6357,plain,
% 1.84/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))))),
% 1.84/2.06 inference(rewrite,[status(thm)],[])).
% 1.84/2.06 tff(6358,plain,
% 1.84/2.06 (((~b(elem!1, s(z))) | (~b(s(s(z)), 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(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))))),
% 1.84/2.06 inference(rewrite,[status(thm)],[])).
% 1.84/2.06 tff(6359,plain,
% 1.84/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z))))))),
% 1.84/2.07 inference(monotonicity,[status(thm)],[6358])).
% 1.84/2.07 tff(6360,plain,
% 1.84/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))))),
% 1.84/2.07 inference(transitivity,[status(thm)],[6359, 6357])).
% 1.84/2.07 tff(6361,plain,
% 1.84/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))))),
% 1.84/2.07 inference(quant_inst,[status(thm)],[])).
% 1.84/2.07 tff(6362,plain,
% 1.84/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z))))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[6361, 6360])).
% 1.84/2.07 tff(6363,plain,
% 1.84/2.07 (~b(elem!1, s(s(z)))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[6362, 75, 107, 5472, 6356])).
% 1.84/2.07 tff(6364,plain,
% 1.84/2.07 ((elem!1 = s(s(z))) | r(elem!1, s(s(z)))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[398, 58, 6363])).
% 1.84/2.07 tff(6365,plain,
% 1.84/2.07 (r(elem!1, s(s(z)))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[6364, 6346])).
% 1.84/2.07 tff(6366,plain,
% 1.84/2.07 (~r(elem!1, z)),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[4401, 6365, 6345])).
% 1.84/2.07 tff(6367,plain,
% 1.84/2.07 (~(s(s(z)) = s(elem!1))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[3261, 6179])).
% 1.84/2.07 tff(6368,plain,
% 1.84/2.07 (b(z, s(s(elem!1)))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[6314, 1955])).
% 1.84/2.07 tff(6369,plain,
% 1.84/2.07 (~r(s(s(z)), s(s(elem!1)))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[6332, 37, 494, 106, 2647])).
% 1.84/2.07 tff(6370,plain,
% 1.84/2.07 (b(s(s(z)), s(s(elem!1)))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[6336, 58, 6369, 6320])).
% 1.84/2.07 tff(6371,plain,
% 1.84/2.07 (~b(s(s(z)), z)),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[6343, 75, 6370, 6368, 1892])).
% 1.84/2.07 tff(6372,plain,
% 1.84/2.07 (r(s(s(z)), z)),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[202, 6371])).
% 1.84/2.07 tff(6373,plain,
% 1.84/2.07 (~r(s(s(z)), s(z))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[6354, 37, 6348, 6372])).
% 1.84/2.07 tff(6374,plain,
% 1.84/2.07 (b(s(s(z)), s(z))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[153, 6373])).
% 1.84/2.07 tff(6375,plain,
% 1.84/2.07 (~b(s(s(s(z))), s(z))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[3403, 1061, 6118, 106, 6374, 107, 2614, 6367, 13, 12, 268, 99])).
% 1.84/2.07 tff(6376,plain,
% 1.84/2.07 (r(s(s(s(z))), s(z))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[1081, 6375])).
% 1.84/2.07 tff(6377,plain,
% 1.84/2.07 (~r(s(s(s(z))), z)),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[6259, 37, 506, 6376])).
% 1.84/2.07 tff(6378,plain,
% 1.84/2.07 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[4541, 6367])).
% 1.84/2.07 tff(6379,plain,
% 1.84/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(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(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 1.84/2.07 inference(rewrite,[status(thm)],[])).
% 1.84/2.07 tff(6380,plain,
% 1.84/2.07 (((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 1.84/2.07 inference(rewrite,[status(thm)],[])).
% 1.84/2.07 tff(6381,plain,
% 1.84/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))))),
% 1.84/2.07 inference(monotonicity,[status(thm)],[6380])).
% 1.84/2.07 tff(6382,plain,
% 1.84/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 1.84/2.07 inference(transitivity,[status(thm)],[6381, 6379])).
% 1.84/2.07 tff(6383,plain,
% 1.84/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.84/2.07 inference(quant_inst,[status(thm)],[])).
% 1.84/2.07 tff(6384,plain,
% 1.84/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[6383, 6382])).
% 1.84/2.07 tff(6385,plain,
% 1.84/2.07 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[6384, 37, 494, 1061, 2647])).
% 1.84/2.07 tff(6386,plain,
% 1.84/2.07 (b(s(s(s(z))), s(s(elem!1)))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[62, 6385, 6378])).
% 1.84/2.07 tff(6387,plain,
% 1.84/2.07 (~b(s(s(s(z))), z)),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[5576, 6386, 1955, 1892])).
% 1.84/2.07 tff(6388,plain,
% 1.84/2.07 ($false),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[1334, 58, 221, 6387, 6377])).
% 1.84/2.07 tff(6389,plain,((~r(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), z)) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | r(elem!1, z) | r(z, elem!1) | r(s(s(s(s(z)))), elem!1) | r(elem!1, s(s(s(s(z))))) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.84/2.07 tff(6390,plain,
% 1.84/2.07 (~r(s(s(s(z))), elem!1)),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[6389, 6326, 6310, 494, 2647, 1892, 107, 6366, 13, 12, 6308, 99])).
% 1.84/2.07 tff(6391,plain,
% 1.84/2.07 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(z))), elem!1)),
% 1.84/2.07 inference(monotonicity,[status(thm)],[3285])).
% 1.84/2.07 tff(6392,plain,
% 1.84/2.07 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 1.84/2.07 inference(symmetry,[status(thm)],[6391])).
% 1.84/2.07 tff(6393,plain,
% 1.84/2.07 ((~r(s(s(s(z))), elem!1)) <=> (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.84/2.07 inference(monotonicity,[status(thm)],[6392])).
% 1.84/2.07 tff(6394,plain,
% 1.84/2.07 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[1710, 6393])).
% 1.84/2.07 tff(6395,plain,
% 1.84/2.07 ($false),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[1308, 6394])).
% 1.84/2.07 tff(6396,plain,((~(s(s(s(s(z)))) = elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.84/2.07 tff(6397,plain,
% 1.84/2.07 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[6396, 6390, 3285])).
% 1.84/2.07 tff(6398,plain,
% 1.84/2.07 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[575, 6397])).
% 1.84/2.07 tff(6399,plain,
% 1.84/2.07 (~b(s(s(s(z))), s(z))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[991, 6398, 6168, 578])).
% 1.84/2.07 tff(6400,plain,
% 1.84/2.07 (r(s(s(s(z))), s(z))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[1081, 6399])).
% 1.84/2.07 tff(6401,plain,
% 1.84/2.07 (~r(s(s(s(z))), z)),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[6259, 37, 6310, 6400])).
% 1.84/2.07 tff(6402,plain,
% 1.84/2.07 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 1.84/2.07 inference(monotonicity,[status(thm)],[3285])).
% 1.84/2.07 tff(6403,plain,
% 1.84/2.07 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 1.84/2.07 inference(transitivity,[status(thm)],[6402, 1028])).
% 1.84/2.07 tff(6404,plain,
% 1.84/2.07 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(z))) = elem!1))),
% 1.84/2.07 inference(monotonicity,[status(thm)],[6403])).
% 1.84/2.07 tff(6405,plain,
% 1.84/2.07 (~(s(s(s(z))) = elem!1)),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[264, 6404])).
% 1.84/2.07 tff(6406,plain,
% 1.84/2.07 (b(s(s(s(z))), elem!1)),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[1115, 6390, 6405])).
% 1.84/2.07 tff(6407,plain,
% 1.84/2.07 (b(elem!1, z)),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[387, 6366, 6184])).
% 1.84/2.07 tff(6408,plain,
% 1.84/2.07 (~b(s(s(s(z))), z)),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[4030, 75, 6125, 6407, 6406])).
% 1.84/2.07 tff(6409,plain,
% 1.84/2.07 ($false),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[1334, 58, 221, 6408, 6401])).
% 1.84/2.07 tff(6410,plain,(b(s(s(z)), elem!1) | (~b(s(z), s(s(s(s(z)))))) | (~(s(s(s(s(z)))) = elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(z), elem!1)) | r(z, elem!1) | r(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.84/2.07 tff(6411,plain,
% 1.84/2.07 (~r(s(s(elem!1)), s(z))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[6410, 6165, 3285, 3657, 2647, 6295, 6126, 13, 12])).
% 1.84/2.07 tff(6412,plain,
% 1.84/2.07 (b(s(s(elem!1)), s(z))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[561, 6411])).
% 1.84/2.07 tff(6413,plain,
% 1.84/2.07 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[6273, 6412, 5472, 6118, 6125, 4487, 6183, 6179, 3656, 6178, 6170])).
% 1.84/2.07 tff(6414,plain,
% 1.84/2.07 (b(s(s(z)), s(s(s(s(z)))))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[465, 6413])).
% 1.84/2.07 tff(6415,plain,
% 1.84/2.07 ($false),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[6414, 6166])).
% 1.84/2.07 tff(6416,plain,(r(s(z), s(s(s(s(z))))) | (~(s(s(s(s(z)))) = elem!1)) | (~r(s(s(elem!1)), elem!1)) | r(z, elem!1) | r(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.84/2.07 tff(6417,plain,
% 1.84/2.07 (r(s(z), s(s(s(s(z)))))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[6416, 3285, 6121, 13, 12])).
% 1.84/2.07 tff(6418,plain,
% 1.84/2.07 (r(s(z), elem!1)),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[6417, 3660])).
% 1.84/2.07 tff(6419,plain,
% 1.84/2.07 (~r(s(z), s(s(elem!1)))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[2653, 37, 6418, 6121])).
% 1.84/2.07 tff(6420,plain,
% 1.84/2.07 (b(s(z), s(s(elem!1)))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[1890, 6419])).
% 1.84/2.07 tff(6421,plain,
% 1.84/2.07 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[4486, 6121, 3285])).
% 1.84/2.07 tff(6422,plain,
% 1.84/2.07 (~r(s(s(elem!1)), s(z))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[1655, 6417, 6421])).
% 1.84/2.07 tff(6423,plain,
% 1.84/2.07 (b(s(s(elem!1)), s(z))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[561, 6422])).
% 1.84/2.07 tff(6424,plain,
% 1.84/2.07 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 1.84/2.07 inference(transitivity,[status(thm)],[6403, 3425])).
% 1.84/2.07 tff(6425,plain,
% 1.84/2.07 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(z)))))),
% 1.84/2.07 inference(monotonicity,[status(thm)],[6424])).
% 1.84/2.07 tff(6426,plain,
% 1.84/2.07 (~(elem!1 = s(s(s(z))))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[264, 6425])).
% 1.84/2.07 tff(6427,plain,
% 1.84/2.07 (~r(s(s(z)), elem!1)),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[2665, 6418, 6118, 6121])).
% 1.84/2.07 tff(6428,plain,
% 1.84/2.07 (b(s(s(z)), elem!1)),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[104, 6427, 6325])).
% 1.84/2.07 tff(6429,plain,
% 1.84/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))))),
% 1.84/2.07 inference(rewrite,[status(thm)],[])).
% 1.84/2.07 tff(6430,plain,
% 1.84/2.07 (((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))))),
% 1.84/2.07 inference(rewrite,[status(thm)],[])).
% 1.84/2.07 tff(6431,plain,
% 1.84/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z)))))),
% 1.84/2.07 inference(monotonicity,[status(thm)],[6430])).
% 1.84/2.07 tff(6432,plain,
% 1.84/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))))),
% 1.84/2.07 inference(transitivity,[status(thm)],[6431, 6429])).
% 1.84/2.07 tff(6433,plain,
% 1.84/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.84/2.07 inference(quant_inst,[status(thm)],[])).
% 1.84/2.07 tff(6434,plain,
% 1.84/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z)))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[6433, 6432])).
% 1.84/2.07 tff(6435,plain,
% 1.84/2.07 ($false),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[6434, 75, 1457, 1391, 1894, 964, 309])).
% 1.84/2.07 tff(6436,plain,((~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.07 tff(6437,plain,
% 1.84/2.07 (~b(s(s(z)), s(z))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[6436, 6423, 5472, 6420, 6428])).
% 1.84/2.07 tff(6438,plain,
% 1.84/2.07 (r(s(s(z)), s(z))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[153, 6437])).
% 1.84/2.07 tff(6439,plain,
% 1.84/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))) | (~b(z, elem!1)))),
% 1.84/2.07 inference(rewrite,[status(thm)],[])).
% 1.84/2.07 tff(6440,plain,
% 1.84/2.07 (((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)))),
% 1.84/2.07 inference(rewrite,[status(thm)],[])).
% 1.84/2.07 tff(6441,plain,
% 1.84/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), 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(X1, 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(elem!1, s(z))) | (~b(z, elem!1))))),
% 1.84/2.07 inference(monotonicity,[status(thm)],[6440])).
% 1.84/2.07 tff(6442,plain,
% 1.84/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), 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(X1, 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(elem!1, s(z))) | (~b(z, elem!1)))),
% 1.84/2.07 inference(transitivity,[status(thm)],[6441, 6439])).
% 1.84/2.07 tff(6443,plain,
% 1.84/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))),
% 1.84/2.07 inference(quant_inst,[status(thm)],[])).
% 1.84/2.07 tff(6444,plain,
% 1.84/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[6443, 6442])).
% 1.84/2.07 tff(6445,plain,
% 1.84/2.07 ($false),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[6444, 75, 1518, 1457, 372, 1391, 1894])).
% 1.84/2.07 tff(6446,plain,((~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.07 tff(6447,plain,
% 1.84/2.07 (~b(z, s(z))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[6446, 6423, 6125, 5472, 6420])).
% 1.84/2.07 tff(6448,plain,
% 1.84/2.07 (r(z, s(z))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[187, 6447])).
% 1.84/2.07 tff(6449,plain,
% 1.84/2.07 (~r(s(s(z)), z)),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[6161, 37, 6448, 6438])).
% 1.84/2.07 tff(6450,plain,
% 1.84/2.07 (b(s(s(z)), z)),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[202, 6449])).
% 1.84/2.07 tff(6451,plain,
% 1.84/2.07 ($false),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[4385, 75, 1518, 1958, 964, 401])).
% 1.84/2.07 tff(6452,plain,((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.07 tff(6453,plain,
% 1.84/2.07 (~b(elem!1, z)),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[6452, 6428, 6125, 6450])).
% 1.84/2.07 tff(6454,plain,
% 1.84/2.07 (r(elem!1, z)),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[387, 6453, 6184])).
% 1.84/2.07 tff(6455,plain,
% 1.84/2.07 ($false),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[537, 37, 506, 115, 331])).
% 1.84/2.07 tff(6456,plain,((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.07 tff(6457,plain,
% 1.84/2.07 (~r(z, s(s(z)))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[6456, 6438, 6448])).
% 1.84/2.07 tff(6458,plain,
% 1.84/2.07 (b(z, s(s(z)))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[351, 6457])).
% 1.84/2.07 tff(6459,plain,
% 1.84/2.07 (r(s(s(s(s(z)))), z)),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[6454, 4743])).
% 1.84/2.07 tff(6460,plain,
% 1.84/2.07 (~r(s(z), z)),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[2586, 6459, 6417])).
% 1.84/2.07 tff(6461,plain,
% 1.84/2.07 (b(s(z), z)),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[169, 6460])).
% 1.84/2.07 tff(6462,plain,
% 1.84/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.84/2.07 inference(rewrite,[status(thm)],[])).
% 1.84/2.07 tff(6463,plain,
% 1.84/2.07 (((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.84/2.07 inference(rewrite,[status(thm)],[])).
% 1.84/2.07 tff(6464,plain,
% 1.84/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z)))))))),
% 1.84/2.07 inference(monotonicity,[status(thm)],[6463])).
% 1.84/2.07 tff(6465,plain,
% 1.84/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.84/2.07 inference(transitivity,[status(thm)],[6464, 6462])).
% 1.84/2.07 tff(6466,plain,
% 1.84/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 1.84/2.07 inference(quant_inst,[status(thm)],[])).
% 1.84/2.07 tff(6467,plain,
% 1.84/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z)))))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[6466, 6465])).
% 1.84/2.07 tff(6468,plain,
% 1.84/2.07 ($false),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[6467, 75, 1518, 964, 401, 1119, 1287])).
% 1.84/2.07 tff(6469,plain,((~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.07 tff(6470,plain,
% 1.84/2.07 (~b(elem!1, s(s(s(z))))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[6469, 1119, 964, 401, 1518])).
% 1.84/2.07 tff(6471,plain,
% 1.84/2.07 (r(elem!1, s(s(s(z))))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[1279, 6470, 1305])).
% 1.84/2.07 tff(6472,assumption,(r(s(s(s(z))), z)), introduced(assumption)).
% 1.84/2.07 tff(6473,plain,
% 1.84/2.07 ($false),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[2130, 37, 155, 1266, 6472])).
% 1.84/2.07 tff(6474,plain,((~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.07 tff(6475,plain,
% 1.84/2.08 (~r(s(s(s(z))), z)),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[6474, 6471, 155])).
% 1.84/2.08 tff(6476,plain,
% 1.84/2.08 (b(s(s(s(z))), z)),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[1334, 58, 221, 6475])).
% 1.84/2.08 tff(6477,plain,
% 1.84/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.84/2.08 inference(rewrite,[status(thm)],[])).
% 1.84/2.08 tff(6478,plain,
% 1.84/2.08 (((~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.84/2.08 inference(rewrite,[status(thm)],[])).
% 1.84/2.08 tff(6479,plain,
% 1.84/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z)))))))),
% 1.84/2.08 inference(monotonicity,[status(thm)],[6478])).
% 1.84/2.08 tff(6480,plain,
% 1.84/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.84/2.08 inference(transitivity,[status(thm)],[6479, 6477])).
% 1.84/2.08 tff(6481,plain,
% 1.84/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.84/2.08 inference(quant_inst,[status(thm)],[])).
% 1.84/2.08 tff(6482,plain,
% 1.84/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z)))))),
% 1.84/2.08 inference(modus_ponens,[status(thm)],[6481, 6480])).
% 1.84/2.08 tff(6483,plain,
% 1.84/2.08 ((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z)))))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[6482, 75, 964, 370, 401, 1119])).
% 1.84/2.08 tff(6484,plain,
% 1.84/2.08 (~b(s(s(z)), s(s(s(z))))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[6483, 6476])).
% 1.84/2.08 tff(6485,plain,
% 1.84/2.08 (r(s(s(z)), s(s(s(z))))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[1559, 58, 1556, 6484])).
% 1.84/2.08 tff(6486,plain,
% 1.84/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.84/2.08 inference(rewrite,[status(thm)],[])).
% 1.84/2.08 tff(6487,plain,
% 1.84/2.08 (((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.84/2.08 inference(rewrite,[status(thm)],[])).
% 1.84/2.08 tff(6488,plain,
% 1.84/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))))),
% 1.84/2.08 inference(monotonicity,[status(thm)],[6487])).
% 1.84/2.08 tff(6489,plain,
% 1.84/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.84/2.08 inference(transitivity,[status(thm)],[6488, 6486])).
% 1.84/2.08 tff(6490,plain,
% 1.84/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.84/2.08 inference(quant_inst,[status(thm)],[])).
% 1.84/2.08 tff(6491,plain,
% 1.84/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))),
% 1.84/2.08 inference(modus_ponens,[status(thm)],[6490, 6489])).
% 1.84/2.08 tff(6492,plain,
% 1.84/2.08 (~b(s(s(s(z))), s(z))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[6491, 75, 371, 370, 401, 6476])).
% 1.84/2.08 tff(6493,plain,
% 1.84/2.08 (r(s(s(s(z))), s(z))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[1081, 6492])).
% 1.84/2.08 tff(6494,assumption,(r(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 1.84/2.08 tff(6495,plain,
% 1.84/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.84/2.08 inference(rewrite,[status(thm)],[])).
% 1.84/2.08 tff(6496,plain,
% 1.84/2.08 (((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.84/2.08 inference(rewrite,[status(thm)],[])).
% 1.84/2.08 tff(6497,plain,
% 1.84/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z)))))))),
% 1.84/2.08 inference(monotonicity,[status(thm)],[6496])).
% 1.84/2.08 tff(6498,plain,
% 1.84/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.84/2.08 inference(transitivity,[status(thm)],[6497, 6495])).
% 1.84/2.08 tff(6499,plain,
% 1.84/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.84/2.08 inference(quant_inst,[status(thm)],[])).
% 1.84/2.08 tff(6500,plain,
% 1.84/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z)))))),
% 1.84/2.08 inference(modus_ponens,[status(thm)],[6499, 6498])).
% 1.84/2.08 tff(6501,plain,
% 1.84/2.08 ($false),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[6500, 37, 115, 1067, 6494])).
% 1.84/2.08 tff(6502,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.08 tff(6503,plain,
% 1.84/2.08 ($false),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[6502, 6493, 6485, 115])).
% 1.84/2.08 tff(6504,plain,((~b(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~r(elem!1, z)) | (elem!1 = s(s(s(z)))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.08 tff(6505,plain,
% 1.84/2.08 (~b(s(s(s(z))), elem!1)),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[6504, 6438, 6461, 6458, 6450, 6428, 6454, 6426, 6125])).
% 1.84/2.08 tff(6506,plain,
% 1.84/2.08 (r(s(s(s(z))), elem!1)),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[1115, 6505, 6405])).
% 1.84/2.08 tff(6507,plain,
% 1.84/2.08 (~b(s(s(s(z))), s(z))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[4506, 6506, 6378, 6121, 6423, 6420])).
% 1.84/2.08 tff(6508,plain,
% 1.84/2.08 (r(s(s(s(z))), s(z))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[1081, 6507])).
% 1.84/2.08 tff(6509,plain,
% 1.84/2.08 ($false),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[1349, 37, 6418, 6506, 6508])).
% 1.84/2.08 tff(6510,plain,((~(s(s(s(s(z)))) = elem!1)) | r(z, elem!1) | r(s(s(s(s(z)))), elem!1) | b(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.84/2.08 tff(6511,plain,
% 1.84/2.08 (~(s(s(s(s(z)))) = elem!1)),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[6510, 1, 12, 13])).
% 1.84/2.08 tff(6512,plain,
% 1.84/2.08 (b(s(s(s(s(z)))), elem!1)),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[283, 6511, 12])).
% 1.84/2.08 tff(6513,plain,
% 1.84/2.08 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 1.84/2.08 inference(monotonicity,[status(thm)],[1020])).
% 1.84/2.08 tff(6514,plain,
% 1.84/2.08 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.84/2.08 inference(symmetry,[status(thm)],[6513])).
% 1.84/2.08 tff(6515,plain,
% 1.84/2.08 (b(s(s(elem!1)), elem!1)),
% 1.84/2.08 inference(modus_ponens,[status(thm)],[287, 6514])).
% 1.84/2.08 tff(6516,plain,
% 1.84/2.08 ($false),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[1, 6515])).
% 1.84/2.08 tff(6517,plain,((~(s(s(elem!1)) = s(s(s(s(z)))))) | b(s(s(elem!1)), elem!1) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.08 tff(6518,plain,
% 1.84/2.08 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[6517, 1, 6512])).
% 1.84/2.08 tff(6519,plain,
% 1.84/2.08 (~(s(s(z)) = elem!1)),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[1013, 6518])).
% 1.84/2.08 tff(6520,plain,
% 1.84/2.08 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[6517, 1, 2561])).
% 1.84/2.08 tff(6521,plain,
% 1.84/2.08 (~(s(s(z)) = elem!1)),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[1013, 6520])).
% 1.84/2.08 tff(6522,plain,
% 1.84/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(z, elem!1)) | (~b(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(X1, 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(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)))),
% 1.84/2.08 inference(rewrite,[status(thm)],[])).
% 1.84/2.08 tff(6523,plain,
% 1.84/2.08 (((~b(s(z), elem!1)) | (~b(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(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)))),
% 1.84/2.08 inference(rewrite,[status(thm)],[])).
% 1.84/2.08 tff(6524,plain,
% 1.84/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z))))),
% 1.84/2.08 inference(monotonicity,[status(thm)],[6523])).
% 1.84/2.08 tff(6525,plain,
% 1.84/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z)))),
% 1.84/2.08 inference(transitivity,[status(thm)],[6524, 6522])).
% 1.84/2.08 tff(6526,plain,
% 1.84/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))),
% 1.84/2.08 inference(quant_inst,[status(thm)],[])).
% 1.84/2.08 tff(6527,plain,
% 1.84/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z))),
% 1.84/2.08 inference(modus_ponens,[status(thm)],[6526, 6525])).
% 1.84/2.08 tff(6528,plain,
% 1.84/2.08 (~b(s(s(s(s(z)))), z)),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[6527, 75, 1518, 107, 1391, 287])).
% 1.84/2.08 tff(6529,plain,
% 1.84/2.08 (~b(s(z), s(s(s(s(z)))))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[5527, 107, 1391, 287])).
% 1.84/2.08 tff(6530,plain,
% 1.84/2.08 (r(s(z), s(s(s(s(z)))))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[489, 6529])).
% 1.84/2.08 tff(6531,plain,
% 1.84/2.08 (~r(s(s(s(s(z)))), z)),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[2586, 3185, 6530])).
% 1.84/2.08 tff(6532,plain,
% 1.84/2.08 ($false),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[1421, 58, 1143, 6531, 6528])).
% 1.84/2.08 tff(6533,plain,((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.08 tff(6534,plain,
% 1.84/2.08 (~b(s(z), elem!1)),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[6533, 2561, 1391, 1518])).
% 1.84/2.08 tff(6535,plain,
% 1.84/2.08 (r(s(z), elem!1)),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[601, 6534, 2478])).
% 1.84/2.08 tff(6536,plain,
% 1.84/2.08 (~r(s(s(z)), elem!1)),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[596, 115, 6535])).
% 1.84/2.08 tff(6537,plain,
% 1.84/2.08 (b(s(s(z)), elem!1)),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[104, 6536, 6521])).
% 1.84/2.08 tff(6538,plain,
% 1.84/2.08 (r(elem!1, s(s(s(s(z)))))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[4820, 6537, 12, 1518, 267])).
% 1.84/2.08 tff(6539,plain,
% 1.84/2.08 (~(z = elem!1)),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[6116, 1391, 12])).
% 1.84/2.08 tff(6540,plain,
% 1.84/2.08 (~(elem!1 = z)),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[304, 6539])).
% 1.84/2.08 tff(6541,plain,
% 1.84/2.08 (((~![X0: $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(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))))),
% 1.84/2.08 inference(rewrite,[status(thm)],[])).
% 1.84/2.08 tff(6542,plain,
% 1.84/2.08 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))))),
% 1.84/2.08 inference(rewrite,[status(thm)],[])).
% 1.84/2.08 tff(6543,plain,
% 1.84/2.08 (((~![X0: $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(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(z))))))),
% 1.84/2.08 inference(monotonicity,[status(thm)],[6542])).
% 1.84/2.08 tff(6544,plain,
% 1.84/2.08 (((~![X0: $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(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))))),
% 1.84/2.09 inference(transitivity,[status(thm)],[6543, 6541])).
% 1.84/2.09 tff(6545,plain,
% 1.84/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))))),
% 1.84/2.09 inference(quant_inst,[status(thm)],[])).
% 1.84/2.09 tff(6546,plain,
% 1.84/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(z))))),
% 1.84/2.09 inference(modus_ponens,[status(thm)],[6545, 6544])).
% 1.84/2.09 tff(6547,plain,
% 1.84/2.09 (~r(elem!1, s(s(z)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[6546, 37, 3195, 467])).
% 1.84/2.09 tff(6548,plain,
% 1.84/2.09 ((elem!1 = s(s(z))) | b(elem!1, s(s(z)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[398, 58, 6547])).
% 1.84/2.09 tff(6549,plain,
% 1.84/2.09 (b(elem!1, s(s(z)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[6548, 1478])).
% 1.84/2.09 tff(6550,plain,
% 1.84/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))),
% 1.84/2.09 inference(rewrite,[status(thm)],[])).
% 1.84/2.09 tff(6551,plain,
% 1.84/2.09 (((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))),
% 1.84/2.09 inference(rewrite,[status(thm)],[])).
% 1.84/2.09 tff(6552,plain,
% 1.84/2.09 (((~![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(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1))))),
% 1.84/2.09 inference(monotonicity,[status(thm)],[6551])).
% 1.84/2.09 tff(6553,plain,
% 1.84/2.09 (((~![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(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))),
% 1.84/2.09 inference(transitivity,[status(thm)],[6552, 6550])).
% 1.84/2.09 tff(6554,plain,
% 1.84/2.09 ((~![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(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))),
% 1.84/2.09 inference(quant_inst,[status(thm)],[])).
% 1.84/2.09 tff(6555,plain,
% 1.84/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1))),
% 1.84/2.09 inference(modus_ponens,[status(thm)],[6554, 6553])).
% 1.84/2.09 tff(6556,plain,
% 1.84/2.09 (~r(s(s(z)), elem!1)),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[6555, 37, 3195, 467])).
% 1.84/2.09 tff(6557,plain,
% 1.84/2.09 (b(s(s(z)), elem!1)),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[104, 6556, 15])).
% 1.84/2.09 tff(6558,plain,
% 1.84/2.09 (~b(s(s(z)), z)),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[4346, 75, 1518, 6557, 6549])).
% 1.84/2.09 tff(6559,plain,
% 1.84/2.09 (r(s(s(z)), z)),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[202, 6558])).
% 1.84/2.09 tff(6560,plain,
% 1.84/2.09 (~r(s(z), s(s(z)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[2015, 6559, 1561])).
% 1.84/2.09 tff(6561,plain,
% 1.84/2.09 (b(s(z), s(s(z)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[416, 6560])).
% 1.84/2.09 tff(6562,plain,
% 1.84/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~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(X1, 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(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))),
% 1.84/2.09 inference(rewrite,[status(thm)],[])).
% 1.84/2.09 tff(6563,plain,
% 1.84/2.09 (((~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(z)))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))),
% 1.84/2.09 inference(rewrite,[status(thm)],[])).
% 1.84/2.09 tff(6564,plain,
% 1.84/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z))))))),
% 1.84/2.09 inference(monotonicity,[status(thm)],[6563])).
% 1.84/2.09 tff(6565,plain,
% 1.84/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))),
% 1.84/2.09 inference(transitivity,[status(thm)],[6564, 6562])).
% 1.84/2.09 tff(6566,plain,
% 1.84/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(z))))),
% 1.84/2.09 inference(quant_inst,[status(thm)],[])).
% 1.84/2.09 tff(6567,plain,
% 1.84/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z))))),
% 1.84/2.09 inference(modus_ponens,[status(thm)],[6566, 6565])).
% 1.84/2.09 tff(6568,plain,
% 1.84/2.09 ($false),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[6567, 75, 1391, 6557, 6561, 6549])).
% 1.84/2.09 tff(6569,plain,((~r(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~r(s(z), z)) | (~b(z, elem!1)) | (s(s(z)) = elem!1) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.09 tff(6570,plain,
% 1.84/2.09 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[6569, 1561, 1391, 1518, 15, 3195])).
% 1.84/2.09 tff(6571,plain,
% 1.84/2.09 (b(s(s(z)), s(s(s(s(z)))))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[465, 6570])).
% 1.84/2.09 tff(6572,plain,
% 1.84/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), 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)))),
% 1.84/2.09 inference(rewrite,[status(thm)],[])).
% 1.84/2.09 tff(6573,plain,
% 1.84/2.09 (((~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)))),
% 1.84/2.09 inference(rewrite,[status(thm)],[])).
% 1.84/2.09 tff(6574,plain,
% 1.84/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, 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))))),
% 1.84/2.09 inference(monotonicity,[status(thm)],[6573])).
% 1.84/2.09 tff(6575,plain,
% 1.84/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, 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)))),
% 1.84/2.09 inference(transitivity,[status(thm)],[6574, 6572])).
% 1.84/2.09 tff(6576,plain,
% 1.84/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), elem!1)))),
% 1.84/2.09 inference(quant_inst,[status(thm)],[])).
% 1.84/2.09 tff(6577,plain,
% 1.84/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(elem!1, z))),
% 1.84/2.09 inference(modus_ponens,[status(thm)],[6576, 6575])).
% 1.84/2.09 tff(6578,plain,
% 1.84/2.09 (~r(s(z), elem!1)),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[6577, 37, 155, 1561])).
% 1.84/2.09 tff(6579,plain,
% 1.84/2.09 (b(s(z), elem!1)),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[601, 6578, 2478])).
% 1.84/2.09 tff(6580,plain,
% 1.84/2.09 (~b(s(s(s(s(z)))), z)),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[6527, 75, 1518, 6579, 1391, 287])).
% 1.84/2.09 tff(6581,plain,
% 1.84/2.09 (~b(s(z), s(s(s(s(z)))))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[5527, 6579, 1391, 287])).
% 1.84/2.09 tff(6582,plain,
% 1.84/2.09 (r(s(z), s(s(s(s(z)))))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[489, 6581])).
% 1.84/2.09 tff(6583,plain,
% 1.84/2.09 (~r(s(s(s(s(z)))), z)),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[2586, 6582, 1561])).
% 1.84/2.09 tff(6584,plain,
% 1.84/2.09 ($false),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[1421, 58, 1143, 6583, 6580])).
% 1.84/2.09 tff(6585,plain,((~r(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.09 tff(6586,plain,
% 1.84/2.09 (~r(elem!1, z)),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[6585, 1561, 1391, 287, 1518])).
% 1.84/2.09 tff(6587,plain,
% 1.84/2.09 (b(elem!1, z)),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[387, 6586, 353])).
% 1.84/2.09 tff(6588,plain,
% 1.84/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)))),
% 1.84/2.09 inference(rewrite,[status(thm)],[])).
% 1.84/2.09 tff(6589,plain,
% 1.84/2.09 (((~b(z, elem!1)) | (~b(s(s(s(s(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(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)))),
% 1.84/2.09 inference(rewrite,[status(thm)],[])).
% 1.84/2.09 tff(6590,plain,
% 1.84/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z))))),
% 1.84/2.09 inference(monotonicity,[status(thm)],[6589])).
% 1.84/2.09 tff(6591,plain,
% 1.84/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)))),
% 1.84/2.09 inference(transitivity,[status(thm)],[6590, 6588])).
% 1.84/2.09 tff(6592,plain,
% 1.84/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))))))),
% 1.84/2.09 inference(quant_inst,[status(thm)],[])).
% 1.84/2.09 tff(6593,plain,
% 1.84/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z))),
% 1.84/2.09 inference(modus_ponens,[status(thm)],[6592, 6591])).
% 1.84/2.09 tff(6594,plain,
% 1.84/2.09 ($false),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[6593, 75, 1518, 6587, 964, 287, 6571])).
% 1.84/2.09 tff(6595,plain,((~r(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (elem!1 = z) | (~b(elem!1, s(z))) | (s(s(z)) = elem!1) | (~r(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.09 tff(6596,plain,
% 1.84/2.09 (~r(s(z), z)),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[6595, 6537, 1518, 2561, 6540, 1391, 6521, 6538])).
% 1.84/2.09 tff(6597,plain,
% 1.84/2.09 (b(s(z), z)),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[169, 6596])).
% 1.84/2.09 tff(6598,plain,
% 1.84/2.09 (~b(z, s(z))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[2596, 6597, 1391, 1518])).
% 1.84/2.09 tff(6599,plain,
% 1.84/2.09 (r(z, s(z))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[187, 6598])).
% 1.84/2.09 tff(6600,plain,
% 1.84/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), 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(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.84/2.09 inference(rewrite,[status(thm)],[])).
% 1.84/2.09 tff(6601,plain,
% 1.84/2.09 (((~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(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.84/2.09 inference(rewrite,[status(thm)],[])).
% 1.84/2.09 tff(6602,plain,
% 1.84/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(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(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z)))))),
% 1.84/2.09 inference(monotonicity,[status(thm)],[6601])).
% 1.84/2.09 tff(6603,plain,
% 1.84/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(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(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.84/2.09 inference(transitivity,[status(thm)],[6602, 6600])).
% 1.84/2.09 tff(6604,plain,
% 1.84/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.84/2.09 inference(quant_inst,[status(thm)],[])).
% 1.84/2.09 tff(6605,plain,
% 1.84/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z)))),
% 1.84/2.09 inference(modus_ponens,[status(thm)],[6604, 6603])).
% 1.84/2.09 tff(6606,plain,
% 1.84/2.09 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[6605, 37, 115, 1409])).
% 1.84/2.09 tff(6607,plain,
% 1.84/2.09 (b(s(s(z)), s(s(s(s(z)))))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[465, 6606])).
% 1.84/2.09 tff(6608,plain,
% 1.84/2.09 (~r(s(s(z)), z)),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[6161, 37, 506, 115])).
% 1.84/2.09 tff(6609,plain,
% 1.84/2.09 (b(s(s(z)), z)),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[202, 6608])).
% 1.84/2.09 tff(6610,plain,
% 1.84/2.09 (~r(z, s(s(z)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[6456, 506, 115])).
% 1.84/2.09 tff(6611,plain,
% 1.84/2.09 (b(z, s(s(z)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[351, 6610])).
% 1.84/2.09 tff(6612,plain,
% 1.84/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))),
% 1.84/2.09 inference(rewrite,[status(thm)],[])).
% 1.84/2.09 tff(6613,plain,
% 1.84/2.09 (((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~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(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))),
% 1.84/2.09 inference(rewrite,[status(thm)],[])).
% 1.84/2.09 tff(6614,plain,
% 1.84/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z))))),
% 1.84/2.09 inference(monotonicity,[status(thm)],[6613])).
% 1.84/2.09 tff(6615,plain,
% 1.84/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))),
% 1.84/2.09 inference(transitivity,[status(thm)],[6614, 6612])).
% 1.84/2.09 tff(6616,plain,
% 1.84/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~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)))))))),
% 1.84/2.09 inference(quant_inst,[status(thm)],[])).
% 1.84/2.09 tff(6617,plain,
% 1.84/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z))),
% 1.84/2.09 inference(modus_ponens,[status(thm)],[6616, 6615])).
% 1.84/2.10 tff(6618,plain,
% 1.84/2.10 ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[6617, 75, 964, 6611, 6609, 287])).
% 1.84/2.10 tff(6619,plain,
% 1.84/2.10 (~b(s(s(s(s(z)))), z)),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[6618, 6607])).
% 1.84/2.10 tff(6620,plain,
% 1.84/2.10 (~r(s(s(s(s(z)))), z)),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[1417, 1409, 506])).
% 1.84/2.10 tff(6621,plain,
% 1.84/2.10 ($false),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[1421, 58, 1143, 6620, 6619])).
% 1.84/2.10 tff(6622,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.10 tff(6623,plain,
% 1.84/2.10 (~r(s(s(s(s(z)))), s(z))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[6622, 6537, 2561, 115, 6599])).
% 1.84/2.10 tff(6624,plain,
% 1.84/2.10 (b(s(s(s(s(z)))), s(z))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[1406, 58, 483, 6623])).
% 1.84/2.10 tff(6625,plain,
% 1.84/2.10 (~r(z, s(s(z)))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[6456, 6599, 115])).
% 1.84/2.10 tff(6626,plain,
% 1.84/2.10 (b(z, s(s(z)))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[351, 6625])).
% 1.84/2.10 tff(6627,plain,
% 1.84/2.10 (~r(s(s(z)), z)),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[6161, 37, 6599, 115])).
% 1.84/2.10 tff(6628,plain,
% 1.84/2.10 (b(s(s(z)), z)),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[202, 6627])).
% 1.84/2.10 tff(6629,plain,
% 1.84/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(elem!1, z)))),
% 1.84/2.10 inference(rewrite,[status(thm)],[])).
% 1.84/2.10 tff(6630,plain,
% 1.84/2.10 (((~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z)))) <=> ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(elem!1, z)))),
% 1.84/2.10 inference(rewrite,[status(thm)],[])).
% 1.84/2.10 tff(6631,plain,
% 1.84/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, 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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(elem!1, z))))),
% 1.84/2.10 inference(monotonicity,[status(thm)],[6630])).
% 1.84/2.10 tff(6632,plain,
% 1.84/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, 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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(elem!1, z)))),
% 1.84/2.10 inference(transitivity,[status(thm)],[6631, 6629])).
% 1.84/2.10 tff(6633,plain,
% 1.84/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))),
% 1.84/2.10 inference(quant_inst,[status(thm)],[])).
% 1.84/2.10 tff(6634,plain,
% 1.84/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(elem!1, z))),
% 1.84/2.10 inference(modus_ponens,[status(thm)],[6633, 6632])).
% 1.84/2.10 tff(6635,plain,
% 1.84/2.10 ($false),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[6634, 75, 1518, 1958, 371, 1391])).
% 1.84/2.10 tff(6636,plain,((~b(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.10 tff(6637,plain,
% 1.84/2.10 (~b(elem!1, z)),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[6636, 6597, 1518, 1391])).
% 1.84/2.10 tff(6638,plain,
% 1.84/2.10 (r(elem!1, z)),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[387, 6637, 6540])).
% 1.84/2.10 tff(6639,plain,
% 1.84/2.10 (r(s(s(elem!1)), elem!1)),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[2673, 2556, 1])).
% 1.84/2.10 tff(6640,plain,
% 1.84/2.10 (~r(s(s(elem!1)), z)),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[4774, 6639, 155])).
% 1.84/2.10 tff(6641,plain,
% 1.84/2.10 (b(s(s(elem!1)), z)),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[2696, 6640])).
% 1.84/2.10 tff(6642,plain,
% 1.84/2.10 (~b(elem!1, s(s(elem!1)))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[5690, 6639, 1391, 588])).
% 1.84/2.10 tff(6643,plain,
% 1.84/2.10 (r(elem!1, s(s(elem!1)))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[1617, 6642, 1908])).
% 1.84/2.10 tff(6644,plain,
% 1.84/2.10 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[3811, 6643, 3195])).
% 1.84/2.10 tff(6645,plain,
% 1.84/2.10 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[1660, 6644, 1011])).
% 1.84/2.10 tff(6646,plain,
% 1.84/2.10 (b(s(s(elem!1)), s(elem!1))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[1865, 6645, 213])).
% 1.84/2.10 tff(6647,plain,
% 1.84/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(s(z)), z)) | (~b(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(X1, 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(z)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)))),
% 1.84/2.10 inference(rewrite,[status(thm)],[])).
% 1.84/2.10 tff(6648,plain,
% 1.84/2.10 (((~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~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(z)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)))),
% 1.84/2.10 inference(rewrite,[status(thm)],[])).
% 1.84/2.10 tff(6649,plain,
% 1.84/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~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(X1, 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(z)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z))))),
% 1.84/2.10 inference(monotonicity,[status(thm)],[6648])).
% 1.84/2.10 tff(6650,plain,
% 1.84/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~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(X1, 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(z)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)))),
% 1.84/2.10 inference(transitivity,[status(thm)],[6649, 6647])).
% 1.84/2.10 tff(6651,plain,
% 1.84/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.84/2.10 inference(quant_inst,[status(thm)],[])).
% 1.84/2.10 tff(6652,plain,
% 1.84/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z))),
% 1.84/2.10 inference(modus_ponens,[status(thm)],[6651, 6650])).
% 1.84/2.10 tff(6653,plain,
% 1.84/2.10 ($false),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[6652, 75, 370, 401, 3069, 798, 1892])).
% 1.84/2.10 tff(6654,plain,((~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.10 tff(6655,plain,
% 1.84/2.10 (~b(s(elem!1), z)),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[6654, 6646, 401, 370, 6641])).
% 1.84/2.10 tff(6656,plain,
% 1.84/2.10 (r(s(elem!1), z)),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[766, 6655])).
% 1.84/2.10 tff(6657,plain,
% 1.84/2.10 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(s(z)))))),
% 1.84/2.10 inference(monotonicity,[status(thm)],[1019])).
% 1.84/2.10 tff(6658,plain,
% 1.84/2.10 (r(elem!1, s(s(s(s(z))))) <=> r(elem!1, s(elem!1))),
% 1.84/2.10 inference(symmetry,[status(thm)],[6657])).
% 1.84/2.10 tff(6659,plain,
% 1.84/2.10 (r(elem!1, s(elem!1))),
% 1.84/2.10 inference(modus_ponens,[status(thm)],[3195, 6658])).
% 1.84/2.10 tff(6660,assumption,(~r(elem!1, s(elem!1))), introduced(assumption)).
% 1.84/2.10 tff(6661,plain,
% 1.84/2.10 ($false),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[6660, 6659])).
% 1.84/2.10 tff(6662,plain,(r(elem!1, s(elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~(s(s(s(z))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.10 tff(6663,plain,
% 1.84/2.10 (r(elem!1, s(elem!1))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[6662, 213, 3195])).
% 1.84/2.10 tff(6664,plain,
% 1.84/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))))),
% 1.84/2.10 inference(rewrite,[status(thm)],[])).
% 1.84/2.10 tff(6665,plain,
% 1.84/2.10 (((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))))),
% 1.84/2.10 inference(rewrite,[status(thm)],[])).
% 1.84/2.10 tff(6666,plain,
% 1.84/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1)))))),
% 1.84/2.10 inference(monotonicity,[status(thm)],[6665])).
% 1.84/2.10 tff(6667,plain,
% 1.84/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))))),
% 1.84/2.10 inference(transitivity,[status(thm)],[6666, 6664])).
% 1.84/2.10 tff(6668,plain,
% 1.84/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))))),
% 1.84/2.10 inference(quant_inst,[status(thm)],[])).
% 1.84/2.10 tff(6669,plain,
% 1.84/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1)))),
% 1.84/2.10 inference(modus_ponens,[status(thm)],[6668, 6667])).
% 1.84/2.10 tff(6670,plain,
% 1.84/2.10 ($false),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[6669, 37, 155, 6663, 6656])).
% 1.84/2.10 tff(6671,plain,((~(s(s(s(z))) = elem!1)) | (~r(elem!1, z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (s(s(elem!1)) = s(s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~r(s(z), elem!1)) | b(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.84/2.10 tff(6672,plain,
% 1.84/2.10 (~(s(s(s(z))) = elem!1)),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[6671, 6638, 6628, 6626, 6520, 6538, 1391, 6535, 1])).
% 1.84/2.10 tff(6673,plain,
% 1.84/2.10 (~(elem!1 = s(s(s(z))))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[1033, 6672])).
% 1.84/2.10 tff(6674,plain,
% 1.84/2.10 (~b(s(s(s(z))), elem!1)),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[6504, 6673, 115, 6597, 6626, 6537, 6638, 6628, 1518])).
% 1.84/2.10 tff(6675,plain,
% 1.84/2.10 (r(s(s(s(z))), elem!1)),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[1115, 6674, 6672])).
% 1.84/2.10 tff(6676,plain,
% 1.84/2.10 (~r(s(z), s(s(s(z))))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[1341, 37, 6535, 6675])).
% 1.84/2.10 tff(6677,plain,
% 1.84/2.10 (b(s(z), s(s(s(z))))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[1263, 6676])).
% 1.84/2.10 tff(6678,plain,
% 1.84/2.10 (~r(s(s(s(z))), s(z))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[1349, 37, 6535, 6675])).
% 1.84/2.10 tff(6679,plain,
% 1.84/2.10 (b(s(s(s(z))), s(z))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[1081, 6678])).
% 1.84/2.10 tff(6680,plain,
% 1.84/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))))),
% 1.84/2.10 inference(rewrite,[status(thm)],[])).
% 1.84/2.10 tff(6681,plain,
% 1.84/2.10 (((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), 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(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))))),
% 1.84/2.10 inference(rewrite,[status(thm)],[])).
% 1.84/2.10 tff(6682,plain,
% 1.84/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), 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(X1, 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(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z)))))),
% 1.84/2.10 inference(monotonicity,[status(thm)],[6681])).
% 1.84/2.10 tff(6683,plain,
% 1.84/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), 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(X1, 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(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))))),
% 1.84/2.10 inference(transitivity,[status(thm)],[6682, 6680])).
% 1.84/2.10 tff(6684,plain,
% 1.84/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), 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)))),
% 1.84/2.10 inference(quant_inst,[status(thm)],[])).
% 1.84/2.10 tff(6685,plain,
% 1.84/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z)))),
% 1.84/2.10 inference(modus_ponens,[status(thm)],[6684, 6683])).
% 1.84/2.10 tff(6686,plain,
% 1.84/2.10 ($false),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[6685, 75, 1391, 6679, 6677, 2561, 6624])).
% 1.84/2.10 tff(6687,plain,((~r(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | b(s(s(elem!1)), elem!1) | r(s(s(s(s(z)))), elem!1) | (s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.84/2.10 tff(6688,plain,
% 1.84/2.10 (~r(s(s(z)), s(z))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[6687, 1, 6125, 5472, 12, 6511])).
% 1.84/2.10 tff(6689,plain,
% 1.84/2.10 (b(s(s(z)), s(z))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[153, 6688])).
% 1.84/2.10 tff(6690,plain,
% 1.84/2.10 (~(elem!1 = s(s(s(s(z)))))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[273, 6511])).
% 1.84/2.10 tff(6691,plain,
% 1.84/2.10 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[6517, 1, 287])).
% 1.84/2.10 tff(6692,plain,
% 1.84/2.10 (~(s(s(z)) = elem!1)),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[1013, 6691])).
% 1.84/2.10 tff(6693,plain,
% 1.84/2.10 (~b(s(z), z)),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[6636, 1958, 1518, 1391])).
% 1.84/2.10 tff(6694,plain,
% 1.84/2.10 (r(s(z), z)),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[169, 6693])).
% 1.84/2.10 tff(6695,plain,
% 1.84/2.10 (~r(s(z), s(s(s(s(z)))))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[2586, 2870, 6694])).
% 1.84/2.10 tff(6696,plain,
% 1.84/2.10 (b(s(z), s(s(s(s(z)))))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[489, 6695])).
% 1.84/2.10 tff(6697,plain,
% 1.84/2.10 (~b(elem!1, s(s(s(s(z)))))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[1438, 6696, 1391, 287])).
% 1.84/2.10 tff(6698,plain,
% 1.84/2.10 (r(elem!1, s(s(s(s(z)))))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[278, 6697, 860])).
% 1.84/2.10 tff(6699,plain,
% 1.84/2.10 (~(s(s(elem!1)) = s(s(z)))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[237, 235])).
% 1.84/2.10 tff(6700,plain,
% 1.84/2.10 (~b(s(s(s(z))), elem!1)),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[4040, 1958, 1518, 287])).
% 1.84/2.10 tff(6701,plain,
% 1.84/2.10 (~b(s(z), elem!1)),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[1792, 372, 1391, 235, 106, 309])).
% 1.84/2.10 tff(6702,plain,
% 1.84/2.10 (r(s(z), elem!1)),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[601, 6701, 2478])).
% 1.84/2.10 tff(6703,plain,
% 1.84/2.10 (~r(s(s(elem!1)), elem!1)),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[2665, 6702, 6699, 106])).
% 1.84/2.10 tff(6704,plain,
% 1.84/2.10 (s(s(elem!1)) = elem!1),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[2673, 6703, 1])).
% 1.84/2.10 tff(6705,plain,
% 1.84/2.10 (elem!1 = s(s(elem!1))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[2555, 6704])).
% 1.84/2.10 tff(6706,plain,
% 1.84/2.10 (~(s(s(s(z))) = elem!1)),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[1612, 6705])).
% 1.84/2.10 tff(6707,plain,
% 1.84/2.10 (r(s(s(s(z))), elem!1)),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[1115, 6706, 100])).
% 1.84/2.10 tff(6708,plain,
% 1.84/2.10 (~r(s(z), s(s(s(z))))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[1341, 37, 6702, 6707])).
% 1.84/2.10 tff(6709,plain,
% 1.84/2.10 (b(s(z), s(s(s(z))))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[1263, 6708])).
% 1.84/2.10 tff(6710,plain,
% 1.84/2.10 (~b(s(z), z)),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[2596, 372, 1391, 1518])).
% 1.84/2.10 tff(6711,plain,
% 1.84/2.10 (r(s(z), z)),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[169, 6710])).
% 1.84/2.10 tff(6712,plain,
% 1.84/2.10 (((~![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(z), 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(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))),
% 1.84/2.10 inference(rewrite,[status(thm)],[])).
% 1.84/2.10 tff(6713,plain,
% 1.84/2.10 (((~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))),
% 1.84/2.10 inference(rewrite,[status(thm)],[])).
% 1.84/2.10 tff(6714,plain,
% 1.84/2.10 (((~![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(z))), elem!1)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1))))),
% 1.84/2.10 inference(monotonicity,[status(thm)],[6713])).
% 1.84/2.10 tff(6715,plain,
% 1.84/2.10 (((~![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(z))), elem!1)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))),
% 1.84/2.11 inference(transitivity,[status(thm)],[6714, 6712])).
% 1.84/2.11 tff(6716,plain,
% 1.84/2.11 ((~![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(s(z))), elem!1)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))),
% 1.84/2.11 inference(quant_inst,[status(thm)],[])).
% 1.84/2.11 tff(6717,plain,
% 1.84/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1))),
% 1.84/2.11 inference(modus_ponens,[status(thm)],[6716, 6715])).
% 1.84/2.11 tff(6718,plain,
% 1.84/2.11 (~r(s(s(s(z))), s(z))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[6717, 37, 6702, 6711, 6707])).
% 1.84/2.11 tff(6719,plain,
% 1.84/2.11 (b(s(s(s(z))), s(z))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[1081, 6718])).
% 1.84/2.11 tff(6720,plain,
% 1.84/2.11 ($false),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[2459, 75, 1958, 372, 1391, 6719, 6709])).
% 1.84/2.11 tff(6721,plain,((~b(z, s(z))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | b(s(s(s(z))), elem!1) | b(s(s(elem!1)), elem!1) | (~r(s(s(z)), elem!1)) | (z = elem!1) | (~b(s(s(z)), s(z))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.11 tff(6722,plain,
% 1.84/2.11 (~b(z, s(z))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[6721, 1958, 1391, 6700, 1, 106, 235, 309, 1518])).
% 1.84/2.11 tff(6723,plain,
% 1.84/2.11 (r(z, s(z))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[187, 6722])).
% 1.84/2.11 tff(6724,plain,
% 1.84/2.11 (~r(s(s(s(s(z)))), s(z))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[1417, 6723, 2870])).
% 1.84/2.11 tff(6725,plain,
% 1.84/2.11 (~r(s(z), s(s(s(s(z)))))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[2586, 6694, 2870])).
% 1.84/2.11 tff(6726,plain,
% 1.84/2.11 (b(s(z), s(s(s(s(z)))))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[489, 6725])).
% 1.84/2.11 tff(6727,plain,
% 1.84/2.11 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[6569, 6694, 1391, 1518, 6692, 3195])).
% 1.84/2.11 tff(6728,plain,
% 1.84/2.11 (b(s(s(z)), s(s(s(s(z)))))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[465, 6727])).
% 1.84/2.11 tff(6729,plain,
% 1.84/2.11 (~b(s(s(s(s(z)))), s(z))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[3906, 6728, 309, 6726])).
% 1.84/2.11 tff(6730,plain,
% 1.84/2.11 ($false),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[1406, 58, 6729, 483, 6724])).
% 1.84/2.11 tff(6731,plain,((~b(elem!1, z)) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | b(s(s(elem!1)), elem!1) | (~r(s(s(z)), elem!1)) | (z = elem!1) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.11 tff(6732,plain,
% 1.84/2.11 (~b(elem!1, z)),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[6731, 309, 1391, 1518, 3195, 1, 106, 235, 287])).
% 1.84/2.11 tff(6733,plain,
% 1.84/2.11 (r(elem!1, z)),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[387, 6732, 2615])).
% 1.84/2.11 tff(6734,plain,
% 1.84/2.11 (~r(s(z), z)),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[6585, 6733, 1391, 287, 1518])).
% 1.84/2.11 tff(6735,plain,
% 1.84/2.11 (b(s(z), z)),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[169, 6734])).
% 1.84/2.11 tff(6736,plain,
% 1.84/2.11 (~b(s(z), elem!1)),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[1526, 6735, 1391, 1518])).
% 1.84/2.11 tff(6737,plain,
% 1.84/2.11 (r(s(z), elem!1)),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[601, 6736, 2478])).
% 1.84/2.11 tff(6738,plain,
% 1.84/2.11 (~r(s(s(elem!1)), elem!1)),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[2665, 6737, 6699, 106])).
% 1.84/2.11 tff(6739,plain,
% 1.84/2.11 (s(s(elem!1)) = elem!1),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[2673, 6738, 1])).
% 1.84/2.11 tff(6740,plain,
% 1.84/2.11 (elem!1 = s(s(elem!1))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[2555, 6739])).
% 1.84/2.11 tff(6741,plain,
% 1.84/2.11 (~(s(s(s(z))) = elem!1)),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[1612, 6740])).
% 1.84/2.11 tff(6742,plain,
% 1.84/2.11 (~(elem!1 = s(s(s(z))))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[1033, 6741])).
% 1.84/2.11 tff(6743,plain,
% 1.84/2.11 ($false),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[1745, 75, 309, 1351, 1343, 2972])).
% 1.84/2.11 tff(6744,plain,((~r(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.11 tff(6745,plain,
% 1.84/2.11 (~r(s(s(s(z))), elem!1)),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[6744, 309, 6737, 106])).
% 1.84/2.11 tff(6746,plain,
% 1.84/2.11 (b(s(s(s(z))), elem!1)),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[1115, 6745, 6741])).
% 1.84/2.11 tff(6747,plain,
% 1.84/2.11 (~(elem!1 = s(s(z)))),
% 1.84/2.11 inference(modus_ponens,[status(thm)],[6692, 308])).
% 1.84/2.11 tff(6748,plain,
% 1.84/2.11 (~r(s(z), s(s(z)))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[2081, 37, 6737, 106])).
% 1.84/2.11 tff(6749,plain,
% 1.84/2.11 (b(s(z), s(s(z)))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[416, 6748])).
% 1.84/2.11 tff(6750,plain,
% 1.84/2.11 (~b(elem!1, s(s(z)))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[1484, 75, 1391, 309, 6749])).
% 1.84/2.11 tff(6751,plain,
% 1.84/2.11 ((elem!1 = s(s(z))) | r(elem!1, s(s(z)))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[398, 58, 6750])).
% 1.84/2.11 tff(6752,plain,
% 1.84/2.11 (r(elem!1, s(s(z)))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[6751, 6747])).
% 1.84/2.11 tff(6753,plain,
% 1.84/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.84/2.11 inference(rewrite,[status(thm)],[])).
% 1.84/2.11 tff(6754,plain,
% 1.84/2.11 (((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.84/2.11 inference(rewrite,[status(thm)],[])).
% 1.84/2.11 tff(6755,plain,
% 1.84/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 1.84/2.11 inference(monotonicity,[status(thm)],[6754])).
% 1.84/2.11 tff(6756,plain,
% 1.84/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.84/2.11 inference(transitivity,[status(thm)],[6755, 6753])).
% 1.84/2.11 tff(6757,plain,
% 1.84/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))),
% 1.84/2.11 inference(quant_inst,[status(thm)],[])).
% 1.84/2.11 tff(6758,plain,
% 1.84/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 1.84/2.11 inference(modus_ponens,[status(thm)],[6757, 6756])).
% 1.84/2.11 tff(6759,plain,
% 1.84/2.11 ($false),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[6758, 75, 1518, 1119, 1287, 1083])).
% 1.84/2.11 tff(6760,plain,((~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.11 tff(6761,plain,
% 1.84/2.11 (~b(elem!1, s(s(s(z))))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[6760, 1083, 1119, 1518])).
% 1.84/2.11 tff(6762,plain,
% 1.84/2.11 (r(elem!1, s(s(s(z))))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[1279, 6761, 1305])).
% 1.84/2.11 tff(6763,assumption,(r(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 1.84/2.11 tff(6764,plain,
% 1.84/2.11 ($false),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[2181, 37, 1266, 1489, 6763])).
% 1.84/2.11 tff(6765,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.11 tff(6766,plain,
% 1.84/2.11 (~r(s(s(s(z))), s(s(z)))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[6765, 6762, 1489])).
% 1.84/2.11 tff(6767,plain,
% 1.84/2.11 ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z)))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[2173, 58, 6766])).
% 1.84/2.11 tff(6768,plain,
% 1.84/2.11 (b(s(s(s(z))), s(s(z)))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[6767, 2150])).
% 1.84/2.11 tff(6769,plain,
% 1.84/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 1.84/2.11 inference(rewrite,[status(thm)],[])).
% 1.84/2.11 tff(6770,plain,
% 1.84/2.11 (((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 1.84/2.11 inference(rewrite,[status(thm)],[])).
% 1.84/2.11 tff(6771,plain,
% 1.84/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z))))))),
% 1.84/2.11 inference(monotonicity,[status(thm)],[6770])).
% 1.84/2.11 tff(6772,plain,
% 1.84/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 1.84/2.11 inference(transitivity,[status(thm)],[6771, 6769])).
% 1.84/2.11 tff(6773,plain,
% 1.84/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))),
% 1.84/2.11 inference(quant_inst,[status(thm)],[])).
% 1.84/2.11 tff(6774,plain,
% 1.84/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z))))),
% 1.84/2.11 inference(modus_ponens,[status(thm)],[6773, 6772])).
% 1.84/2.11 tff(6775,plain,
% 1.84/2.11 ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[6774, 75, 371, 309, 402, 1083])).
% 1.84/2.11 tff(6776,plain,
% 1.84/2.11 (~b(s(z), s(s(s(z))))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[6775, 6768])).
% 1.84/2.11 tff(6777,plain,
% 1.84/2.11 (r(s(z), s(s(s(z))))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[1263, 6776])).
% 1.84/2.11 tff(6778,plain,
% 1.84/2.11 (((~![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(elem!1, z)) | (~r(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(z), elem!1)) | (~r(elem!1, z)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.84/2.11 inference(rewrite,[status(thm)],[])).
% 1.84/2.11 tff(6779,plain,
% 1.84/2.11 (((~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(z), elem!1))) <=> ((~r(s(z), elem!1)) | (~r(elem!1, z)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.84/2.11 inference(rewrite,[status(thm)],[])).
% 1.84/2.11 tff(6780,plain,
% 1.84/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, z)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))))),
% 1.84/2.11 inference(monotonicity,[status(thm)],[6779])).
% 1.84/2.11 tff(6781,plain,
% 1.84/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, z)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.84/2.11 inference(transitivity,[status(thm)],[6780, 6778])).
% 1.84/2.11 tff(6782,plain,
% 1.84/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(z), elem!1)))),
% 1.84/2.11 inference(quant_inst,[status(thm)],[])).
% 1.84/2.11 tff(6783,plain,
% 1.84/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, z)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))),
% 1.84/2.11 inference(modus_ponens,[status(thm)],[6782, 6781])).
% 1.84/2.11 tff(6784,plain,
% 1.84/2.11 ($false),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[6783, 37, 155, 588, 6762, 6777])).
% 1.84/2.11 tff(6785,plain,((~b(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))) | (elem!1 = s(s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.11 tff(6786,plain,
% 1.84/2.11 (~b(s(s(s(z))), z)),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[6785, 6733, 6737, 6735, 309, 6749, 6752, 6742, 6746, 1518])).
% 1.84/2.11 tff(6787,plain,
% 1.84/2.11 (r(s(s(s(z))), z)),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[1334, 58, 221, 6786])).
% 1.84/2.11 tff(6788,plain,
% 1.84/2.11 (~r(elem!1, s(s(s(z))))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[6474, 6787, 6733])).
% 1.84/2.11 tff(6789,plain,
% 1.84/2.11 (b(elem!1, s(s(s(z))))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[1279, 6788, 6742])).
% 1.84/2.11 tff(6790,plain,
% 1.84/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 1.84/2.11 inference(rewrite,[status(thm)],[])).
% 1.84/2.11 tff(6791,plain,
% 1.84/2.11 (((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 1.84/2.11 inference(rewrite,[status(thm)],[])).
% 1.84/2.11 tff(6792,plain,
% 1.84/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), z))))),
% 1.84/2.11 inference(monotonicity,[status(thm)],[6791])).
% 1.84/2.11 tff(6793,plain,
% 1.84/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 1.84/2.11 inference(transitivity,[status(thm)],[6792, 6790])).
% 1.84/2.11 tff(6794,plain,
% 1.84/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), z)))),
% 1.84/2.11 inference(quant_inst,[status(thm)],[])).
% 1.84/2.11 tff(6795,plain,
% 1.84/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), z))),
% 1.84/2.11 inference(modus_ponens,[status(thm)],[6794, 6793])).
% 1.84/2.11 tff(6796,plain,
% 1.84/2.11 (~b(s(s(s(s(z)))), z)),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[6795, 75, 1518, 6746, 6789, 287])).
% 1.84/2.11 tff(6797,plain,
% 1.84/2.11 (r(s(s(s(s(z)))), z)),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[1421, 58, 1143, 6796])).
% 1.84/2.11 tff(6798,plain,
% 1.84/2.11 ($false),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[4847, 37, 6733, 3195, 6797])).
% 1.84/2.11 tff(6799,plain,((~b(s(s(z)), s(z))) | (~r(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | b(s(s(elem!1)), elem!1) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.84/2.11 tff(6800,plain,
% 1.84/2.11 (~r(s(s(z)), elem!1)),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[6799, 6698, 1518, 287, 309, 1391, 1, 235])).
% 1.84/2.11 tff(6801,plain,
% 1.84/2.11 (~b(s(s(z)), elem!1)),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[6595, 6698, 1518, 287, 2615, 1391, 6692, 6694])).
% 1.84/2.11 tff(6802,plain,
% 1.84/2.11 ($false),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[104, 6801, 6800, 6692])).
% 1.84/2.11 tff(6803,plain,((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | b(s(s(elem!1)), elem!1) | (z = elem!1) | (elem!1 = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.11 tff(6804,plain,
% 1.84/2.11 (~b(elem!1, z)),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[6803, 6512, 6125, 5472, 6689, 1, 6117, 6690])).
% 1.84/2.11 tff(6805,plain,
% 1.84/2.11 (r(elem!1, z)),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[387, 6804, 6184])).
% 1.84/2.11 tff(6806,plain,
% 1.84/2.11 (~r(s(z), z)),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[6585, 6805, 5472, 6512, 6125])).
% 1.84/2.11 tff(6807,plain,
% 1.84/2.11 (b(s(z), z)),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[169, 6806])).
% 1.84/2.11 tff(6808,plain,
% 1.84/2.11 (~b(z, s(z))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[2596, 6807, 5472, 6125])).
% 1.84/2.11 tff(6809,plain,
% 1.84/2.11 (r(z, s(z))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[187, 6808])).
% 1.84/2.11 tff(6810,plain,
% 1.84/2.11 (~r(elem!1, s(z))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[177, 6809, 6805])).
% 1.84/2.12 tff(6811,plain,
% 1.84/2.12 (r(elem!1, s(s(s(s(z)))))),
% 1.84/2.12 inference(unit_resolution,[status(thm)],[2606, 6810, 6179, 12, 6125, 6511])).
% 1.84/2.12 tff(6812,plain,
% 1.84/2.12 (~r(s(s(z)), elem!1)),
% 1.84/2.12 inference(unit_resolution,[status(thm)],[6799, 6811, 6125, 6512, 6689, 5472, 1, 6117])).
% 1.84/2.12 tff(6813,plain,
% 1.84/2.12 (b(s(s(z)), elem!1)),
% 1.84/2.12 inference(unit_resolution,[status(thm)],[104, 6812, 6519])).
% 1.84/2.12 tff(6814,plain,
% 1.84/2.12 (~b(s(z), elem!1)),
% 1.84/2.12 inference(unit_resolution,[status(thm)],[6533, 6512, 5472, 6125])).
% 1.84/2.12 tff(6815,plain,
% 1.84/2.12 (r(s(z), elem!1)),
% 1.84/2.12 inference(unit_resolution,[status(thm)],[601, 6814, 6179])).
% 1.84/2.12 tff(6816,plain,
% 1.84/2.12 (~b(s(s(elem!1)), s(z))),
% 1.84/2.12 inference(unit_resolution,[status(thm)],[6436, 5674, 1391, 309, 964])).
% 1.84/2.12 tff(6817,plain,
% 1.84/2.12 (r(s(s(elem!1)), s(z))),
% 1.84/2.12 inference(unit_resolution,[status(thm)],[561, 6816])).
% 1.84/2.12 tff(6818,plain,
% 1.84/2.12 ($false),
% 1.84/2.12 inference(unit_resolution,[status(thm)],[5680, 37, 6817, 588, 2647])).
% 1.84/2.12 tff(6819,plain,((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.12 tff(6820,plain,
% 1.84/2.12 (~r(s(s(elem!1)), elem!1)),
% 1.84/2.12 inference(unit_resolution,[status(thm)],[6819, 6815, 5472, 6689, 6813])).
% 1.84/2.12 tff(6821,plain,
% 1.84/2.12 (s(s(elem!1)) = elem!1),
% 1.84/2.12 inference(unit_resolution,[status(thm)],[2673, 6820, 1])).
% 1.84/2.12 tff(6822,plain,
% 1.84/2.12 (elem!1 = s(s(elem!1))),
% 1.84/2.12 inference(unit_resolution,[status(thm)],[2555, 6821])).
% 1.84/2.12 tff(6823,plain,
% 1.84/2.12 (~(s(s(s(z))) = elem!1)),
% 1.84/2.12 inference(unit_resolution,[status(thm)],[1612, 6822])).
% 1.84/2.12 tff(6824,plain,
% 1.84/2.12 (~(elem!1 = s(s(s(z))))),
% 1.84/2.12 inference(unit_resolution,[status(thm)],[1033, 6823])).
% 1.84/2.12 tff(6825,plain,
% 1.84/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))))),
% 1.84/2.12 inference(rewrite,[status(thm)],[])).
% 1.84/2.12 tff(6826,plain,
% 1.84/2.12 (((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))))),
% 1.84/2.12 inference(rewrite,[status(thm)],[])).
% 1.84/2.12 tff(6827,plain,
% 1.84/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z)))))),
% 1.84/2.12 inference(monotonicity,[status(thm)],[6826])).
% 1.84/2.12 tff(6828,plain,
% 1.84/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))))),
% 1.84/2.12 inference(transitivity,[status(thm)],[6827, 6825])).
% 1.84/2.12 tff(6829,plain,
% 1.84/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.84/2.12 inference(quant_inst,[status(thm)],[])).
% 1.84/2.12 tff(6830,plain,
% 1.84/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z)))),
% 1.84/2.12 inference(modus_ponens,[status(thm)],[6829, 6828])).
% 1.84/2.12 tff(6831,plain,
% 1.84/2.12 ($false),
% 1.84/2.12 inference(unit_resolution,[status(thm)],[6830, 75, 1391, 964, 309, 1351, 1343])).
% 1.84/2.12 tff(6832,plain,((~r(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.12 tff(6833,plain,
% 1.84/2.12 (~r(s(s(s(z))), elem!1)),
% 1.84/2.12 inference(unit_resolution,[status(thm)],[6832, 6813, 5472, 6689, 6815])).
% 1.84/2.12 tff(6834,plain,
% 1.84/2.12 (b(s(s(s(z))), elem!1)),
% 1.84/2.12 inference(unit_resolution,[status(thm)],[1115, 6833, 6823])).
% 1.84/2.12 tff(6835,plain,
% 1.84/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), z)))),
% 1.84/2.12 inference(rewrite,[status(thm)],[])).
% 1.84/2.12 tff(6836,plain,
% 1.84/2.12 (((~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), z)))),
% 1.84/2.12 inference(rewrite,[status(thm)],[])).
% 1.84/2.12 tff(6837,plain,
% 1.84/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), z))))),
% 1.84/2.12 inference(monotonicity,[status(thm)],[6836])).
% 1.84/2.12 tff(6838,plain,
% 1.84/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), z)))),
% 1.84/2.12 inference(transitivity,[status(thm)],[6837, 6835])).
% 1.84/2.12 tff(6839,plain,
% 1.84/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))),
% 1.84/2.12 inference(quant_inst,[status(thm)],[])).
% 1.84/2.12 tff(6840,plain,
% 1.84/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), z))),
% 1.84/2.12 inference(modus_ponens,[status(thm)],[6839, 6838])).
% 1.84/2.12 tff(6841,plain,
% 1.84/2.12 ($false),
% 1.84/2.12 inference(unit_resolution,[status(thm)],[6840, 75, 1518, 964, 1119, 2247, 1083])).
% 1.84/2.12 tff(6842,plain,((~b(elem!1, s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.12 tff(6843,plain,
% 1.84/2.12 (~b(elem!1, s(s(z)))),
% 1.84/2.12 inference(unit_resolution,[status(thm)],[6842, 1083, 964, 1119, 1518])).
% 1.84/2.12 tff(6844,plain,
% 1.84/2.12 ((elem!1 = s(s(z))) | r(elem!1, s(s(z)))),
% 1.84/2.12 inference(unit_resolution,[status(thm)],[398, 58, 6843])).
% 1.84/2.12 tff(6845,plain,
% 1.84/2.12 (r(elem!1, s(s(z)))),
% 1.84/2.12 inference(unit_resolution,[status(thm)],[6844, 1478])).
% 1.84/2.12 tff(6846,plain,
% 1.84/2.12 (~b(s(z), s(s(z)))),
% 1.84/2.12 inference(unit_resolution,[status(thm)],[6785, 6845, 588, 309, 155, 371, 1083, 1305, 1119, 1518])).
% 1.84/2.12 tff(6847,plain,
% 1.84/2.12 (r(s(z), s(s(z)))),
% 1.84/2.12 inference(unit_resolution,[status(thm)],[416, 6846])).
% 1.84/2.12 tff(6848,plain,
% 1.84/2.12 (((~![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(z)))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))))),
% 1.84/2.12 inference(rewrite,[status(thm)],[])).
% 1.84/2.12 tff(6849,plain,
% 1.84/2.12 (((~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(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))))),
% 1.84/2.12 inference(rewrite,[status(thm)],[])).
% 1.84/2.12 tff(6850,plain,
% 1.84/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(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(s(z), s(s(z)))) | (~r(elem!1, s(s(z))))))),
% 1.84/2.12 inference(monotonicity,[status(thm)],[6849])).
% 1.84/2.12 tff(6851,plain,
% 1.84/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(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(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))))),
% 1.84/2.12 inference(transitivity,[status(thm)],[6850, 6848])).
% 1.84/2.12 tff(6852,plain,
% 1.84/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(z), elem!1)))),
% 1.84/2.12 inference(quant_inst,[status(thm)],[])).
% 1.84/2.12 tff(6853,plain,
% 1.84/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z))))),
% 1.84/2.12 inference(modus_ponens,[status(thm)],[6852, 6851])).
% 1.84/2.12 tff(6854,plain,
% 1.84/2.12 ($false),
% 1.84/2.12 inference(unit_resolution,[status(thm)],[6853, 37, 588, 6847, 6845])).
% 1.84/2.12 tff(6855,plain,((~b(s(s(s(z))), z)) | (~r(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~r(elem!1, z)) | (~b(s(z), z)) | (elem!1 = s(s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (s(s(z)) = elem!1) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.12 tff(6856,plain,
% 1.84/2.12 (~b(s(s(s(z))), z)),
% 1.84/2.12 inference(unit_resolution,[status(thm)],[6855, 6815, 6689, 6805, 6807, 6824, 6834, 6125, 6519, 6813])).
% 1.84/2.12 tff(6857,plain,
% 1.84/2.12 (r(s(s(s(z))), z)),
% 1.84/2.12 inference(unit_resolution,[status(thm)],[1334, 58, 221, 6856])).
% 1.84/2.12 tff(6858,plain,
% 1.84/2.12 (~r(elem!1, s(s(s(z))))),
% 1.84/2.12 inference(unit_resolution,[status(thm)],[6474, 6857, 6805])).
% 1.84/2.12 tff(6859,plain,
% 1.84/2.12 (b(elem!1, s(s(s(z))))),
% 1.84/2.12 inference(unit_resolution,[status(thm)],[1279, 6858, 6824])).
% 1.84/2.12 tff(6860,plain,
% 1.84/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, 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(X1, 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(z)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.84/2.12 inference(rewrite,[status(thm)],[])).
% 1.84/2.12 tff(6861,plain,
% 1.84/2.12 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.84/2.12 inference(rewrite,[status(thm)],[])).
% 1.84/2.12 tff(6862,plain,
% 1.84/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 1.84/2.12 inference(monotonicity,[status(thm)],[6861])).
% 1.84/2.12 tff(6863,plain,
% 1.84/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.84/2.12 inference(transitivity,[status(thm)],[6862, 6860])).
% 1.84/2.12 tff(6864,plain,
% 1.84/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 1.84/2.12 inference(quant_inst,[status(thm)],[])).
% 1.84/2.12 tff(6865,plain,
% 1.84/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))),
% 1.84/2.12 inference(modus_ponens,[status(thm)],[6864, 6863])).
% 1.84/2.12 tff(6866,plain,
% 1.84/2.12 ((~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))),
% 1.84/2.12 inference(unit_resolution,[status(thm)],[6865, 75, 5472, 6813, 6689, 6834])).
% 1.84/2.12 tff(6867,plain,
% 1.84/2.12 (~b(s(s(z)), s(s(s(z))))),
% 1.84/2.12 inference(unit_resolution,[status(thm)],[6866, 6859])).
% 1.84/2.12 tff(6868,plain,
% 1.84/2.12 (r(s(s(z)), s(s(s(z))))),
% 1.84/2.12 inference(unit_resolution,[status(thm)],[1559, 58, 1556, 6867])).
% 1.84/2.12 tff(6869,plain,
% 1.84/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.84/2.12 inference(rewrite,[status(thm)],[])).
% 1.84/2.12 tff(6870,plain,
% 1.84/2.12 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.94/2.13 inference(rewrite,[status(thm)],[])).
% 1.94/2.13 tff(6871,plain,
% 1.94/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z)))))))),
% 1.94/2.13 inference(monotonicity,[status(thm)],[6870])).
% 1.94/2.13 tff(6872,plain,
% 1.94/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.94/2.13 inference(transitivity,[status(thm)],[6871, 6869])).
% 1.94/2.13 tff(6873,plain,
% 1.94/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.94/2.13 inference(quant_inst,[status(thm)],[])).
% 1.94/2.13 tff(6874,plain,
% 1.94/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z)))))),
% 1.94/2.13 inference(modus_ponens,[status(thm)],[6873, 6872])).
% 1.94/2.13 tff(6875,plain,
% 1.94/2.13 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.94/2.13 inference(unit_resolution,[status(thm)],[6874, 75, 6813, 6834, 6859, 6512])).
% 1.94/2.13 tff(6876,plain,
% 1.94/2.13 (r(s(s(z)), s(s(s(s(z)))))),
% 1.94/2.13 inference(unit_resolution,[status(thm)],[465, 6875])).
% 1.94/2.13 tff(6877,plain,
% 1.94/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.94/2.13 inference(rewrite,[status(thm)],[])).
% 1.94/2.13 tff(6878,plain,
% 1.94/2.13 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(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(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.94/2.13 inference(rewrite,[status(thm)],[])).
% 1.94/2.13 tff(6879,plain,
% 1.94/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.94/2.13 inference(monotonicity,[status(thm)],[6878])).
% 1.94/2.13 tff(6880,plain,
% 1.94/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.94/2.13 inference(transitivity,[status(thm)],[6879, 6877])).
% 1.94/2.13 tff(6881,plain,
% 1.94/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.94/2.13 inference(quant_inst,[status(thm)],[])).
% 1.94/2.13 tff(6882,plain,
% 1.94/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.94/2.13 inference(modus_ponens,[status(thm)],[6881, 6880])).
% 1.94/2.13 tff(6883,plain,
% 1.94/2.13 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.94/2.13 inference(unit_resolution,[status(thm)],[6882, 75, 6834, 6859, 6512])).
% 1.94/2.13 tff(6884,plain,
% 1.94/2.13 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.94/2.13 inference(unit_resolution,[status(thm)],[2898, 6883])).
% 1.94/2.13 tff(6885,plain,
% 1.94/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.94/2.13 inference(rewrite,[status(thm)],[])).
% 1.94/2.13 tff(6886,plain,
% 1.94/2.13 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.94/2.13 inference(rewrite,[status(thm)],[])).
% 1.94/2.13 tff(6887,plain,
% 1.94/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))))),
% 1.94/2.13 inference(monotonicity,[status(thm)],[6886])).
% 1.94/2.13 tff(6888,plain,
% 1.94/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.94/2.13 inference(transitivity,[status(thm)],[6887, 6885])).
% 1.94/2.13 tff(6889,plain,
% 1.94/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.94/2.13 inference(quant_inst,[status(thm)],[])).
% 1.94/2.13 tff(6890,plain,
% 1.94/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))),
% 1.94/2.13 inference(modus_ponens,[status(thm)],[6889, 6888])).
% 1.94/2.13 tff(6891,plain,
% 1.94/2.13 ($false),
% 1.94/2.13 inference(unit_resolution,[status(thm)],[6890, 37, 6884, 6876, 6868])).
% 1.94/2.13 tff(6892,plain,(b(s(s(elem!1)), elem!1) | r(s(s(s(s(z)))), elem!1) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.94/2.13 tff(6893,plain,
% 1.94/2.13 (b(s(s(elem!1)), elem!1)),
% 1.94/2.13 inference(unit_resolution,[status(thm)],[6892, 12, 13])).
% 1.94/2.13 tff(6894,plain,
% 1.94/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.94/2.13 inference(rewrite,[status(thm)],[])).
% 1.94/2.13 tff(6895,plain,
% 1.94/2.13 (((~b(s(z), elem!1)) | (~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(z), elem!1)) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.94/2.13 inference(rewrite,[status(thm)],[])).
% 1.94/2.13 tff(6896,plain,
% 1.94/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), 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(X1, 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)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))))),
% 1.94/2.13 inference(monotonicity,[status(thm)],[6895])).
% 1.94/2.13 tff(6897,plain,
% 1.94/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), 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(X1, 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)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.94/2.13 inference(transitivity,[status(thm)],[6896, 6894])).
% 1.94/2.13 tff(6898,plain,
% 1.94/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), 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)))))),
% 1.94/2.13 inference(quant_inst,[status(thm)],[])).
% 1.94/2.13 tff(6899,plain,
% 1.94/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))),
% 1.94/2.13 inference(modus_ponens,[status(thm)],[6898, 6897])).
% 1.94/2.13 tff(6900,plain,
% 1.94/2.13 (~b(s(z), s(s(elem!1)))),
% 1.94/2.13 inference(unit_resolution,[status(thm)],[6899, 75, 107, 1391, 707])).
% 1.94/2.13 tff(6901,plain,
% 1.94/2.13 (r(s(z), s(s(elem!1)))),
% 1.94/2.13 inference(unit_resolution,[status(thm)],[1890, 6900])).
% 1.94/2.13 tff(6902,plain,
% 1.94/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)))),
% 1.94/2.13 inference(rewrite,[status(thm)],[])).
% 1.94/2.13 tff(6903,plain,
% 1.94/2.13 (((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(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(z, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)))),
% 1.94/2.13 inference(rewrite,[status(thm)],[])).
% 1.94/2.13 tff(6904,plain,
% 1.94/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1))))),
% 1.94/2.13 inference(monotonicity,[status(thm)],[6903])).
% 1.94/2.13 tff(6905,plain,
% 1.94/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)))),
% 1.94/2.13 inference(transitivity,[status(thm)],[6904, 6902])).
% 1.94/2.13 tff(6906,plain,
% 1.94/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))),
% 1.94/2.13 inference(quant_inst,[status(thm)],[])).
% 1.94/2.13 tff(6907,plain,
% 1.94/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1))),
% 1.94/2.13 inference(modus_ponens,[status(thm)],[6906, 6905])).
% 1.94/2.13 tff(6908,plain,
% 1.94/2.13 (~b(z, s(s(elem!1)))),
% 1.94/2.13 inference(unit_resolution,[status(thm)],[6907, 75, 1518, 107, 1391, 707])).
% 1.94/2.13 tff(6909,plain,
% 1.94/2.13 (r(z, s(s(elem!1)))),
% 1.94/2.13 inference(unit_resolution,[status(thm)],[6314, 6908])).
% 1.94/2.13 tff(6910,plain,
% 1.94/2.13 ($false),
% 1.94/2.13 inference(unit_resolution,[status(thm)],[5301, 6909, 6901, 3185])).
% 1.94/2.13 tff(6911,plain,((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.13 tff(6912,plain,
% 1.94/2.13 (~b(s(z), elem!1)),
% 1.94/2.13 inference(unit_resolution,[status(thm)],[6911, 1518, 1391, 707])).
% 1.94/2.13 tff(6913,plain,
% 1.94/2.13 (r(s(z), elem!1)),
% 1.94/2.13 inference(unit_resolution,[status(thm)],[601, 6912, 2478])).
% 1.94/2.13 tff(6914,plain,
% 1.94/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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, z)))),
% 1.94/2.13 inference(rewrite,[status(thm)],[])).
% 1.94/2.13 tff(6915,plain,
% 1.94/2.13 (((~b(z, elem!1)) | (~b(s(s(elem!1)), 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(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, z)))),
% 1.94/2.13 inference(rewrite,[status(thm)],[])).
% 1.94/2.13 tff(6916,plain,
% 1.94/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), 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(X1, 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, z))))),
% 1.94/2.13 inference(monotonicity,[status(thm)],[6915])).
% 1.94/2.13 tff(6917,plain,
% 1.94/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), 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(X1, 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, z)))),
% 1.94/2.13 inference(transitivity,[status(thm)],[6916, 6914])).
% 1.94/2.13 tff(6918,plain,
% 1.94/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), 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)))))),
% 1.94/2.13 inference(quant_inst,[status(thm)],[])).
% 1.94/2.13 tff(6919,plain,
% 1.94/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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, z))),
% 1.94/2.13 inference(modus_ponens,[status(thm)],[6918, 6917])).
% 1.94/2.13 tff(6920,plain,
% 1.94/2.13 (~b(z, s(s(elem!1)))),
% 1.94/2.13 inference(unit_resolution,[status(thm)],[6919, 75, 1518, 1958, 707])).
% 1.94/2.13 tff(6921,plain,
% 1.94/2.13 (r(z, s(s(elem!1)))),
% 1.94/2.13 inference(unit_resolution,[status(thm)],[6314, 6920])).
% 1.94/2.13 tff(6922,plain,
% 1.94/2.13 (~r(s(z), s(s(elem!1)))),
% 1.94/2.13 inference(unit_resolution,[status(thm)],[5301, 6921, 1561])).
% 1.94/2.13 tff(6923,plain,
% 1.94/2.13 (b(s(z), s(s(elem!1)))),
% 1.94/2.13 inference(unit_resolution,[status(thm)],[1890, 6922])).
% 1.94/2.13 tff(6924,plain,
% 1.94/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)))),
% 1.94/2.13 inference(rewrite,[status(thm)],[])).
% 1.94/2.13 tff(6925,plain,
% 1.94/2.13 (((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)))),
% 1.94/2.13 inference(rewrite,[status(thm)],[])).
% 1.94/2.13 tff(6926,plain,
% 1.94/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(elem!1)), z))))),
% 1.94/2.13 inference(monotonicity,[status(thm)],[6925])).
% 1.94/2.13 tff(6927,plain,
% 1.94/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)))),
% 1.94/2.14 inference(transitivity,[status(thm)],[6926, 6924])).
% 1.94/2.14 tff(6928,plain,
% 1.94/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))))),
% 1.94/2.14 inference(quant_inst,[status(thm)],[])).
% 1.94/2.14 tff(6929,plain,
% 1.94/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(s(s(elem!1)), z))),
% 1.94/2.14 inference(modus_ponens,[status(thm)],[6928, 6927])).
% 1.94/2.14 tff(6930,plain,
% 1.94/2.14 (~r(s(s(elem!1)), s(z))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[6929, 37, 6913, 1561, 4692])).
% 1.94/2.14 tff(6931,plain,
% 1.94/2.14 (b(s(s(elem!1)), s(z))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[561, 6930])).
% 1.94/2.14 tff(6932,plain,
% 1.94/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))))),
% 1.94/2.14 inference(rewrite,[status(thm)],[])).
% 1.94/2.14 tff(6933,plain,
% 1.94/2.14 (((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~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(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))))),
% 1.94/2.14 inference(rewrite,[status(thm)],[])).
% 1.94/2.14 tff(6934,plain,
% 1.94/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~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(X1, 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)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z)))))),
% 1.94/2.14 inference(monotonicity,[status(thm)],[6933])).
% 1.94/2.14 tff(6935,plain,
% 1.94/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~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(X1, 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)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))))),
% 1.94/2.14 inference(transitivity,[status(thm)],[6934, 6932])).
% 1.94/2.14 tff(6936,plain,
% 1.94/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~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)))),
% 1.94/2.14 inference(quant_inst,[status(thm)],[])).
% 1.94/2.14 tff(6937,plain,
% 1.94/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z)))),
% 1.94/2.14 inference(modus_ponens,[status(thm)],[6936, 6935])).
% 1.94/2.14 tff(6938,plain,
% 1.94/2.14 ($false),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[6937, 75, 6931, 1391, 6923, 707])).
% 1.94/2.14 tff(6939,plain,((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~r(s(z), z)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.14 tff(6940,plain,
% 1.94/2.14 (~b(elem!1, z)),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[6939, 1561, 707, 1391, 1518])).
% 1.94/2.14 tff(6941,plain,
% 1.94/2.14 (r(elem!1, z)),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[387, 6940, 6540])).
% 1.94/2.14 tff(6942,plain,
% 1.94/2.14 (~b(s(s(s(s(z)))), elem!1)),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[6585, 6941, 1391, 1561, 1518])).
% 1.94/2.14 tff(6943,plain,
% 1.94/2.14 (s(s(s(s(z)))) = elem!1),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[283, 6942, 12])).
% 1.94/2.14 tff(6944,plain,
% 1.94/2.14 (r(s(s(s(s(z)))), z) <=> r(elem!1, z)),
% 1.94/2.14 inference(monotonicity,[status(thm)],[6943])).
% 1.94/2.14 tff(6945,plain,
% 1.94/2.14 (r(elem!1, z) <=> r(s(s(s(s(z)))), z)),
% 1.94/2.14 inference(symmetry,[status(thm)],[6944])).
% 1.94/2.14 tff(6946,plain,
% 1.94/2.14 (r(s(s(s(s(z)))), z)),
% 1.94/2.14 inference(modus_ponens,[status(thm)],[6941, 6945])).
% 1.94/2.14 tff(6947,plain,
% 1.94/2.14 (r(s(z), s(s(s(s(z)))))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[3669, 6943, 6912])).
% 1.94/2.14 tff(6948,plain,
% 1.94/2.14 (~r(s(s(s(s(z)))), z)),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[2586, 6947, 1561])).
% 1.94/2.14 tff(6949,plain,
% 1.94/2.14 ($false),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[6948, 6946])).
% 1.94/2.14 tff(6950,plain,((~r(s(z), z)) | r(s(s(s(s(z)))), elem!1) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.14 tff(6951,plain,
% 1.94/2.14 (~r(s(z), z)),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[6950, 12, 1391, 1518, 707])).
% 1.94/2.14 tff(6952,plain,
% 1.94/2.14 (b(s(z), z)),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[169, 6951])).
% 1.94/2.14 tff(6953,plain,
% 1.94/2.14 (~b(z, s(z))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[2596, 6952, 1391, 1518])).
% 1.94/2.14 tff(6954,plain,
% 1.94/2.14 (r(z, s(z))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[187, 6953])).
% 1.94/2.14 tff(6955,plain,
% 1.94/2.14 (~b(elem!1, z)),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[6636, 6952, 1518, 1391])).
% 1.94/2.14 tff(6956,plain,
% 1.94/2.14 (~b(elem!1, s(s(elem!1)))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[4577, 494, 1518, 506])).
% 1.94/2.14 tff(6957,plain,
% 1.94/2.14 (~r(s(s(elem!1)), z)),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[6190, 494, 506])).
% 1.94/2.14 tff(6958,plain,
% 1.94/2.14 (b(s(s(elem!1)), z)),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[2696, 6957])).
% 1.94/2.14 tff(6959,plain,
% 1.94/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))))),
% 1.94/2.14 inference(rewrite,[status(thm)],[])).
% 1.94/2.14 tff(6960,plain,
% 1.94/2.14 (((~b(s(s(elem!1)), z)) | (~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(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))))),
% 1.94/2.14 inference(rewrite,[status(thm)],[])).
% 1.94/2.14 tff(6961,plain,
% 1.94/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1))))))),
% 1.94/2.14 inference(monotonicity,[status(thm)],[6960])).
% 1.94/2.14 tff(6962,plain,
% 1.94/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))))),
% 1.94/2.14 inference(transitivity,[status(thm)],[6961, 6959])).
% 1.94/2.14 tff(6963,plain,
% 1.94/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))))),
% 1.94/2.14 inference(quant_inst,[status(thm)],[])).
% 1.94/2.14 tff(6964,plain,
% 1.94/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1))))),
% 1.94/2.14 inference(modus_ponens,[status(thm)],[6963, 6962])).
% 1.94/2.14 tff(6965,plain,
% 1.94/2.14 (~b(s(z), s(s(elem!1)))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[6964, 75, 371, 6368, 6958])).
% 1.94/2.14 tff(6966,plain,
% 1.94/2.14 (r(s(z), s(s(elem!1)))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[1890, 6965])).
% 1.94/2.14 tff(6967,plain,
% 1.94/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(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(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 1.94/2.14 inference(rewrite,[status(thm)],[])).
% 1.94/2.14 tff(6968,plain,
% 1.94/2.14 (((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1))) <=> ((~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 1.94/2.14 inference(rewrite,[status(thm)],[])).
% 1.94/2.14 tff(6969,plain,
% 1.94/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(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(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))))),
% 1.94/2.14 inference(monotonicity,[status(thm)],[6968])).
% 1.94/2.14 tff(6970,plain,
% 1.94/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(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(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 1.94/2.14 inference(transitivity,[status(thm)],[6969, 6967])).
% 1.94/2.14 tff(6971,plain,
% 1.94/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)))),
% 1.94/2.14 inference(quant_inst,[status(thm)],[])).
% 1.94/2.14 tff(6972,plain,
% 1.94/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))),
% 1.94/2.14 inference(modus_ponens,[status(thm)],[6971, 6970])).
% 1.94/2.14 tff(6973,plain,
% 1.94/2.14 ($false),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[6972, 37, 588, 1490, 1871])).
% 1.94/2.14 tff(6974,plain,((~r(elem!1, s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.14 tff(6975,plain,
% 1.94/2.14 (~r(elem!1, s(s(elem!1)))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[6974, 6966, 588])).
% 1.94/2.14 tff(6976,plain,
% 1.94/2.14 (elem!1 = s(s(elem!1))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[1617, 6975, 6956])).
% 1.94/2.14 tff(6977,plain,
% 1.94/2.14 (b(elem!1, z) <=> b(s(s(elem!1)), z)),
% 1.94/2.14 inference(monotonicity,[status(thm)],[6976])).
% 1.94/2.14 tff(6978,plain,
% 1.94/2.14 (b(s(s(elem!1)), z) <=> b(elem!1, z)),
% 1.94/2.14 inference(symmetry,[status(thm)],[6977])).
% 1.94/2.14 tff(6979,plain,
% 1.94/2.14 (b(elem!1, z)),
% 1.94/2.14 inference(modus_ponens,[status(thm)],[6958, 6978])).
% 1.94/2.14 tff(6980,assumption,(~b(elem!1, z)), introduced(assumption)).
% 1.94/2.14 tff(6981,plain,
% 1.94/2.14 ($false),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[6980, 6979])).
% 1.94/2.14 tff(6982,plain,((~r(s(s(elem!1)), s(z))) | b(elem!1, z) | (~r(s(z), elem!1)) | (~b(s(z), z)) | (~r(z, s(z))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.14 tff(6983,plain,
% 1.94/2.14 (~r(s(s(elem!1)), s(z))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[6982, 6955, 6913, 6952, 6954, 1518])).
% 1.94/2.14 tff(6984,plain,
% 1.94/2.14 (b(s(s(elem!1)), s(z))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[561, 6983])).
% 1.94/2.14 tff(6985,assumption,(~b(s(s(z)), s(z))), introduced(assumption)).
% 1.94/2.14 tff(6986,plain,
% 1.94/2.14 (r(s(s(z)), s(z))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[153, 6985])).
% 1.94/2.14 tff(6987,plain,
% 1.94/2.14 (~r(s(s(z)), elem!1)),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[596, 6986, 588])).
% 1.94/2.14 tff(6988,plain,
% 1.94/2.14 (s(s(z)) = elem!1),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[104, 6987, 99])).
% 1.94/2.14 tff(6989,plain,
% 1.94/2.14 (b(s(s(z)), s(z)) <=> b(elem!1, s(z))),
% 1.94/2.14 inference(monotonicity,[status(thm)],[6988])).
% 1.94/2.14 tff(6990,plain,
% 1.94/2.14 (b(elem!1, s(z)) <=> b(s(s(z)), s(z))),
% 1.94/2.14 inference(symmetry,[status(thm)],[6989])).
% 1.94/2.14 tff(6991,plain,
% 1.94/2.14 (b(s(s(z)), s(z))),
% 1.94/2.14 inference(modus_ponens,[status(thm)],[1391, 6990])).
% 1.94/2.14 tff(6992,plain,
% 1.94/2.14 ($false),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[6985, 6991])).
% 1.94/2.14 tff(6993,plain,(b(s(s(z)), s(z)) | (~b(elem!1, s(z))) | b(s(s(z)), elem!1) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.14 tff(6994,plain,
% 1.94/2.14 (b(s(s(z)), s(z))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[6993, 99, 1391, 6913])).
% 1.94/2.14 tff(6995,plain,
% 1.94/2.14 (~b(s(z), s(s(z)))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[5914, 6994, 1391, 707, 6984])).
% 1.94/2.14 tff(6996,plain,
% 1.94/2.14 (r(s(z), s(s(z)))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[416, 6995])).
% 1.94/2.14 tff(6997,plain,
% 1.94/2.14 ($false),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[2081, 37, 588, 106, 1997])).
% 1.94/2.14 tff(6998,plain,((~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.14 tff(6999,plain,
% 1.94/2.14 (~r(s(s(z)), elem!1)),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[6998, 6996, 6913])).
% 1.94/2.14 tff(7000,plain,
% 1.94/2.14 (s(s(z)) = elem!1),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[104, 6999, 99])).
% 1.94/2.14 tff(7001,plain,
% 1.94/2.14 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[1013, 7000])).
% 1.94/2.14 tff(7002,plain,
% 1.94/2.14 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 1.94/2.14 inference(monotonicity,[status(thm)],[7001])).
% 1.94/2.14 tff(7003,plain,
% 1.94/2.14 (b(s(s(s(s(z)))), s(z))),
% 1.94/2.14 inference(modus_ponens,[status(thm)],[6984, 7002])).
% 1.94/2.14 tff(7004,plain,
% 1.94/2.14 (~(s(s(elem!1)) = s(s(z)))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[237, 6539])).
% 1.94/2.14 tff(7005,plain,
% 1.94/2.14 (r(elem!1, z)),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[387, 6955, 6540])).
% 1.94/2.14 tff(7006,plain,
% 1.94/2.14 (r(s(s(z)), elem!1)),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[104, 6325, 99])).
% 1.94/2.14 tff(7007,plain,
% 1.94/2.14 (~r(s(z), s(s(z)))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[2081, 37, 6913, 7006])).
% 1.94/2.14 tff(7008,plain,
% 1.94/2.14 (b(s(z), s(s(z)))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[416, 7007])).
% 1.94/2.14 tff(7009,plain,
% 1.94/2.14 (~b(elem!1, s(s(z)))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[1484, 75, 1391, 6994, 7008])).
% 1.94/2.14 tff(7010,plain,
% 1.94/2.14 ((elem!1 = s(s(z))) | r(elem!1, s(s(z)))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[398, 58, 7009])).
% 1.94/2.14 tff(7011,plain,
% 1.94/2.14 (r(elem!1, s(s(z)))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[7010, 6346])).
% 1.94/2.14 tff(7012,plain,
% 1.94/2.14 (r(s(s(s(s(z)))), z)),
% 1.94/2.14 inference(modus_ponens,[status(thm)],[155, 4743])).
% 1.94/2.14 tff(7013,plain,
% 1.94/2.14 (~b(z, s(z))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[2596, 371, 1391, 1518])).
% 1.94/2.14 tff(7014,plain,
% 1.94/2.14 (r(z, s(z))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[187, 7013])).
% 1.94/2.14 tff(7015,plain,
% 1.94/2.14 (~r(elem!1, s(z))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[177, 155, 7014])).
% 1.94/2.14 tff(7016,plain,
% 1.94/2.14 (~(elem!1 = s(s(elem!1)))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[4475, 4461, 266])).
% 1.94/2.14 tff(7017,plain,
% 1.94/2.14 (b(elem!1, s(s(elem!1)))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[1617, 7016, 2217])).
% 1.94/2.14 tff(7018,plain,
% 1.94/2.14 (~b(s(z), elem!1)),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[6176, 2568, 1518, 7017])).
% 1.94/2.14 tff(7019,plain,
% 1.94/2.14 (r(s(z), elem!1)),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[601, 7018, 108])).
% 1.94/2.14 tff(7020,plain,
% 1.94/2.14 (r(s(z), s(s(s(s(z)))))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[3664, 7019, 3285])).
% 1.94/2.14 tff(7021,plain,
% 1.94/2.14 (~r(s(z), z)),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[2586, 7020, 7012])).
% 1.94/2.14 tff(7022,plain,
% 1.94/2.14 (b(s(z), z)),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[169, 7021])).
% 1.94/2.14 tff(7023,plain,
% 1.94/2.14 (~(s(s(elem!1)) = elem!1)),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[2555, 7016])).
% 1.94/2.14 tff(7024,plain,
% 1.94/2.14 (~r(s(s(elem!1)), elem!1)),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[5690, 7019, 2568, 7017])).
% 1.94/2.14 tff(7025,plain,
% 1.94/2.14 (b(s(s(elem!1)), elem!1)),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[2673, 7024, 7023])).
% 1.94/2.14 tff(7026,plain,
% 1.94/2.14 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(z)) = elem!1)),
% 1.94/2.14 inference(monotonicity,[status(thm)],[3285])).
% 1.94/2.14 tff(7027,plain,
% 1.94/2.14 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(z)) = elem!1))),
% 1.94/2.14 inference(monotonicity,[status(thm)],[7026])).
% 1.94/2.14 tff(7028,plain,
% 1.94/2.14 (~(s(s(z)) = elem!1)),
% 1.94/2.14 inference(modus_ponens,[status(thm)],[459, 7027])).
% 1.94/2.14 tff(7029,plain,
% 1.94/2.14 (~b(s(s(z)), elem!1)),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[4730, 7025, 1518, 7017, 266])).
% 1.94/2.14 tff(7030,plain,
% 1.94/2.14 (r(s(s(z)), elem!1)),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[104, 7029, 7028])).
% 1.94/2.14 tff(7031,plain,
% 1.94/2.14 (~r(s(z), s(s(z)))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[2081, 37, 7019, 7030])).
% 1.94/2.14 tff(7032,plain,
% 1.94/2.14 (b(s(z), s(s(z)))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[416, 7031])).
% 1.94/2.14 tff(7033,plain,
% 1.94/2.14 (~r(s(s(z)), s(z))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[594, 37, 7019, 7030])).
% 1.94/2.14 tff(7034,plain,
% 1.94/2.14 (b(s(s(z)), s(z))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[153, 7033])).
% 1.94/2.14 tff(7035,plain,
% 1.94/2.14 (~b(s(s(elem!1)), s(z))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[5914, 2568, 7034, 7032, 7025])).
% 1.94/2.14 tff(7036,plain,
% 1.94/2.14 (r(s(s(elem!1)), s(z))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[561, 7035])).
% 1.94/2.14 tff(7037,plain,
% 1.94/2.14 (~r(z, s(z))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[4577, 7036, 1518, 7017])).
% 1.94/2.14 tff(7038,plain,
% 1.94/2.14 (b(z, s(z))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[187, 7037])).
% 1.94/2.14 tff(7039,plain,
% 1.94/2.14 ($false),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[2594, 75, 1518, 7038, 7022, 2568])).
% 1.94/2.14 tff(7040,plain,((~(s(s(s(s(z)))) = elem!1)) | (~b(z, elem!1)) | (s(s(elem!1)) = s(s(z))) | (s(z) = elem!1) | r(elem!1, s(z)) | r(elem!1, s(s(elem!1))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.14 tff(7041,plain,
% 1.94/2.14 (r(elem!1, s(s(elem!1)))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[7040, 3285, 2478, 1518, 266, 155, 7015])).
% 1.94/2.14 tff(7042,plain,
% 1.94/2.14 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.94/2.14 inference(modus_ponens,[status(thm)],[7041, 4740])).
% 1.94/2.14 tff(7043,plain,
% 1.94/2.14 (~r(s(s(elem!1)), z)),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[2707, 7042, 7012])).
% 1.94/2.14 tff(7044,plain,
% 1.94/2.14 (b(s(s(elem!1)), z)),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[2696, 7043])).
% 1.94/2.14 tff(7045,plain,
% 1.94/2.14 (~b(s(s(elem!1)), s(z))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[5914, 7008, 1391, 707, 6994])).
% 1.94/2.14 tff(7046,plain,
% 1.94/2.14 (r(s(s(elem!1)), s(z))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[561, 7045])).
% 1.94/2.14 tff(7047,plain,
% 1.94/2.14 (~r(z, s(s(elem!1)))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[1830, 37, 7046, 7014])).
% 1.94/2.14 tff(7048,plain,
% 1.94/2.14 (b(z, s(s(elem!1)))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[6314, 7047])).
% 1.94/2.14 tff(7049,plain,
% 1.94/2.14 (~b(s(z), s(s(elem!1)))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[6964, 75, 371, 7048, 7044])).
% 1.94/2.14 tff(7050,plain,
% 1.94/2.14 (r(s(z), s(s(elem!1)))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[1890, 7049])).
% 1.94/2.14 tff(7051,plain,
% 1.94/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(z)))))),
% 1.94/2.14 inference(rewrite,[status(thm)],[])).
% 1.94/2.14 tff(7052,plain,
% 1.94/2.14 (((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(z)))) | (~r(s(z), elem!1))) <=> ((~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(z)))))),
% 1.94/2.14 inference(rewrite,[status(thm)],[])).
% 1.94/2.14 tff(7053,plain,
% 1.94/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(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(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(z))))))),
% 1.94/2.14 inference(monotonicity,[status(thm)],[7052])).
% 1.94/2.14 tff(7054,plain,
% 1.94/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(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(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(z)))))),
% 1.94/2.14 inference(transitivity,[status(thm)],[7053, 7051])).
% 1.94/2.14 tff(7055,plain,
% 1.94/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(z)))) | (~r(s(z), elem!1)))),
% 1.94/2.14 inference(quant_inst,[status(thm)],[])).
% 1.94/2.14 tff(7056,plain,
% 1.94/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(z))))),
% 1.94/2.14 inference(modus_ponens,[status(thm)],[7055, 7054])).
% 1.94/2.14 tff(7057,plain,
% 1.94/2.14 ($false),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[7056, 37, 6913, 7041, 7050, 7011])).
% 1.94/2.14 tff(7058,plain,((~(s(s(s(s(z)))) = elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | b(s(s(z)), elem!1) | (~r(elem!1, z)) | (~b(z, elem!1)) | (s(s(elem!1)) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.14 tff(7059,plain,
% 1.94/2.14 (~(s(s(s(s(z)))) = elem!1)),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[7058, 99, 1391, 707, 6952, 7005, 1518, 7004])).
% 1.94/2.14 tff(7060,plain,
% 1.94/2.14 (b(s(s(s(s(z)))), elem!1)),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[283, 7059, 12])).
% 1.94/2.14 tff(7061,plain,
% 1.94/2.14 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(s(z)))))),
% 1.94/2.14 inference(monotonicity,[status(thm)],[7001])).
% 1.94/2.14 tff(7062,plain,
% 1.94/2.14 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(s(s(z)))))),
% 1.94/2.14 inference(monotonicity,[status(thm)],[7001])).
% 1.94/2.14 tff(7063,plain,
% 1.94/2.14 (r(elem!1, s(s(s(s(z))))) <=> r(elem!1, s(s(elem!1)))),
% 1.94/2.14 inference(symmetry,[status(thm)],[7062])).
% 1.94/2.14 tff(7064,plain,
% 1.94/2.14 (r(elem!1, s(s(s(s(z)))))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[3193, 7059, 12, 7004, 99])).
% 1.94/2.14 tff(7065,plain,
% 1.94/2.14 (r(elem!1, s(s(elem!1)))),
% 1.94/2.14 inference(modus_ponens,[status(thm)],[7064, 7063])).
% 1.94/2.14 tff(7066,plain,
% 1.94/2.14 (~r(s(z), s(s(elem!1)))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[6974, 7065, 6913])).
% 1.94/2.14 tff(7067,plain,
% 1.94/2.14 (b(s(z), s(s(elem!1)))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[1890, 7066])).
% 1.94/2.14 tff(7068,plain,
% 1.94/2.14 (b(s(z), s(s(s(s(z)))))),
% 1.94/2.14 inference(modus_ponens,[status(thm)],[7067, 7061])).
% 1.94/2.14 tff(7069,plain,
% 1.94/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.94/2.14 inference(rewrite,[status(thm)],[])).
% 1.94/2.14 tff(7070,plain,
% 1.94/2.14 (((~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~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(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.94/2.15 inference(rewrite,[status(thm)],[])).
% 1.94/2.15 tff(7071,plain,
% 1.94/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))), s(z))) | (~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(X1, 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)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 1.94/2.15 inference(monotonicity,[status(thm)],[7070])).
% 1.94/2.15 tff(7072,plain,
% 1.94/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))), s(z))) | (~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(X1, 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)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.94/2.15 inference(transitivity,[status(thm)],[7071, 7069])).
% 1.94/2.15 tff(7073,plain,
% 1.94/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))), s(z))) | (~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)))),
% 1.94/2.15 inference(quant_inst,[status(thm)],[])).
% 1.94/2.15 tff(7074,plain,
% 1.94/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 1.94/2.15 inference(modus_ponens,[status(thm)],[7073, 7072])).
% 1.94/2.15 tff(7075,plain,
% 1.94/2.15 ($false),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[7074, 75, 1391, 7068, 7060, 7003])).
% 1.94/2.15 tff(7076,plain,(b(s(s(z)), elem!1) | (~b(elem!1, s(z))) | r(s(s(s(s(z)))), elem!1) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.15 tff(7077,plain,
% 1.94/2.15 (b(s(s(z)), elem!1)),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[7076, 5472, 12, 6893, 6125])).
% 1.94/2.15 tff(7078,plain,
% 1.94/2.15 (~b(elem!1, s(s(elem!1)))),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[4730, 7077, 6125, 6893, 6118])).
% 1.94/2.15 tff(7079,plain,
% 1.94/2.15 (~b(s(z), elem!1)),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[6911, 6125, 5472, 6893])).
% 1.94/2.15 tff(7080,plain,
% 1.94/2.15 (r(s(z), elem!1)),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[601, 7079, 6179])).
% 1.94/2.15 tff(7081,plain,
% 1.94/2.15 (~r(s(z), z)),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[6950, 12, 5472, 6125, 6893])).
% 1.94/2.15 tff(7082,plain,
% 1.94/2.15 (b(s(z), z)),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[169, 7081])).
% 1.94/2.15 tff(7083,plain,
% 1.94/2.15 (~b(z, s(z))),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[2596, 7082, 5472, 6125])).
% 1.94/2.15 tff(7084,plain,
% 1.94/2.15 (r(z, s(z))),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[187, 7083])).
% 1.94/2.15 tff(7085,plain,
% 1.94/2.15 (~b(elem!1, z)),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[6636, 7082, 6125, 5472])).
% 1.94/2.15 tff(7086,plain,
% 1.94/2.15 (~r(s(s(elem!1)), s(z))),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[6982, 7085, 7080, 7082, 7084, 6125])).
% 1.94/2.15 tff(7087,plain,
% 1.94/2.15 (b(s(s(elem!1)), s(z))),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[561, 7086])).
% 1.94/2.15 tff(7088,plain,
% 1.94/2.15 ($false),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[6937, 75, 1457, 1391, 1894, 707])).
% 1.94/2.15 tff(7089,plain,((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.15 tff(7090,plain,
% 1.94/2.15 (~b(s(z), s(s(elem!1)))),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[7089, 7087, 5472, 6893])).
% 1.94/2.15 tff(7091,plain,
% 1.94/2.15 (r(s(z), s(s(elem!1)))),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[1890, 7090])).
% 1.94/2.15 tff(7092,plain,
% 1.94/2.15 (~r(elem!1, s(s(elem!1)))),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[6974, 7091, 7080])).
% 1.94/2.15 tff(7093,plain,
% 1.94/2.15 (elem!1 = s(s(elem!1))),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[1617, 7092, 7078])).
% 1.94/2.15 tff(7094,plain,
% 1.94/2.15 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(s(elem!1)))),
% 1.94/2.15 inference(monotonicity,[status(thm)],[7093])).
% 1.94/2.15 tff(7095,plain,
% 1.94/2.15 (b(s(s(elem!1)), s(s(elem!1))) <=> b(s(s(elem!1)), elem!1)),
% 1.94/2.15 inference(symmetry,[status(thm)],[7094])).
% 1.94/2.15 tff(7096,plain,
% 1.94/2.15 ((~b(s(s(elem!1)), s(s(elem!1)))) <=> (~b(s(s(elem!1)), elem!1))),
% 1.94/2.15 inference(monotonicity,[status(thm)],[7095])).
% 1.94/2.15 tff(7097,plain,
% 1.94/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(elem!1)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(elem!1)))) | (~b(z, elem!1)))),
% 1.94/2.15 inference(rewrite,[status(thm)],[])).
% 1.94/2.15 tff(7098,plain,
% 1.94/2.15 (((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(elem!1))))) <=> ((~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(elem!1)))) | (~b(z, elem!1)))),
% 1.94/2.15 inference(rewrite,[status(thm)],[])).
% 1.94/2.15 tff(7099,plain,
% 1.94/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(elem!1)))) | (~b(z, elem!1))))),
% 1.94/2.15 inference(monotonicity,[status(thm)],[7098])).
% 1.94/2.15 tff(7100,plain,
% 1.94/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(elem!1)))) | (~b(z, elem!1)))),
% 1.94/2.15 inference(transitivity,[status(thm)],[7099, 7097])).
% 1.94/2.15 tff(7101,plain,
% 1.94/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(elem!1)))))),
% 1.94/2.15 inference(quant_inst,[status(thm)],[])).
% 1.94/2.15 tff(7102,plain,
% 1.94/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(elem!1)))) | (~b(z, elem!1))),
% 1.94/2.15 inference(modus_ponens,[status(thm)],[7101, 7100])).
% 1.94/2.15 tff(7103,plain,
% 1.94/2.15 ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(elem!1))))),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[7102, 75, 6125, 7082, 6893])).
% 1.94/2.15 tff(7104,plain,
% 1.94/2.15 (~b(s(s(elem!1)), s(s(elem!1)))),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[7103, 7087])).
% 1.94/2.15 tff(7105,plain,
% 1.94/2.15 (~b(s(s(elem!1)), elem!1)),
% 1.94/2.15 inference(modus_ponens,[status(thm)],[7104, 7096])).
% 1.94/2.15 tff(7106,plain,
% 1.94/2.15 ($false),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[6893, 7105])).
% 1.94/2.15 tff(7107,plain,(r(s(s(s(s(z)))), elem!1) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.94/2.15 tff(7108,plain,
% 1.94/2.15 (r(z, elem!1)),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[7107, 12])).
% 1.94/2.15 tff(7109,plain,
% 1.94/2.15 (~r(elem!1, s(z))),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[367, 506, 7108])).
% 1.94/2.15 tff(7110,plain,
% 1.94/2.15 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 1.94/2.15 inference(symmetry,[status(thm)],[3642])).
% 1.94/2.15 tff(7111,plain,
% 1.94/2.15 (s(s(s(z))) = s(s(elem!1))),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[84, 17])).
% 1.94/2.15 tff(7112,plain,
% 1.94/2.15 (~(s(s(elem!1)) = s(s(z)))),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[4866, 7111])).
% 1.94/2.15 tff(7113,plain,
% 1.94/2.15 (~b(s(s(z)), s(z))),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[358, 17, 99])).
% 1.94/2.15 tff(7114,plain,
% 1.94/2.15 (r(s(s(z)), s(z))),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[153, 7113])).
% 1.94/2.15 tff(7115,plain,
% 1.94/2.15 (~r(s(s(elem!1)), s(z))),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[548, 7114, 300, 506, 7112])).
% 1.94/2.15 tff(7116,plain,
% 1.94/2.15 (b(s(s(elem!1)), s(z))),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[561, 7115])).
% 1.94/2.15 tff(7117,plain,
% 1.94/2.15 (b(s(s(elem!1)), elem!1)),
% 1.94/2.15 inference(modus_ponens,[status(thm)],[7116, 7110])).
% 1.94/2.15 tff(7118,plain,
% 1.94/2.15 ($false),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[1, 7117])).
% 1.94/2.15 tff(7119,plain,((~(elem!1 = s(z))) | b(s(s(elem!1)), elem!1) | (~r(z, elem!1)) | (~r(z, s(z))) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.94/2.15 tff(7120,plain,
% 1.94/2.15 (~(elem!1 = s(z))),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[7119, 1, 7108, 506, 99])).
% 1.94/2.15 tff(7121,plain,
% 1.94/2.15 (b(elem!1, s(z))),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[89, 7120, 7109])).
% 1.94/2.15 tff(7122,plain,
% 1.94/2.15 (~(z = elem!1)),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[6116, 7121, 12])).
% 1.94/2.15 tff(7123,plain,
% 1.94/2.15 (~(elem!1 = z)),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[304, 7122])).
% 1.94/2.15 tff(7124,plain,
% 1.94/2.15 (~(s(z) = elem!1)),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[97, 7120])).
% 1.94/2.15 tff(7125,plain,
% 1.94/2.15 (~(s(s(elem!1)) = s(s(z)))),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[237, 7122])).
% 1.94/2.15 tff(7126,plain,
% 1.94/2.15 ((s(s(elem!1)) = s(s(s(s(z))))) <=> (s(s(elem!1)) = elem!1)),
% 1.94/2.15 inference(monotonicity,[status(thm)],[3285])).
% 1.94/2.15 tff(7127,plain,
% 1.94/2.15 ((s(s(elem!1)) = s(s(s(s(z))))) <=> (elem!1 = s(s(elem!1)))),
% 1.94/2.15 inference(transitivity,[status(thm)],[7126, 3428])).
% 1.94/2.15 tff(7128,plain,
% 1.94/2.15 ((elem!1 = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 1.94/2.15 inference(symmetry,[status(thm)],[7127])).
% 1.94/2.15 tff(7129,plain,
% 1.94/2.15 ((~(elem!1 = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(s(s(s(z))))))),
% 1.94/2.15 inference(monotonicity,[status(thm)],[7128])).
% 1.94/2.15 tff(7130,plain,
% 1.94/2.15 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 1.94/2.15 inference(modus_ponens,[status(thm)],[4476, 7129])).
% 1.94/2.15 tff(7131,plain,
% 1.94/2.15 ((~r(s(z), elem!1)) <=> (~r(s(z), s(s(s(s(z))))))),
% 1.94/2.15 inference(monotonicity,[status(thm)],[3661])).
% 1.94/2.15 tff(7132,plain,
% 1.94/2.15 (((~![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)))),
% 1.94/2.15 inference(rewrite,[status(thm)],[])).
% 1.94/2.15 tff(7133,plain,
% 1.94/2.15 (((~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)))),
% 1.94/2.15 inference(rewrite,[status(thm)],[])).
% 1.94/2.15 tff(7134,plain,
% 1.94/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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))))),
% 1.94/2.15 inference(monotonicity,[status(thm)],[7133])).
% 1.94/2.15 tff(7135,plain,
% 1.94/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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)))),
% 1.94/2.15 inference(transitivity,[status(thm)],[7134, 7132])).
% 1.94/2.15 tff(7136,plain,
% 1.94/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))),
% 1.94/2.15 inference(quant_inst,[status(thm)],[])).
% 1.94/2.15 tff(7137,plain,
% 1.94/2.15 ((~![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))),
% 1.94/2.15 inference(modus_ponens,[status(thm)],[7136, 7135])).
% 1.94/2.15 tff(7138,plain,
% 1.94/2.15 (~r(z, s(s(elem!1)))),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[7137, 37, 300, 2647])).
% 1.94/2.15 tff(7139,plain,
% 1.94/2.15 ((z = s(s(elem!1))) | b(z, s(s(elem!1)))),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[1834, 58, 7138])).
% 1.94/2.15 tff(7140,plain,
% 1.94/2.15 (b(z, s(s(elem!1)))),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[7139, 1824])).
% 1.94/2.15 tff(7141,plain,
% 1.94/2.15 (b(z, s(z))),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[187, 2071])).
% 1.94/2.15 tff(7142,plain,
% 1.94/2.15 (r(s(z), s(s(s(s(z)))))),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[3664, 588, 3285])).
% 1.94/2.15 tff(7143,plain,
% 1.94/2.15 (~r(s(s(elem!1)), s(z))),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[1655, 7142, 1647])).
% 1.94/2.15 tff(7144,plain,
% 1.94/2.15 (b(s(s(elem!1)), s(z))),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[561, 7143])).
% 1.94/2.15 tff(7145,plain,
% 1.94/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.94/2.15 inference(rewrite,[status(thm)],[])).
% 1.94/2.15 tff(7146,plain,
% 1.94/2.15 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.94/2.15 inference(rewrite,[status(thm)],[])).
% 1.94/2.15 tff(7147,plain,
% 1.94/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))))),
% 1.94/2.15 inference(monotonicity,[status(thm)],[7146])).
% 1.94/2.15 tff(7148,plain,
% 1.94/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.94/2.15 inference(transitivity,[status(thm)],[7147, 7145])).
% 1.94/2.15 tff(7149,plain,
% 1.94/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))))),
% 1.94/2.15 inference(quant_inst,[status(thm)],[])).
% 1.94/2.15 tff(7150,plain,
% 1.94/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))),
% 1.94/2.15 inference(modus_ponens,[status(thm)],[7149, 7148])).
% 1.94/2.15 tff(7151,plain,
% 1.94/2.15 ($false),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[7150, 75, 7144, 7141, 5776, 7140])).
% 1.94/2.15 tff(7152,plain,((~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~(s(s(s(s(z)))) = elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.15 tff(7153,plain,
% 1.94/2.15 (~r(s(z), elem!1)),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[7152, 1647, 3285, 300, 2647])).
% 1.94/2.15 tff(7154,plain,
% 1.94/2.15 (~r(s(z), s(s(s(s(z)))))),
% 1.94/2.15 inference(modus_ponens,[status(thm)],[7153, 7131])).
% 1.94/2.15 tff(7155,plain,
% 1.94/2.15 (r(z, elem!1)),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[298, 294, 285])).
% 1.94/2.15 tff(7156,plain,
% 1.94/2.15 (~(s(z) = elem!1)),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[998, 7155, 3657, 266, 2219, 895])).
% 1.94/2.15 tff(7157,plain,
% 1.94/2.15 (~(s(s(z)) = s(elem!1))),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[3261, 7156])).
% 1.94/2.15 tff(7158,plain,
% 1.94/2.15 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[4541, 7157])).
% 1.94/2.15 tff(7159,plain,
% 1.94/2.15 (((~![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)))))))),
% 1.94/2.15 inference(rewrite,[status(thm)],[])).
% 1.94/2.15 tff(7160,plain,
% 1.94/2.15 (((~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)))))))),
% 1.94/2.15 inference(rewrite,[status(thm)],[])).
% 1.94/2.15 tff(7161,plain,
% 1.94/2.15 (((~![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(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))))))))),
% 1.94/2.15 inference(monotonicity,[status(thm)],[7160])).
% 1.94/2.15 tff(7162,plain,
% 1.94/2.15 (((~![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(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)))))))),
% 1.94/2.15 inference(transitivity,[status(thm)],[7161, 7159])).
% 1.94/2.15 tff(7163,plain,
% 1.94/2.15 ((~![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(z)))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(s(s(z)))))))),
% 1.94/2.15 inference(quant_inst,[status(thm)],[])).
% 1.94/2.15 tff(7164,plain,
% 1.94/2.15 ((~![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))))))),
% 1.94/2.15 inference(modus_ponens,[status(thm)],[7163, 7162])).
% 1.94/2.15 tff(7165,plain,
% 1.94/2.15 (~r(z, s(s(s(s(z)))))),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[7164, 37, 300, 698])).
% 1.94/2.15 tff(7166,plain,
% 1.94/2.15 ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z)))))),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[1515, 58, 7165])).
% 1.94/2.15 tff(7167,plain,
% 1.94/2.15 (b(z, s(s(s(s(z)))))),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[7166, 1503])).
% 1.94/2.16 tff(7168,plain,
% 1.94/2.16 (((~![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)))),
% 1.94/2.16 inference(rewrite,[status(thm)],[])).
% 1.94/2.16 tff(7169,plain,
% 1.94/2.16 (((~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)))),
% 1.94/2.16 inference(rewrite,[status(thm)],[])).
% 1.94/2.16 tff(7170,plain,
% 1.94/2.16 (((~![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))))),
% 1.94/2.16 inference(monotonicity,[status(thm)],[7169])).
% 1.94/2.16 tff(7171,plain,
% 1.94/2.16 (((~![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)))),
% 1.94/2.16 inference(transitivity,[status(thm)],[7170, 7168])).
% 1.94/2.16 tff(7172,plain,
% 1.94/2.16 ((~![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)))),
% 1.94/2.16 inference(quant_inst,[status(thm)],[])).
% 1.94/2.16 tff(7173,plain,
% 1.94/2.16 ((~![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))),
% 1.94/2.16 inference(modus_ponens,[status(thm)],[7172, 7171])).
% 1.94/2.16 tff(7174,plain,
% 1.94/2.16 (~r(s(s(s(s(z)))), z)),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[7173, 37, 300, 698])).
% 1.94/2.16 tff(7175,plain,
% 1.94/2.16 (b(s(s(s(s(z)))), z)),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[1421, 58, 1143, 7174])).
% 1.94/2.16 tff(7176,plain,
% 1.94/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.94/2.16 inference(rewrite,[status(thm)],[])).
% 1.94/2.16 tff(7177,plain,
% 1.94/2.16 (((~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), 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(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.94/2.16 inference(rewrite,[status(thm)],[])).
% 1.94/2.16 tff(7178,plain,
% 1.94/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), 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(X1, 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(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))))),
% 1.94/2.16 inference(monotonicity,[status(thm)],[7177])).
% 1.94/2.16 tff(7179,plain,
% 1.94/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), 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(X1, 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(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.94/2.16 inference(transitivity,[status(thm)],[7178, 7176])).
% 1.94/2.16 tff(7180,plain,
% 1.94/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))),
% 1.94/2.16 inference(quant_inst,[status(thm)],[])).
% 1.94/2.16 tff(7181,plain,
% 1.94/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))),
% 1.94/2.16 inference(modus_ponens,[status(thm)],[7180, 7179])).
% 1.94/2.16 tff(7182,plain,
% 1.94/2.16 ($false),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[7181, 75, 372, 578, 7175, 7167])).
% 1.94/2.16 tff(7183,plain,((~r(s(s(s(s(z)))), elem!1)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.16 tff(7184,plain,
% 1.94/2.16 (~b(z, s(z))),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[7183, 698, 578, 300])).
% 1.94/2.16 tff(7185,plain,
% 1.94/2.16 (r(z, s(z))),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[187, 7184])).
% 1.94/2.16 tff(7186,plain,
% 1.94/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.94/2.16 inference(rewrite,[status(thm)],[])).
% 1.94/2.16 tff(7187,plain,
% 1.94/2.16 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.94/2.16 inference(rewrite,[status(thm)],[])).
% 1.94/2.16 tff(7188,plain,
% 1.94/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))))),
% 1.94/2.16 inference(monotonicity,[status(thm)],[7187])).
% 1.94/2.16 tff(7189,plain,
% 1.94/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.94/2.16 inference(transitivity,[status(thm)],[7188, 7186])).
% 1.94/2.16 tff(7190,plain,
% 1.94/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))),
% 1.94/2.16 inference(quant_inst,[status(thm)],[])).
% 1.94/2.16 tff(7191,plain,
% 1.94/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))),
% 1.94/2.16 inference(modus_ponens,[status(thm)],[7190, 7189])).
% 1.94/2.16 tff(7192,plain,
% 1.94/2.16 (~b(z, s(s(z)))),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[7191, 75, 895, 7175, 7167])).
% 1.94/2.16 tff(7193,plain,
% 1.94/2.16 (r(z, s(s(z)))),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[351, 7192])).
% 1.94/2.16 tff(7194,plain,
% 1.94/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.94/2.16 inference(rewrite,[status(thm)],[])).
% 1.94/2.16 tff(7195,plain,
% 1.94/2.16 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.94/2.16 inference(rewrite,[status(thm)],[])).
% 1.94/2.16 tff(7196,plain,
% 1.94/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))))),
% 1.94/2.16 inference(monotonicity,[status(thm)],[7195])).
% 1.94/2.16 tff(7197,plain,
% 1.94/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.94/2.16 inference(transitivity,[status(thm)],[7196, 7194])).
% 1.94/2.16 tff(7198,plain,
% 1.94/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))),
% 1.94/2.16 inference(quant_inst,[status(thm)],[])).
% 1.94/2.16 tff(7199,plain,
% 1.94/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))),
% 1.94/2.16 inference(modus_ponens,[status(thm)],[7198, 7197])).
% 1.94/2.16 tff(7200,plain,
% 1.94/2.16 (~b(s(z), s(s(z)))),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[7199, 75, 578, 895, 7175, 7167])).
% 1.94/2.16 tff(7201,plain,
% 1.94/2.16 (r(s(z), s(s(z)))),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[416, 7200])).
% 1.94/2.16 tff(7202,plain,
% 1.94/2.16 ($false),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[2005, 7201, 7193, 7185])).
% 1.94/2.16 tff(7203,plain,((~r(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.16 tff(7204,plain,
% 1.94/2.16 (~r(s(s(s(s(z)))), elem!1)),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[7203, 300, 895, 3657])).
% 1.94/2.16 tff(7205,plain,
% 1.94/2.16 (~(s(z) = elem!1)),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[998, 300, 3657, 266, 2219, 895])).
% 1.94/2.16 tff(7206,plain,
% 1.94/2.16 (~r(z, s(z))),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[367, 113, 300])).
% 1.94/2.16 tff(7207,plain,
% 1.94/2.16 (b(z, s(z))),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[187, 7206])).
% 1.94/2.16 tff(7208,plain,
% 1.94/2.16 (~r(s(s(s(s(z)))), elem!1)),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[7183, 7207, 3657, 300])).
% 1.94/2.16 tff(7209,plain,
% 1.94/2.16 (r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.94/2.16 inference(monotonicity,[status(thm)],[4553])).
% 1.94/2.16 tff(7210,plain,
% 1.94/2.16 (r(s(s(s(s(z)))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.94/2.16 inference(symmetry,[status(thm)],[7209])).
% 1.94/2.16 tff(7211,plain,
% 1.94/2.16 (r(elem!1, s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.94/2.16 inference(monotonicity,[status(thm)],[270])).
% 1.94/2.16 tff(7212,plain,
% 1.94/2.16 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.94/2.16 inference(modus_ponens,[status(thm)],[1490, 7211])).
% 1.94/2.16 tff(7213,plain,
% 1.94/2.16 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.94/2.16 inference(modus_ponens,[status(thm)],[7212, 7210])).
% 1.94/2.16 tff(7214,plain,
% 1.94/2.16 (r(s(s(s(s(s(s(z)))))), s(z)) <=> r(s(s(elem!1)), s(z))),
% 1.94/2.16 inference(monotonicity,[status(thm)],[4553])).
% 1.94/2.16 tff(7215,plain,
% 1.94/2.16 (r(s(s(elem!1)), s(z)) <=> r(s(s(s(s(s(s(z)))))), s(z))),
% 1.94/2.16 inference(symmetry,[status(thm)],[7214])).
% 1.94/2.16 tff(7216,plain,
% 1.94/2.16 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(s(s(z)))))), s(z))),
% 1.94/2.16 inference(monotonicity,[status(thm)],[4466])).
% 1.94/2.16 tff(7217,plain,
% 1.94/2.16 (b(s(s(s(s(s(s(z)))))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.94/2.16 inference(symmetry,[status(thm)],[7216])).
% 1.94/2.16 tff(7218,plain,
% 1.94/2.16 ((~b(s(s(s(s(s(s(z)))))), s(z))) <=> (~b(s(s(elem!1)), s(z)))),
% 1.94/2.16 inference(monotonicity,[status(thm)],[7217])).
% 1.94/2.16 tff(7219,plain,
% 1.94/2.16 (~r(z, s(s(elem!1)))),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[2372, 1490, 300])).
% 1.94/2.16 tff(7220,plain,
% 1.94/2.16 ((z = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = z)),
% 1.94/2.16 inference(commutativity,[status(thm)],[])).
% 1.94/2.16 tff(7221,plain,
% 1.94/2.16 ((s(s(s(s(s(s(z)))))) = z) <=> (z = s(s(s(s(s(s(z)))))))),
% 1.94/2.16 inference(symmetry,[status(thm)],[7220])).
% 1.94/2.16 tff(7222,plain,
% 1.94/2.16 ((~(s(s(s(s(s(s(z)))))) = z)) <=> (~(z = s(s(s(s(s(s(z))))))))),
% 1.94/2.16 inference(monotonicity,[status(thm)],[7221])).
% 1.94/2.16 tff(7223,plain,
% 1.94/2.16 (~(z = s(s(s(s(s(s(z)))))))),
% 1.94/2.16 inference(modus_ponens,[status(thm)],[717, 7222])).
% 1.94/2.16 tff(7224,plain,
% 1.94/2.16 (r(z, s(s(s(s(s(s(z))))))) <=> r(z, s(s(elem!1)))),
% 1.94/2.16 inference(monotonicity,[status(thm)],[4553])).
% 1.94/2.16 tff(7225,plain,
% 1.94/2.16 (r(z, s(s(elem!1))) <=> r(z, s(s(s(s(s(s(z)))))))),
% 1.94/2.16 inference(symmetry,[status(thm)],[7224])).
% 1.94/2.16 tff(7226,plain,
% 1.94/2.16 ((~r(z, s(s(elem!1)))) <=> (~r(z, s(s(s(s(s(s(z))))))))),
% 1.94/2.16 inference(monotonicity,[status(thm)],[7225])).
% 1.94/2.16 tff(7227,plain,
% 1.94/2.16 (~r(z, s(s(s(s(s(s(z)))))))),
% 1.94/2.16 inference(modus_ponens,[status(thm)],[5566, 7226])).
% 1.94/2.16 tff(7228,assumption,(~b(z, s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.94/2.16 tff(7229,plain,
% 1.94/2.16 (((~![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))))))))),
% 1.94/2.16 inference(rewrite,[status(thm)],[])).
% 1.94/2.16 tff(7230,plain,
% 1.94/2.16 ((~![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))))))))),
% 1.94/2.16 inference(quant_inst,[status(thm)],[])).
% 1.94/2.16 tff(7231,plain,
% 1.94/2.16 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(s(z))))))) | b(z, s(s(s(s(s(s(z))))))) | r(z, s(s(s(s(s(s(z)))))))),
% 1.94/2.17 inference(modus_ponens,[status(thm)],[7230, 7229])).
% 1.94/2.17 tff(7232,plain,
% 1.94/2.17 ((z = s(s(s(s(s(s(z))))))) | r(z, s(s(s(s(s(s(z)))))))),
% 1.94/2.17 inference(unit_resolution,[status(thm)],[7231, 58, 7228])).
% 1.94/2.17 tff(7233,plain,
% 1.94/2.17 ($false),
% 1.94/2.17 inference(unit_resolution,[status(thm)],[7232, 7227, 7223])).
% 1.94/2.17 tff(7234,plain,(b(z, s(s(s(s(s(s(z))))))) | r(z, s(s(elem!1))) | (~(elem!1 = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.17 tff(7235,plain,
% 1.94/2.17 (b(z, s(s(s(s(s(s(z)))))))),
% 1.94/2.17 inference(unit_resolution,[status(thm)],[7234, 7219, 270])).
% 1.94/2.17 tff(7236,plain,
% 1.94/2.17 (b(s(z), s(s(s(s(s(s(z))))))) <=> b(s(z), s(s(elem!1)))),
% 1.94/2.17 inference(monotonicity,[status(thm)],[4553])).
% 1.94/2.17 tff(7237,plain,
% 1.94/2.17 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(s(s(s(z)))))))),
% 1.94/2.17 inference(symmetry,[status(thm)],[7236])).
% 1.94/2.17 tff(7238,plain,
% 1.94/2.17 (~r(s(z), s(s(elem!1)))),
% 1.94/2.17 inference(unit_resolution,[status(thm)],[3615, 1490, 114])).
% 1.94/2.17 tff(7239,plain,
% 1.94/2.17 (b(s(z), s(s(elem!1)))),
% 1.94/2.17 inference(unit_resolution,[status(thm)],[1890, 7238])).
% 1.94/2.17 tff(7240,plain,
% 1.94/2.17 (b(s(z), s(s(s(s(s(s(z)))))))),
% 1.94/2.17 inference(modus_ponens,[status(thm)],[7239, 7237])).
% 1.94/2.17 tff(7241,assumption,(b(z, s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.94/2.17 tff(7242,assumption,(b(s(z), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.94/2.17 tff(7243,plain,
% 1.94/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.94/2.17 inference(rewrite,[status(thm)],[])).
% 1.94/2.17 tff(7244,plain,
% 1.94/2.17 (((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(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(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.94/2.17 inference(rewrite,[status(thm)],[])).
% 1.94/2.17 tff(7245,plain,
% 1.94/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z))))))))))),
% 1.94/2.17 inference(monotonicity,[status(thm)],[7244])).
% 1.94/2.17 tff(7246,plain,
% 1.94/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.94/2.17 inference(transitivity,[status(thm)],[7245, 7243])).
% 1.94/2.17 tff(7247,plain,
% 1.94/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(z))))),
% 1.94/2.17 inference(quant_inst,[status(thm)],[])).
% 1.94/2.17 tff(7248,plain,
% 1.94/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z))))))))),
% 1.94/2.17 inference(modus_ponens,[status(thm)],[7247, 7246])).
% 1.94/2.17 tff(7249,plain,
% 1.94/2.17 ($false),
% 1.94/2.17 inference(unit_resolution,[status(thm)],[7248, 75, 372, 4587, 7242, 7241])).
% 1.94/2.17 tff(7250,plain,((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.17 tff(7251,plain,
% 1.94/2.17 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 1.94/2.17 inference(unit_resolution,[status(thm)],[7250, 7240, 1049, 7235])).
% 1.94/2.17 tff(7252,plain,
% 1.94/2.17 (~b(s(s(elem!1)), s(z))),
% 1.94/2.17 inference(modus_ponens,[status(thm)],[7251, 7218])).
% 1.94/2.17 tff(7253,plain,
% 1.94/2.17 (r(s(s(elem!1)), s(z))),
% 1.94/2.17 inference(unit_resolution,[status(thm)],[561, 7252])).
% 1.94/2.17 tff(7254,plain,
% 1.94/2.17 (r(s(s(s(s(s(s(z)))))), s(z))),
% 1.94/2.17 inference(modus_ponens,[status(thm)],[7253, 7215])).
% 1.94/2.17 tff(7255,plain,
% 1.94/2.17 (r(elem!1, s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 1.94/2.17 inference(monotonicity,[status(thm)],[270])).
% 1.94/2.17 tff(7256,plain,
% 1.94/2.17 (r(s(s(s(s(z)))), s(z))),
% 1.94/2.17 inference(modus_ponens,[status(thm)],[114, 7255])).
% 1.94/2.17 tff(7257,plain,
% 1.94/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(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(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.94/2.17 inference(rewrite,[status(thm)],[])).
% 1.94/2.17 tff(7258,plain,
% 1.94/2.17 (((~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(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.94/2.17 inference(rewrite,[status(thm)],[])).
% 1.94/2.17 tff(7259,plain,
% 1.94/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), 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(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(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 1.94/2.17 inference(monotonicity,[status(thm)],[7258])).
% 1.94/2.17 tff(7260,plain,
% 1.94/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), 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(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(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.94/2.17 inference(transitivity,[status(thm)],[7259, 7257])).
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% 1.94/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), 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(z)))), s(s(s(s(s(s(z)))))))))),
% 1.94/2.17 inference(quant_inst,[status(thm)],[])).
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% 1.94/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 1.94/2.17 inference(modus_ponens,[status(thm)],[7261, 7260])).
% 1.94/2.17 tff(7263,plain,
% 1.94/2.17 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.94/2.17 inference(unit_resolution,[status(thm)],[7262, 37, 7256, 7254])).
% 1.94/2.17 tff(7264,plain,
% 1.94/2.17 ($false),
% 1.94/2.17 inference(unit_resolution,[status(thm)],[7263, 7213])).
% 1.94/2.17 tff(7265,plain,((~r(elem!1, s(s(elem!1)))) | (~(elem!1 = s(s(s(s(z)))))) | (~r(z, elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.17 tff(7266,plain,
% 1.94/2.17 (~r(elem!1, s(s(elem!1)))),
% 1.94/2.17 inference(unit_resolution,[status(thm)],[7265, 270, 300, 114])).
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% 1.94/2.17 inference(unit_resolution,[status(thm)],[1617, 7266, 4563])).
% 1.94/2.17 tff(7268,plain,
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% 1.94/2.17 inference(unit_resolution,[status(thm)],[273, 270])).
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% 1.94/2.17 inference(unit_resolution,[status(thm)],[3664, 7268, 3656])).
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% 1.94/2.17 inference(unit_resolution,[status(thm)],[601, 7269, 108])).
% 1.94/2.17 tff(7271,plain,
% 1.94/2.17 (~(s(s(elem!1)) = elem!1)),
% 1.94/2.17 inference(unit_resolution,[status(thm)],[2555, 4563])).
% 1.94/2.17 tff(7272,plain,
% 1.94/2.17 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.94/2.17 inference(monotonicity,[status(thm)],[270])).
% 1.94/2.17 tff(7273,plain,
% 1.94/2.17 (r(s(s(elem!1)), s(s(s(s(z))))) <=> r(s(s(elem!1)), elem!1)),
% 1.94/2.17 inference(symmetry,[status(thm)],[7272])).
% 1.94/2.17 tff(7274,plain,
% 1.94/2.17 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) <=> r(s(s(elem!1)), elem!1)),
% 1.94/2.17 inference(transitivity,[status(thm)],[4558, 7273])).
% 1.94/2.17 tff(7275,plain,
% 1.94/2.17 ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) <=> (~r(s(s(elem!1)), elem!1))),
% 1.94/2.17 inference(monotonicity,[status(thm)],[7274])).
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% 1.94/2.17 (b(elem!1, s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.94/2.17 inference(monotonicity,[status(thm)],[270])).
% 1.94/2.17 tff(7277,plain,
% 1.94/2.17 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.94/2.17 inference(modus_ponens,[status(thm)],[7267, 7276])).
% 1.94/2.17 tff(7278,plain,
% 1.94/2.17 (r(z, elem!1) <=> r(z, s(s(s(s(z)))))),
% 1.94/2.17 inference(monotonicity,[status(thm)],[270])).
% 1.94/2.17 tff(7279,plain,
% 1.94/2.17 (r(z, s(s(s(s(z)))))),
% 1.94/2.17 inference(modus_ponens,[status(thm)],[300, 7278])).
% 1.94/2.17 tff(7280,plain,
% 1.94/2.17 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.94/2.17 inference(unit_resolution,[status(thm)],[5720, 1457, 578, 5712])).
% 1.94/2.17 tff(7281,plain,
% 1.94/2.17 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.94/2.17 inference(unit_resolution,[status(thm)],[1660, 7280, 1011])).
% 1.94/2.17 tff(7282,plain,
% 1.94/2.17 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.94/2.17 inference(modus_ponens,[status(thm)],[7281, 4559])).
% 1.94/2.17 tff(7283,plain,
% 1.94/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 1.94/2.17 inference(rewrite,[status(thm)],[])).
% 1.94/2.17 tff(7284,plain,
% 1.94/2.17 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), z))) <=> ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 1.94/2.17 inference(rewrite,[status(thm)],[])).
% 1.94/2.17 tff(7285,plain,
% 1.94/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), z))))),
% 1.94/2.17 inference(monotonicity,[status(thm)],[7284])).
% 1.94/2.17 tff(7286,plain,
% 1.94/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 1.94/2.17 inference(transitivity,[status(thm)],[7285, 7283])).
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% 1.94/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 1.94/2.17 inference(quant_inst,[status(thm)],[])).
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% 1.94/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), z))),
% 1.94/2.17 inference(modus_ponens,[status(thm)],[7287, 7286])).
% 1.94/2.17 tff(7289,plain,
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% 1.94/2.17 inference(unit_resolution,[status(thm)],[7288, 37, 7282, 2747])).
% 1.94/2.17 tff(7290,plain,
% 1.94/2.17 (((~![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))),
% 1.94/2.17 inference(rewrite,[status(thm)],[])).
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% 1.94/2.17 ((~![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))),
% 1.94/2.17 inference(quant_inst,[status(thm)],[])).
% 1.94/2.17 tff(7292,plain,
% 1.94/2.17 ((~![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)),
% 1.94/2.17 inference(modus_ponens,[status(thm)],[7291, 7290])).
% 1.94/2.17 tff(7293,plain,
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% 1.94/2.17 inference(unit_resolution,[status(thm)],[7292, 58, 717, 7289])).
% 1.94/2.17 tff(7294,plain,
% 1.94/2.17 (b(s(s(s(s(s(s(z)))))), s(z))),
% 1.94/2.17 inference(modus_ponens,[status(thm)],[1457, 7216])).
% 1.94/2.17 tff(7295,plain,
% 1.94/2.17 (b(elem!1, z) <=> b(s(s(s(s(z)))), z)),
% 1.94/2.17 inference(monotonicity,[status(thm)],[270])).
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% 1.94/2.17 (b(s(s(s(s(z)))), z) <=> b(elem!1, z)),
% 1.94/2.17 inference(symmetry,[status(thm)],[7295])).
% 1.94/2.17 tff(7297,plain,
% 1.94/2.17 ((~b(s(s(s(s(z)))), z)) <=> (~b(elem!1, z))),
% 1.94/2.17 inference(monotonicity,[status(thm)],[7296])).
% 1.94/2.17 tff(7298,plain,
% 1.94/2.17 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 1.94/2.17 inference(symmetry,[status(thm)],[7276])).
% 1.94/2.17 tff(7299,plain,
% 1.94/2.17 (b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.94/2.17 inference(monotonicity,[status(thm)],[4553])).
% 1.94/2.17 tff(7300,plain,
% 1.94/2.17 (b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) <=> b(elem!1, s(s(elem!1)))),
% 1.94/2.17 inference(transitivity,[status(thm)],[7299, 7298])).
% 1.94/2.17 tff(7301,plain,
% 1.94/2.17 ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) <=> (~b(elem!1, s(s(elem!1))))),
% 1.94/2.17 inference(monotonicity,[status(thm)],[7300])).
% 1.94/2.17 tff(7302,plain,
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% 1.94/2.17 inference(unit_resolution,[status(thm)],[7288, 37, 4601, 2747])).
% 1.94/2.17 tff(7303,plain,
% 1.94/2.17 (b(s(s(s(s(s(s(z)))))), z)),
% 1.94/2.17 inference(unit_resolution,[status(thm)],[7292, 58, 717, 7302])).
% 1.94/2.17 tff(7304,plain,
% 1.94/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~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, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 1.94/2.17 inference(rewrite,[status(thm)],[])).
% 1.94/2.17 tff(7305,plain,
% 1.94/2.17 (((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z))))))))) <=> ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 1.94/2.17 inference(rewrite,[status(thm)],[])).
% 1.94/2.17 tff(7306,plain,
% 1.94/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~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, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z))))))))))),
% 1.94/2.17 inference(monotonicity,[status(thm)],[7305])).
% 1.94/2.17 tff(7307,plain,
% 1.94/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~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, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 1.94/2.17 inference(transitivity,[status(thm)],[7306, 7304])).
% 1.94/2.17 tff(7308,plain,
% 1.94/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 1.94/2.17 inference(quant_inst,[status(thm)],[])).
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% 1.94/2.17 inference(modus_ponens,[status(thm)],[7308, 7307])).
% 1.94/2.17 tff(7310,plain,
% 1.94/2.17 (~r(z, s(s(s(s(s(s(z)))))))),
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% 1.94/2.17 tff(7311,plain,
% 1.94/2.17 ((z = s(s(s(s(s(s(z))))))) | b(z, s(s(s(s(s(s(z)))))))),
% 1.94/2.17 inference(unit_resolution,[status(thm)],[7231, 58, 7310])).
% 1.94/2.17 tff(7312,plain,
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% 1.94/2.17 inference(unit_resolution,[status(thm)],[7311, 7223])).
% 1.94/2.17 tff(7313,plain,
% 1.94/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.94/2.17 inference(rewrite,[status(thm)],[])).
% 1.94/2.17 tff(7314,plain,
% 1.94/2.17 (((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), 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(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.94/2.17 inference(rewrite,[status(thm)],[])).
% 1.94/2.17 tff(7315,plain,
% 1.94/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(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(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z))))))))))),
% 1.94/2.17 inference(monotonicity,[status(thm)],[7314])).
% 1.94/2.17 tff(7316,plain,
% 1.94/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(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(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.94/2.17 inference(transitivity,[status(thm)],[7315, 7313])).
% 1.94/2.17 tff(7317,plain,
% 1.94/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(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(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 1.94/2.18 inference(quant_inst,[status(thm)],[])).
% 1.94/2.18 tff(7318,plain,
% 1.94/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z))))))))),
% 1.94/2.18 inference(modus_ponens,[status(thm)],[7317, 7316])).
% 1.94/2.18 tff(7319,plain,
% 1.94/2.18 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.94/2.18 inference(unit_resolution,[status(thm)],[7318, 75, 1423, 7312, 7303])).
% 1.94/2.18 tff(7320,plain,
% 1.94/2.18 (~b(elem!1, s(s(elem!1)))),
% 1.94/2.18 inference(modus_ponens,[status(thm)],[7319, 7301])).
% 1.94/2.18 tff(7321,plain,
% 1.94/2.18 (r(elem!1, s(s(elem!1)))),
% 1.94/2.18 inference(unit_resolution,[status(thm)],[1617, 7320, 1630])).
% 1.94/2.18 tff(7322,plain,
% 1.94/2.18 (~r(s(z), s(s(elem!1)))),
% 1.94/2.18 inference(unit_resolution,[status(thm)],[3615, 7321, 114])).
% 1.94/2.18 tff(7323,plain,
% 1.94/2.18 (b(s(z), s(s(elem!1)))),
% 1.94/2.18 inference(unit_resolution,[status(thm)],[1890, 7322])).
% 1.94/2.18 tff(7324,plain,
% 1.94/2.18 (b(s(z), s(s(s(s(s(s(z)))))))),
% 1.94/2.18 inference(modus_ponens,[status(thm)],[7323, 7237])).
% 1.94/2.18 tff(7325,plain,
% 1.94/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.94/2.18 inference(rewrite,[status(thm)],[])).
% 1.94/2.18 tff(7326,plain,
% 1.94/2.18 (((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.94/2.18 inference(rewrite,[status(thm)],[])).
% 1.94/2.18 tff(7327,plain,
% 1.94/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z))))))))))),
% 1.94/2.18 inference(monotonicity,[status(thm)],[7326])).
% 1.94/2.18 tff(7328,plain,
% 1.94/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.94/2.18 inference(transitivity,[status(thm)],[7327, 7325])).
% 1.94/2.18 tff(7329,plain,
% 1.94/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(z))))),
% 1.94/2.18 inference(quant_inst,[status(thm)],[])).
% 1.94/2.18 tff(7330,plain,
% 1.94/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z))))))))),
% 1.94/2.18 inference(modus_ponens,[status(thm)],[7329, 7328])).
% 1.94/2.18 tff(7331,plain,
% 1.94/2.18 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 1.94/2.18 inference(unit_resolution,[status(thm)],[7330, 75, 372, 7312, 7303])).
% 1.94/2.18 tff(7332,plain,
% 1.94/2.18 ($false),
% 1.94/2.18 inference(unit_resolution,[status(thm)],[7331, 7324])).
% 1.94/2.18 tff(7333,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~(elem!1 = s(s(s(s(z)))))) | (~b(z, s(z))) | (~r(elem!1, s(z))) | (elem!1 = s(s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.18 tff(7334,plain,
% 1.94/2.18 (~b(s(s(s(s(z)))), z)),
% 1.94/2.18 inference(unit_resolution,[status(thm)],[7333, 7282, 372, 114, 1630, 270, 2747])).
% 1.94/2.18 tff(7335,plain,
% 1.94/2.18 (~b(elem!1, z)),
% 1.94/2.18 inference(modus_ponens,[status(thm)],[7334, 7297])).
% 1.94/2.18 tff(7336,plain,
% 1.94/2.18 (r(elem!1, z)),
% 1.94/2.18 inference(unit_resolution,[status(thm)],[387, 7335, 353])).
% 1.94/2.18 tff(7337,plain,
% 1.94/2.18 (~r(s(z), z)),
% 1.94/2.18 inference(unit_resolution,[status(thm)],[162, 7336, 114])).
% 1.94/2.18 tff(7338,plain,
% 1.94/2.18 (b(s(z), z)),
% 1.94/2.18 inference(unit_resolution,[status(thm)],[169, 7337])).
% 1.94/2.18 tff(7339,plain,
% 1.94/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))))), 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(X1, 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)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 1.94/2.18 inference(rewrite,[status(thm)],[])).
% 1.94/2.18 tff(7340,plain,
% 1.94/2.18 (((~b(z, s(z))) | (~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)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 1.94/2.18 inference(rewrite,[status(thm)],[])).
% 1.94/2.18 tff(7341,plain,
% 1.94/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z))))),
% 1.94/2.18 inference(monotonicity,[status(thm)],[7340])).
% 1.94/2.18 tff(7342,plain,
% 1.94/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 1.94/2.18 inference(transitivity,[status(thm)],[7341, 7339])).
% 1.94/2.18 tff(7343,plain,
% 1.94/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))),
% 1.94/2.18 inference(quant_inst,[status(thm)],[])).
% 1.94/2.18 tff(7344,plain,
% 1.94/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 1.94/2.18 inference(modus_ponens,[status(thm)],[7343, 7342])).
% 1.94/2.18 tff(7345,plain,
% 1.94/2.18 ($false),
% 1.94/2.18 inference(unit_resolution,[status(thm)],[7344, 75, 372, 7338, 7294, 7293])).
% 1.94/2.18 tff(7346,plain,((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~r(elem!1, s(z))) | (elem!1 = z) | (~(elem!1 = s(s(s(s(z)))))) | (elem!1 = s(s(elem!1))) | (~r(z, s(s(s(s(z)))))) | (s(s(elem!1)) = s(s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.18 tff(7347,plain,
% 1.94/2.18 (~b(s(s(elem!1)), s(z))),
% 1.94/2.18 inference(unit_resolution,[status(thm)],[7346, 270, 114, 305, 1049, 4563, 7279, 1011, 3657, 7277])).
% 1.94/2.18 tff(7348,plain,
% 1.94/2.18 (r(s(s(elem!1)), s(z))),
% 1.94/2.18 inference(unit_resolution,[status(thm)],[561, 7347])).
% 1.94/2.18 tff(7349,plain,
% 1.94/2.18 (r(s(s(s(s(s(s(z)))))), s(z))),
% 1.94/2.18 inference(modus_ponens,[status(thm)],[7348, 7215])).
% 1.94/2.18 tff(7350,plain,
% 1.94/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), 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(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 1.94/2.18 inference(rewrite,[status(thm)],[])).
% 1.94/2.18 tff(7351,plain,
% 1.94/2.18 (((~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(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 1.94/2.18 inference(rewrite,[status(thm)],[])).
% 1.94/2.18 tff(7352,plain,
% 1.94/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(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(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z)))))),
% 1.94/2.18 inference(monotonicity,[status(thm)],[7351])).
% 1.94/2.18 tff(7353,plain,
% 1.94/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(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(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 1.94/2.18 inference(transitivity,[status(thm)],[7352, 7350])).
% 1.94/2.18 tff(7354,plain,
% 1.94/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(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)))))))),
% 1.94/2.18 inference(quant_inst,[status(thm)],[])).
% 1.94/2.18 tff(7355,plain,
% 1.94/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z)))),
% 1.94/2.18 inference(modus_ponens,[status(thm)],[7354, 7353])).
% 1.94/2.18 tff(7356,plain,
% 1.94/2.18 ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z)))),
% 1.94/2.18 inference(unit_resolution,[status(thm)],[7355, 37, 7256])).
% 1.94/2.18 tff(7357,plain,
% 1.94/2.18 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.94/2.18 inference(unit_resolution,[status(thm)],[7356, 7349])).
% 1.94/2.18 tff(7358,plain,
% 1.94/2.18 (~r(s(s(elem!1)), elem!1)),
% 1.94/2.18 inference(modus_ponens,[status(thm)],[7357, 7275])).
% 1.94/2.18 tff(7359,plain,
% 1.94/2.18 (b(s(s(elem!1)), elem!1)),
% 1.94/2.18 inference(unit_resolution,[status(thm)],[2673, 7358, 7271])).
% 1.94/2.18 tff(7360,plain,
% 1.94/2.18 ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) <=> (~r(s(s(elem!1)), s(s(s(s(z))))))),
% 1.94/2.18 inference(monotonicity,[status(thm)],[4558])).
% 1.94/2.18 tff(7361,plain,
% 1.94/2.18 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.94/2.18 inference(modus_ponens,[status(thm)],[7357, 7360])).
% 1.94/2.18 tff(7362,plain,
% 1.94/2.18 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.94/2.18 inference(unit_resolution,[status(thm)],[1660, 7361, 1011])).
% 1.94/2.18 tff(7363,plain,
% 1.94/2.18 (r(s(s(s(s(s(s(z)))))), s(s(z))) <=> r(s(s(elem!1)), s(s(z)))),
% 1.94/2.18 inference(monotonicity,[status(thm)],[4553])).
% 1.94/2.18 tff(7364,plain,
% 1.94/2.18 (r(s(s(elem!1)), s(s(z))) <=> r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.94/2.18 inference(symmetry,[status(thm)],[7363])).
% 1.94/2.18 tff(7365,plain,
% 1.94/2.18 (b(s(s(elem!1)), s(s(z))) <=> b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.94/2.18 inference(monotonicity,[status(thm)],[4466])).
% 1.94/2.18 tff(7366,plain,
% 1.94/2.18 (b(s(s(s(s(s(s(z)))))), s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 1.94/2.18 inference(symmetry,[status(thm)],[7365])).
% 1.94/2.18 tff(7367,plain,
% 1.94/2.18 ((~b(s(s(s(s(s(s(z)))))), s(s(z)))) <=> (~b(s(s(elem!1)), s(s(z))))),
% 1.94/2.18 inference(monotonicity,[status(thm)],[7366])).
% 1.94/2.18 tff(7368,plain,
% 1.94/2.18 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.94/2.18 inference(symmetry,[status(thm)],[7299])).
% 1.94/2.18 tff(7369,plain,
% 1.94/2.18 (b(elem!1, s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.94/2.18 inference(transitivity,[status(thm)],[7276, 7368])).
% 1.94/2.18 tff(7370,plain,
% 1.94/2.18 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.94/2.18 inference(modus_ponens,[status(thm)],[1620, 7369])).
% 1.94/2.18 tff(7371,plain,
% 1.94/2.18 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.94/2.18 inference(symmetry,[status(thm)],[4565])).
% 1.94/2.18 tff(7372,plain,
% 1.94/2.18 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.94/2.18 inference(modus_ponens,[status(thm)],[1619, 7371])).
% 1.94/2.18 tff(7373,plain,
% 1.94/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(z)))))),
% 1.94/2.18 inference(rewrite,[status(thm)],[])).
% 1.94/2.18 tff(7374,plain,
% 1.94/2.18 (((~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(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(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(z))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 1.94/2.18 inference(rewrite,[status(thm)],[])).
% 1.94/2.18 tff(7375,plain,
% 1.94/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(s(s(s(z)))))))) | (~b(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(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(z))))))),
% 1.94/2.18 inference(monotonicity,[status(thm)],[7374])).
% 1.94/2.18 tff(7376,plain,
% 1.94/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(s(s(s(z)))))))) | (~b(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(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(z)))))),
% 1.94/2.18 inference(transitivity,[status(thm)],[7375, 7373])).
% 1.94/2.18 tff(7377,plain,
% 1.94/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(s(s(s(z)))))))) | (~b(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(z)))))),
% 1.94/2.18 inference(quant_inst,[status(thm)],[])).
% 1.94/2.18 tff(7378,plain,
% 1.94/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(z))))),
% 1.94/2.18 inference(modus_ponens,[status(thm)],[7377, 7376])).
% 1.94/2.18 tff(7379,plain,
% 1.94/2.18 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.94/2.18 inference(unit_resolution,[status(thm)],[7378, 75, 895, 7372, 7370])).
% 1.94/2.18 tff(7380,plain,
% 1.94/2.18 (~b(s(s(elem!1)), s(s(z)))),
% 1.94/2.18 inference(modus_ponens,[status(thm)],[7379, 7367])).
% 1.94/2.18 tff(7381,plain,
% 1.94/2.18 (r(s(s(elem!1)), s(s(z)))),
% 1.94/2.18 inference(unit_resolution,[status(thm)],[1476, 7380, 266])).
% 1.94/2.18 tff(7382,plain,
% 1.94/2.18 (r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 1.94/2.18 inference(modus_ponens,[status(thm)],[7381, 7364])).
% 1.94/2.18 tff(7383,plain,
% 1.94/2.18 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.94/2.18 inference(modus_ponens,[status(thm)],[1620, 7276])).
% 1.94/2.18 tff(7384,plain,
% 1.94/2.18 (~b(s(s(elem!1)), s(z))),
% 1.94/2.18 inference(unit_resolution,[status(thm)],[5720, 7383, 578, 1619])).
% 1.94/2.18 tff(7385,plain,
% 1.94/2.18 (r(s(s(elem!1)), s(z))),
% 1.94/2.18 inference(unit_resolution,[status(thm)],[561, 7384])).
% 1.94/2.18 tff(7386,plain,
% 1.94/2.18 (r(s(s(s(s(s(s(z)))))), s(z))),
% 1.94/2.18 inference(modus_ponens,[status(thm)],[7385, 7215])).
% 1.94/2.18 tff(7387,plain,
% 1.94/2.18 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(s(z)))))),
% 1.94/2.18 inference(monotonicity,[status(thm)],[270])).
% 1.94/2.18 tff(7388,plain,
% 1.94/2.18 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(z)), elem!1)),
% 1.94/2.18 inference(symmetry,[status(thm)],[7387])).
% 1.94/2.18 tff(7389,plain,
% 1.94/2.18 (b(s(s(z)), elem!1)),
% 1.94/2.18 inference(modus_ponens,[status(thm)],[895, 7388])).
% 1.94/2.18 tff(7390,plain,
% 1.94/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(z), elem!1)))),
% 1.94/2.18 inference(rewrite,[status(thm)],[])).
% 1.94/2.18 tff(7391,plain,
% 1.94/2.18 (((~b(s(s(elem!1)), elem!1)) | (~b(s(z), 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(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(z), elem!1)))),
% 1.94/2.18 inference(rewrite,[status(thm)],[])).
% 1.94/2.18 tff(7392,plain,
% 1.94/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), 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(X1, 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)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(z), elem!1))))),
% 1.94/2.18 inference(monotonicity,[status(thm)],[7391])).
% 1.94/2.18 tff(7393,plain,
% 1.94/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), 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(X1, 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)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(z), elem!1)))),
% 1.94/2.19 inference(transitivity,[status(thm)],[7392, 7390])).
% 1.94/2.19 tff(7394,plain,
% 1.94/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), 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))))),
% 1.94/2.19 inference(quant_inst,[status(thm)],[])).
% 1.94/2.19 tff(7395,plain,
% 1.94/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(z), elem!1))),
% 1.94/2.19 inference(modus_ponens,[status(thm)],[7394, 7393])).
% 1.94/2.19 tff(7396,plain,
% 1.94/2.19 ($false),
% 1.94/2.19 inference(unit_resolution,[status(thm)],[7395, 75, 107, 1620, 964, 309, 707])).
% 1.94/2.19 tff(7397,plain,((~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.19 tff(7398,plain,
% 1.94/2.19 (~b(s(s(z)), s(z))),
% 1.94/2.19 inference(unit_resolution,[status(thm)],[7397, 1620, 7389, 107, 707])).
% 1.94/2.19 tff(7399,plain,
% 1.94/2.19 (r(s(s(z)), s(z))),
% 1.94/2.19 inference(unit_resolution,[status(thm)],[153, 7398])).
% 1.94/2.19 tff(7400,plain,
% 1.94/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(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(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 1.94/2.19 inference(rewrite,[status(thm)],[])).
% 1.94/2.19 tff(7401,plain,
% 1.94/2.19 (((~r(s(s(z)), s(z))) | (~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(s(z))))) <=> ((~r(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(z)))))),
% 1.94/2.19 inference(rewrite,[status(thm)],[])).
% 1.94/2.19 tff(7402,plain,
% 1.94/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~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(s(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(s(s(s(s(z)))))), s(s(z))))))),
% 1.94/2.19 inference(monotonicity,[status(thm)],[7401])).
% 1.94/2.19 tff(7403,plain,
% 1.94/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~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(s(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(s(s(s(s(z)))))), s(s(z)))))),
% 1.94/2.19 inference(transitivity,[status(thm)],[7402, 7400])).
% 1.94/2.19 tff(7404,plain,
% 1.94/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~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(s(z)))))),
% 1.94/2.19 inference(quant_inst,[status(thm)],[])).
% 1.94/2.19 tff(7405,plain,
% 1.94/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(z))))),
% 1.94/2.19 inference(modus_ponens,[status(thm)],[7404, 7403])).
% 1.94/2.19 tff(7406,plain,
% 1.94/2.19 ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(z))))),
% 1.94/2.19 inference(unit_resolution,[status(thm)],[7405, 37, 7399])).
% 1.94/2.19 tff(7407,plain,
% 1.94/2.19 ($false),
% 1.94/2.19 inference(unit_resolution,[status(thm)],[7406, 7386, 7382])).
% 1.94/2.19 tff(7408,plain,((~b(elem!1, s(s(elem!1)))) | (~(elem!1 = s(s(s(s(z)))))) | (s(s(elem!1)) = s(s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.19 tff(7409,plain,
% 1.94/2.19 ($false),
% 1.94/2.19 inference(unit_resolution,[status(thm)],[7408, 7362, 7359, 266, 3657, 270, 895, 7270, 7267])).
% 1.94/2.19 tff(7410,plain,((~(elem!1 = s(s(s(s(z)))))) | (s(s(elem!1)) = s(s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (s(s(elem!1)) = s(s(s(s(z))))) | (~r(elem!1, s(z))) | (~r(z, elem!1)) | (s(z) = elem!1) | r(s(z), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.19 tff(7411,plain,
% 1.94/2.19 (~(elem!1 = s(s(s(s(z)))))),
% 1.94/2.19 inference(unit_resolution,[status(thm)],[7410, 113, 895, 1011, 266, 300, 108, 3656])).
% 1.94/2.19 tff(7412,plain,
% 1.94/2.19 (~(s(s(s(s(z)))) = elem!1)),
% 1.94/2.19 inference(modus_ponens,[status(thm)],[7411, 4532])).
% 1.94/2.19 tff(7413,plain,
% 1.94/2.19 (b(s(s(s(s(z)))), elem!1)),
% 1.94/2.19 inference(unit_resolution,[status(thm)],[283, 7412, 7208])).
% 1.94/2.19 tff(7414,plain,
% 1.94/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(elem!1, 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, elem!1)) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 1.94/2.19 inference(rewrite,[status(thm)],[])).
% 1.94/2.19 tff(7415,plain,
% 1.94/2.19 (((~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 1.94/2.19 inference(rewrite,[status(thm)],[])).
% 1.94/2.19 tff(7416,plain,
% 1.94/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))))),
% 1.94/2.19 inference(monotonicity,[status(thm)],[7415])).
% 1.94/2.19 tff(7417,plain,
% 1.94/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 1.94/2.19 inference(transitivity,[status(thm)],[7416, 7414])).
% 1.94/2.19 tff(7418,plain,
% 1.94/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~r(z, elem!1)))),
% 1.94/2.19 inference(quant_inst,[status(thm)],[])).
% 1.94/2.19 tff(7419,plain,
% 1.94/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))),
% 1.94/2.19 inference(modus_ponens,[status(thm)],[7418, 7417])).
% 1.94/2.19 tff(7420,plain,
% 1.94/2.19 ($false),
% 1.94/2.19 inference(unit_resolution,[status(thm)],[7419, 37, 300, 114, 3195, 2747])).
% 1.94/2.19 tff(7421,plain,((~r(z, s(s(s(s(z)))))) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.19 tff(7422,plain,
% 1.94/2.19 (~r(z, s(s(s(s(z)))))),
% 1.94/2.19 inference(unit_resolution,[status(thm)],[7421, 3195, 114, 300])).
% 1.94/2.19 tff(7423,plain,
% 1.94/2.19 ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z)))))),
% 1.94/2.19 inference(unit_resolution,[status(thm)],[1515, 58, 7422])).
% 1.94/2.19 tff(7424,plain,
% 1.94/2.19 (b(z, s(s(s(s(z)))))),
% 1.94/2.19 inference(unit_resolution,[status(thm)],[7423, 1503])).
% 1.94/2.19 tff(7425,plain,
% 1.94/2.19 (~b(s(s(s(s(z)))), s(z))),
% 1.94/2.19 inference(unit_resolution,[status(thm)],[6153, 7424, 578, 1049])).
% 1.94/2.19 tff(7426,plain,
% 1.94/2.19 (r(s(s(s(s(z)))), s(z))),
% 1.94/2.19 inference(unit_resolution,[status(thm)],[1406, 58, 7425, 483])).
% 1.94/2.19 tff(7427,plain,
% 1.94/2.19 ($false),
% 1.94/2.19 inference(unit_resolution,[status(thm)],[3249, 37, 114, 3195, 7426])).
% 1.94/2.19 tff(7428,plain,((~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.19 tff(7429,plain,
% 1.94/2.19 (~r(elem!1, s(s(s(s(z)))))),
% 1.94/2.19 inference(unit_resolution,[status(thm)],[7428, 113, 3657, 300])).
% 1.94/2.19 tff(7430,plain,
% 1.94/2.19 (b(elem!1, s(s(s(s(z)))))),
% 1.94/2.19 inference(unit_resolution,[status(thm)],[278, 7411, 7429])).
% 1.94/2.19 tff(7431,plain,
% 1.94/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(z)))) | (~b(s(s(z)), s(s(s(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(X1, 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(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.94/2.19 inference(rewrite,[status(thm)],[])).
% 1.94/2.19 tff(7432,plain,
% 1.94/2.19 (((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(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, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.94/2.19 inference(rewrite,[status(thm)],[])).
% 1.94/2.19 tff(7433,plain,
% 1.94/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(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)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z))))))))),
% 1.94/2.19 inference(monotonicity,[status(thm)],[7432])).
% 1.94/2.19 tff(7434,plain,
% 1.94/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(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)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.94/2.19 inference(transitivity,[status(thm)],[7433, 7431])).
% 1.94/2.19 tff(7435,plain,
% 1.94/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(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)))))) | (~b(s(z), s(s(z)))))),
% 1.94/2.19 inference(quant_inst,[status(thm)],[])).
% 1.94/2.19 tff(7436,plain,
% 1.94/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z))))))),
% 1.94/2.19 inference(modus_ponens,[status(thm)],[7435, 7434])).
% 1.94/2.19 tff(7437,plain,
% 1.94/2.19 (~b(s(z), s(s(z)))),
% 1.94/2.19 inference(unit_resolution,[status(thm)],[7436, 75, 3657, 7430, 7413, 895])).
% 1.94/2.19 tff(7438,plain,
% 1.94/2.19 (r(s(z), s(s(z)))),
% 1.94/2.19 inference(unit_resolution,[status(thm)],[416, 7437])).
% 1.94/2.19 tff(7439,plain,
% 1.94/2.19 (~b(s(s(z)), s(z))),
% 1.94/2.19 inference(unit_resolution,[status(thm)],[3918, 75, 3657, 7430, 7413, 895])).
% 1.94/2.19 tff(7440,plain,
% 1.94/2.19 (r(s(s(z)), s(z))),
% 1.94/2.19 inference(unit_resolution,[status(thm)],[153, 7439])).
% 1.94/2.19 tff(7441,plain,
% 1.94/2.19 (((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.94/2.19 inference(rewrite,[status(thm)],[])).
% 1.94/2.19 tff(7442,plain,
% 1.94/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~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(X1, 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(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.94/2.19 inference(monotonicity,[status(thm)],[7441])).
% 1.94/2.19 tff(7443,plain,
% 1.94/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~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(X1, 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(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.94/2.19 inference(transitivity,[status(thm)],[7442, 4813])).
% 1.94/2.19 tff(7444,plain,
% 1.94/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 1.94/2.19 inference(quant_inst,[status(thm)],[])).
% 1.94/2.19 tff(7445,plain,
% 1.94/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))),
% 1.94/2.19 inference(modus_ponens,[status(thm)],[7444, 7443])).
% 1.94/2.19 tff(7446,plain,
% 1.94/2.19 (~b(s(s(z)), elem!1)),
% 1.94/2.19 inference(unit_resolution,[status(thm)],[7445, 75, 7430, 7413, 895])).
% 1.94/2.19 tff(7447,plain,
% 1.94/2.19 (r(s(s(z)), elem!1)),
% 1.94/2.19 inference(unit_resolution,[status(thm)],[104, 7446, 2219])).
% 1.94/2.19 tff(7448,plain,
% 1.94/2.19 (~b(s(z), elem!1)),
% 1.94/2.19 inference(unit_resolution,[status(thm)],[586, 7413, 3657, 7430])).
% 1.94/2.19 tff(7449,plain,
% 1.94/2.19 (r(s(z), elem!1)),
% 1.94/2.19 inference(unit_resolution,[status(thm)],[601, 7448, 108])).
% 1.94/2.19 tff(7450,plain,
% 1.94/2.19 (((~![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(z)))) | (~r(s(s(z)), 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(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))),
% 1.94/2.19 inference(rewrite,[status(thm)],[])).
% 1.94/2.19 tff(7451,plain,
% 1.94/2.19 (((~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))),
% 1.94/2.20 inference(rewrite,[status(thm)],[])).
% 1.94/2.20 tff(7452,plain,
% 1.94/2.20 (((~![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)), 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(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1))))),
% 1.94/2.20 inference(monotonicity,[status(thm)],[7451])).
% 1.94/2.20 tff(7453,plain,
% 1.94/2.20 (((~![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)), 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(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))),
% 1.94/2.20 inference(transitivity,[status(thm)],[7452, 7450])).
% 1.94/2.20 tff(7454,plain,
% 1.94/2.20 ((~![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)), s(z))) | (~r(s(z), s(s(z)))))),
% 1.94/2.20 inference(quant_inst,[status(thm)],[])).
% 1.94/2.20 tff(7455,plain,
% 1.94/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1))),
% 1.94/2.20 inference(modus_ponens,[status(thm)],[7454, 7453])).
% 1.94/2.20 tff(7456,plain,
% 1.94/2.20 ($false),
% 1.94/2.20 inference(unit_resolution,[status(thm)],[7455, 37, 7449, 7447, 7440, 7438])).
% 1.94/2.20 tff(7457,plain,((s(z) = elem!1) | (~b(s(s(z)), s(s(s(s(z)))))) | (s(s(elem!1)) = s(s(s(s(z))))) | (s(s(elem!1)) = s(s(z))) | (~r(z, elem!1)) | r(s(z), s(s(s(s(z))))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.20 tff(7458,plain,
% 1.94/2.20 (b(elem!1, s(z))),
% 1.94/2.20 inference(unit_resolution,[status(thm)],[7457, 7205, 1011, 266, 300, 3656, 895])).
% 1.94/2.20 tff(7459,plain,
% 1.94/2.20 (b(s(z), elem!1)),
% 1.94/2.20 inference(unit_resolution,[status(thm)],[601, 1395, 7205])).
% 1.94/2.20 tff(7460,plain,
% 1.94/2.20 (~b(s(s(s(s(z)))), elem!1)),
% 1.94/2.20 inference(unit_resolution,[status(thm)],[5527, 7459, 7458, 3657])).
% 1.94/2.20 tff(7461,plain,
% 1.94/2.20 (s(s(s(s(z)))) = elem!1),
% 1.94/2.20 inference(unit_resolution,[status(thm)],[283, 7460, 7204])).
% 1.94/2.20 tff(7462,plain,
% 1.94/2.20 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(z)), elem!1)),
% 1.94/2.20 inference(monotonicity,[status(thm)],[7461])).
% 1.94/2.20 tff(7463,plain,
% 1.94/2.20 (b(s(s(z)), elem!1)),
% 1.94/2.20 inference(modus_ponens,[status(thm)],[895, 7462])).
% 1.94/2.20 tff(7464,plain,
% 1.94/2.20 (~b(s(s(s(z))), s(z))),
% 1.94/2.20 inference(unit_resolution,[status(thm)],[991, 983, 578, 6136])).
% 1.94/2.20 tff(7465,plain,
% 1.94/2.20 (r(s(s(s(z))), s(z))),
% 1.94/2.20 inference(unit_resolution,[status(thm)],[1081, 7464])).
% 1.94/2.20 tff(7466,plain,
% 1.94/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.94/2.20 inference(rewrite,[status(thm)],[])).
% 1.94/2.20 tff(7467,plain,
% 1.94/2.20 (((~b(s(z), elem!1)) | (~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(s(z)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.94/2.20 inference(rewrite,[status(thm)],[])).
% 1.94/2.20 tff(7468,plain,
% 1.94/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))))),
% 2.02/2.20 inference(monotonicity,[status(thm)],[7467])).
% 2.02/2.20 tff(7469,plain,
% 2.02/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 2.02/2.20 inference(transitivity,[status(thm)],[7468, 7466])).
% 2.02/2.20 tff(7470,plain,
% 2.02/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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))))),
% 2.02/2.20 inference(quant_inst,[status(thm)],[])).
% 2.02/2.20 tff(7471,plain,
% 2.02/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))),
% 2.02/2.20 inference(modus_ponens,[status(thm)],[7470, 7469])).
% 2.02/2.20 tff(7472,plain,
% 2.02/2.20 (~b(s(s(z)), s(z))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[7471, 75, 107, 1391, 964])).
% 2.02/2.20 tff(7473,plain,
% 2.02/2.20 (r(s(s(z)), s(z))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[153, 7472])).
% 2.02/2.20 tff(7474,plain,
% 2.02/2.20 (~r(s(s(z)), s(s(s(z))))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[6500, 37, 7473, 7465])).
% 2.02/2.20 tff(7475,plain,
% 2.02/2.20 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(z))), elem!1)),
% 2.02/2.20 inference(monotonicity,[status(thm)],[3285])).
% 2.02/2.20 tff(7476,plain,
% 2.02/2.20 (b(s(s(s(z))), elem!1)),
% 2.02/2.20 inference(modus_ponens,[status(thm)],[983, 7475])).
% 2.02/2.20 tff(7477,plain,
% 2.02/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(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(X1, 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(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(s(s(z))))))),
% 2.02/2.20 inference(rewrite,[status(thm)],[])).
% 2.02/2.20 tff(7478,plain,
% 2.02/2.20 (((~b(s(z), elem!1)) | (~b(s(s(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(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(s(s(z))))))),
% 2.02/2.20 inference(rewrite,[status(thm)],[])).
% 2.02/2.20 tff(7479,plain,
% 2.02/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), 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(X1, 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(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(s(s(z)))))))),
% 2.02/2.20 inference(monotonicity,[status(thm)],[7478])).
% 2.02/2.20 tff(7480,plain,
% 2.02/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), 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(X1, 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(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(s(s(z))))))),
% 2.02/2.20 inference(transitivity,[status(thm)],[7479, 7477])).
% 2.02/2.20 tff(7481,plain,
% 2.02/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), 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))))))),
% 2.02/2.20 inference(quant_inst,[status(thm)],[])).
% 2.02/2.20 tff(7482,plain,
% 2.02/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(s(s(z)))))),
% 2.02/2.20 inference(modus_ponens,[status(thm)],[7481, 7480])).
% 2.02/2.20 tff(7483,plain,
% 2.02/2.20 (~b(s(s(z)), s(s(s(z))))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[7482, 75, 107, 1391, 964, 7476])).
% 2.02/2.20 tff(7484,plain,
% 2.02/2.20 ($false),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[1559, 58, 1556, 7483, 7474])).
% 2.02/2.20 tff(7485,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~(s(s(s(s(z)))) = elem!1)) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.20 tff(7486,plain,
% 2.02/2.20 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[7485, 7459, 7458, 7463, 7461, 3657])).
% 2.02/2.20 tff(7487,plain,
% 2.02/2.20 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[575, 7486])).
% 2.02/2.20 tff(7488,plain,
% 2.02/2.20 (r(s(s(s(z))), elem!1)),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[6396, 7487, 7461])).
% 2.02/2.20 tff(7489,plain,
% 2.02/2.20 (~r(s(s(s(z))), z)),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[1330, 37, 300, 7488])).
% 2.02/2.20 tff(7490,plain,
% 2.02/2.20 (r(s(s(elem!1)), s(s(s(s(z))))) <=> r(s(s(elem!1)), elem!1)),
% 2.02/2.20 inference(monotonicity,[status(thm)],[7461])).
% 2.02/2.20 tff(7491,plain,
% 2.02/2.20 (elem!1 = s(s(s(s(z))))),
% 2.02/2.20 inference(modus_ponens,[status(thm)],[7461, 239])).
% 2.02/2.20 tff(7492,plain,
% 2.02/2.20 (~b(s(s(z)), s(z))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[7471, 75, 7459, 7458, 7463])).
% 2.02/2.20 tff(7493,plain,
% 2.02/2.20 (r(s(s(z)), s(z))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[153, 7492])).
% 2.02/2.20 tff(7494,plain,
% 2.02/2.20 (~r(s(s(elem!1)), s(z))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[548, 7493, 506, 300, 266])).
% 2.02/2.20 tff(7495,plain,
% 2.02/2.20 (b(s(s(elem!1)), s(z))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[561, 7494])).
% 2.02/2.20 tff(7496,plain,
% 2.02/2.20 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.02/2.20 inference(monotonicity,[status(thm)],[270])).
% 2.02/2.20 tff(7497,plain,
% 2.02/2.20 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(s(s(elem!1)), elem!1)),
% 2.02/2.20 inference(symmetry,[status(thm)],[7496])).
% 2.02/2.20 tff(7498,plain,
% 2.02/2.20 (b(s(s(elem!1)), elem!1)),
% 2.02/2.20 inference(modus_ponens,[status(thm)],[1619, 7497])).
% 2.02/2.20 tff(7499,plain,
% 2.02/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(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(X1, 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(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.02/2.20 inference(rewrite,[status(thm)],[])).
% 2.02/2.20 tff(7500,plain,
% 2.02/2.20 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.02/2.20 inference(rewrite,[status(thm)],[])).
% 2.02/2.20 tff(7501,plain,
% 2.02/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))))),
% 2.02/2.20 inference(monotonicity,[status(thm)],[7500])).
% 2.02/2.20 tff(7502,plain,
% 2.02/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.02/2.20 inference(transitivity,[status(thm)],[7501, 7499])).
% 2.02/2.20 tff(7503,plain,
% 2.02/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 2.02/2.20 inference(quant_inst,[status(thm)],[])).
% 2.02/2.20 tff(7504,plain,
% 2.02/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))),
% 2.02/2.20 inference(modus_ponens,[status(thm)],[7503, 7502])).
% 2.02/2.20 tff(7505,plain,
% 2.02/2.20 ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[7504, 75, 1457, 1391, 3657, 1619])).
% 2.02/2.20 tff(7506,plain,
% 2.02/2.20 (~b(s(s(elem!1)), elem!1)),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[7505, 7270])).
% 2.02/2.20 tff(7507,plain,
% 2.02/2.20 ($false),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[7506, 7498])).
% 2.02/2.20 tff(7508,plain,((~(elem!1 = s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (s(z) = elem!1) | r(s(z), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.20 tff(7509,plain,
% 2.02/2.20 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[7508, 7495, 7458, 7491, 7205, 3656])).
% 2.02/2.20 tff(7510,plain,
% 2.02/2.20 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[1660, 7509, 1011])).
% 2.02/2.20 tff(7511,plain,
% 2.02/2.20 (r(s(s(elem!1)), elem!1)),
% 2.02/2.20 inference(modus_ponens,[status(thm)],[7510, 7490])).
% 2.02/2.20 tff(7512,plain,
% 2.02/2.20 (~r(s(s(elem!1)), z)),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[5114, 37, 300, 7511])).
% 2.02/2.20 tff(7513,plain,
% 2.02/2.20 (b(s(s(elem!1)), z)),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[2696, 7512])).
% 2.02/2.20 tff(7514,plain,
% 2.02/2.20 ((s(s(elem!1)) = s(s(s(s(z))))) <=> (s(s(elem!1)) = elem!1)),
% 2.02/2.20 inference(monotonicity,[status(thm)],[7461])).
% 2.02/2.20 tff(7515,plain,
% 2.02/2.20 ((s(s(elem!1)) = s(s(s(s(z))))) <=> (elem!1 = s(s(elem!1)))),
% 2.02/2.20 inference(transitivity,[status(thm)],[7514, 3428])).
% 2.02/2.20 tff(7516,plain,
% 2.02/2.20 ((~(s(s(elem!1)) = s(s(s(s(z)))))) <=> (~(elem!1 = s(s(elem!1))))),
% 2.02/2.20 inference(monotonicity,[status(thm)],[7515])).
% 2.02/2.20 tff(7517,plain,
% 2.02/2.20 (~(elem!1 = s(s(elem!1)))),
% 2.02/2.20 inference(modus_ponens,[status(thm)],[1011, 7516])).
% 2.02/2.20 tff(7518,plain,
% 2.02/2.20 (~b(elem!1, s(s(elem!1)))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[1638, 7495, 7458, 7459])).
% 2.02/2.20 tff(7519,plain,
% 2.02/2.20 (r(elem!1, s(s(elem!1)))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[1617, 7518, 7517])).
% 2.02/2.20 tff(7520,plain,
% 2.02/2.20 (~r(z, s(s(elem!1)))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[2372, 7519, 300])).
% 2.02/2.20 tff(7521,plain,
% 2.02/2.20 ((z = s(s(elem!1))) | b(z, s(s(elem!1)))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[1834, 58, 7520])).
% 2.02/2.20 tff(7522,plain,
% 2.02/2.20 (b(z, s(s(elem!1)))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[7521, 1824])).
% 2.02/2.20 tff(7523,plain,
% 2.02/2.20 (~(s(s(z)) = s(elem!1))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[3261, 7205])).
% 2.02/2.20 tff(7524,plain,
% 2.02/2.20 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[4541, 7523])).
% 2.02/2.20 tff(7525,plain,
% 2.02/2.20 (s(s(s(s(s(z))))) = s(elem!1)),
% 2.02/2.20 inference(monotonicity,[status(thm)],[7461])).
% 2.02/2.20 tff(7526,plain,
% 2.02/2.20 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 2.02/2.20 inference(monotonicity,[status(thm)],[7525])).
% 2.02/2.20 tff(7527,plain,
% 2.02/2.20 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) <=> r(s(s(elem!1)), elem!1)),
% 2.02/2.20 inference(monotonicity,[status(thm)],[7526, 7461])).
% 2.02/2.20 tff(7528,plain,
% 2.02/2.20 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.02/2.20 inference(symmetry,[status(thm)],[7527])).
% 2.02/2.20 tff(7529,plain,
% 2.02/2.20 (r(s(s(elem!1)), s(s(s(s(z))))) <=> r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.02/2.20 inference(transitivity,[status(thm)],[7490, 7528])).
% 2.02/2.20 tff(7530,plain,
% 2.02/2.20 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.02/2.20 inference(modus_ponens,[status(thm)],[7510, 7529])).
% 2.02/2.20 tff(7531,plain,
% 2.02/2.20 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[4613, 7487, 7491, 7530])).
% 2.02/2.20 tff(7532,plain,
% 2.02/2.20 (b(s(s(s(z))), s(s(elem!1)))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[62, 7531, 7524])).
% 2.02/2.20 tff(7533,plain,
% 2.02/2.20 (((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.02/2.20 inference(rewrite,[status(thm)],[])).
% 2.02/2.20 tff(7534,plain,
% 2.02/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), z)) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 2.02/2.20 inference(monotonicity,[status(thm)],[7533])).
% 2.02/2.20 tff(7535,plain,
% 2.02/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.02/2.20 inference(transitivity,[status(thm)],[7534, 5569])).
% 2.02/2.20 tff(7536,plain,
% 2.02/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), z)))),
% 2.02/2.20 inference(quant_inst,[status(thm)],[])).
% 2.02/2.20 tff(7537,plain,
% 2.02/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1))))),
% 2.02/2.20 inference(modus_ponens,[status(thm)],[7536, 7535])).
% 2.02/2.21 tff(7538,plain,
% 2.02/2.21 (~b(s(s(s(z))), z)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[7537, 75, 7532, 7522, 7513])).
% 2.02/2.21 tff(7539,plain,
% 2.02/2.21 ($false),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[1334, 58, 221, 7538, 7489])).
% 2.02/2.21 tff(7540,plain,((~r(z, s(z))) | (~r(z, elem!1)) | (s(s(elem!1)) = s(s(s(s(z))))) | r(s(z), s(s(s(s(z))))) | (s(s(elem!1)) = s(s(z))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.21 tff(7541,plain,
% 2.02/2.21 (~r(z, s(z))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[7540, 7155, 1011, 3656, 266, 895])).
% 2.02/2.21 tff(7542,plain,
% 2.02/2.21 (b(z, s(z))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[187, 7541])).
% 2.02/2.21 tff(7543,plain,
% 2.02/2.21 (b(elem!1, s(z))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[7457, 7156, 1011, 266, 7155, 3656, 895])).
% 2.02/2.21 tff(7544,plain,
% 2.02/2.21 (~r(s(s(s(s(z)))), elem!1)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[7203, 300, 895, 578])).
% 2.02/2.21 tff(7545,plain,
% 2.02/2.21 (b(s(s(s(s(z)))), elem!1)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[283, 267, 7544])).
% 2.02/2.21 tff(7546,plain,
% 2.02/2.21 (~b(elem!1, s(s(s(s(z)))))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[1438, 7545, 578, 1391])).
% 2.02/2.21 tff(7547,plain,
% 2.02/2.21 (r(elem!1, s(s(s(s(z)))))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[278, 7546, 274])).
% 2.02/2.21 tff(7548,plain,
% 2.02/2.21 (~(s(s(z)) = s(s(elem!1)))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[6319, 266])).
% 2.02/2.21 tff(7549,plain,
% 2.02/2.21 (~(s(z) = elem!1)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[998, 300, 578, 266, 2219, 895])).
% 2.02/2.21 tff(7550,plain,
% 2.02/2.21 (~b(s(z), elem!1)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[5527, 7545, 1391, 578])).
% 2.02/2.21 tff(7551,plain,
% 2.02/2.21 (r(s(z), elem!1)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[601, 7550, 7549])).
% 2.02/2.21 tff(7552,plain,
% 2.02/2.21 (~r(s(s(z)), elem!1)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[2083, 7551, 372, 300])).
% 2.02/2.21 tff(7553,plain,
% 2.02/2.21 (b(s(s(z)), elem!1)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[104, 7552, 2219])).
% 2.02/2.21 tff(7554,plain,
% 2.02/2.21 ($false),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[1237, 37, 300, 588, 1561])).
% 2.02/2.21 tff(7555,plain,((~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.21 tff(7556,plain,
% 2.02/2.21 (~r(s(z), z)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[7555, 7551, 300])).
% 2.02/2.21 tff(7557,plain,
% 2.02/2.21 (b(s(z), z)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[169, 7556])).
% 2.02/2.21 tff(7558,plain,
% 2.02/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))))),
% 2.02/2.21 inference(rewrite,[status(thm)],[])).
% 2.02/2.21 tff(7559,plain,
% 2.02/2.21 (((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))))),
% 2.02/2.21 inference(rewrite,[status(thm)],[])).
% 2.02/2.21 tff(7560,plain,
% 2.02/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), s(z))) | (~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(X1, 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)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z)))))),
% 2.02/2.21 inference(monotonicity,[status(thm)],[7559])).
% 2.02/2.21 tff(7561,plain,
% 2.02/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), s(z))) | (~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(X1, 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)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))))),
% 2.02/2.21 inference(transitivity,[status(thm)],[7560, 7558])).
% 2.02/2.21 tff(7562,plain,
% 2.02/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 2.02/2.21 inference(quant_inst,[status(thm)],[])).
% 2.02/2.21 tff(7563,plain,
% 2.02/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z)))),
% 2.02/2.21 inference(modus_ponens,[status(thm)],[7562, 7561])).
% 2.02/2.21 tff(7564,plain,
% 2.02/2.21 ($false),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[7563, 75, 372, 371, 1391, 964, 309])).
% 2.02/2.21 tff(7565,plain,((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.21 tff(7566,plain,
% 2.02/2.21 (~b(s(s(z)), s(z))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[7565, 7557, 372, 1391, 7553])).
% 2.02/2.21 tff(7567,plain,
% 2.02/2.21 (r(s(s(z)), s(z))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[153, 7566])).
% 2.02/2.21 tff(7568,plain,
% 2.02/2.21 (~r(s(s(s(z))), elem!1)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[1362, 7551, 300])).
% 2.02/2.21 tff(7569,plain,
% 2.02/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))))),
% 2.02/2.21 inference(rewrite,[status(thm)],[])).
% 2.02/2.21 tff(7570,plain,
% 2.02/2.21 (((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))))),
% 2.02/2.21 inference(rewrite,[status(thm)],[])).
% 2.02/2.21 tff(7571,plain,
% 2.02/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z)))))),
% 2.02/2.21 inference(monotonicity,[status(thm)],[7570])).
% 2.02/2.21 tff(7572,plain,
% 2.02/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))))),
% 2.02/2.21 inference(transitivity,[status(thm)],[7571, 7569])).
% 2.02/2.21 tff(7573,plain,
% 2.02/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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, s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))))),
% 2.02/2.21 inference(quant_inst,[status(thm)],[])).
% 2.02/2.21 tff(7574,plain,
% 2.02/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z)))),
% 2.02/2.21 inference(modus_ponens,[status(thm)],[7573, 7572])).
% 2.02/2.21 tff(7575,plain,
% 2.02/2.21 (~b(elem!1, s(s(elem!1)))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[7574, 75, 1457, 372, 371, 1391])).
% 2.02/2.21 tff(7576,plain,
% 2.02/2.21 (~b(s(s(elem!1)), z)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[4752, 75, 1457, 372, 371])).
% 2.02/2.21 tff(7577,plain,
% 2.02/2.21 (r(s(s(elem!1)), z)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[2696, 7576])).
% 2.02/2.21 tff(7578,plain,
% 2.02/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))) | (~b(elem!1, z)))),
% 2.02/2.21 inference(rewrite,[status(thm)],[])).
% 2.02/2.21 tff(7579,plain,
% 2.02/2.21 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))),
% 2.02/2.21 inference(rewrite,[status(thm)],[])).
% 2.02/2.21 tff(7580,plain,
% 2.02/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))) | (~b(s(z), z)) | (~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(X1, 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(elem!1, s(z))) | (~b(elem!1, z))))),
% 2.02/2.21 inference(monotonicity,[status(thm)],[7579])).
% 2.02/2.21 tff(7581,plain,
% 2.02/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))) | (~b(s(z), z)) | (~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(X1, 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(elem!1, s(z))) | (~b(elem!1, z)))),
% 2.02/2.21 inference(transitivity,[status(thm)],[7580, 7578])).
% 2.02/2.21 tff(7582,plain,
% 2.02/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))),
% 2.02/2.21 inference(quant_inst,[status(thm)],[])).
% 2.02/2.21 tff(7583,plain,
% 2.02/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))) | (~b(elem!1, z))),
% 2.02/2.21 inference(modus_ponens,[status(thm)],[7582, 7581])).
% 2.02/2.21 tff(7584,plain,
% 2.02/2.21 (~b(elem!1, z)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[7583, 75, 372, 371, 1391])).
% 2.02/2.21 tff(7585,plain,
% 2.02/2.21 (r(elem!1, z)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[387, 7584, 305])).
% 2.02/2.21 tff(7586,plain,
% 2.02/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))))),
% 2.02/2.21 inference(rewrite,[status(thm)],[])).
% 2.02/2.21 tff(7587,plain,
% 2.02/2.21 (((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))))),
% 2.02/2.21 inference(rewrite,[status(thm)],[])).
% 2.02/2.21 tff(7588,plain,
% 2.02/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1))))))),
% 2.02/2.21 inference(monotonicity,[status(thm)],[7587])).
% 2.02/2.21 tff(7589,plain,
% 2.02/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))))),
% 2.02/2.21 inference(transitivity,[status(thm)],[7588, 7586])).
% 2.02/2.21 tff(7590,plain,
% 2.02/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))))),
% 2.02/2.21 inference(quant_inst,[status(thm)],[])).
% 2.02/2.21 tff(7591,plain,
% 2.02/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1))))),
% 2.02/2.21 inference(modus_ponens,[status(thm)],[7590, 7589])).
% 2.02/2.21 tff(7592,plain,
% 2.02/2.21 (~r(elem!1, s(s(elem!1)))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[7591, 37, 7585, 7577])).
% 2.02/2.21 tff(7593,plain,
% 2.02/2.21 (elem!1 = s(s(elem!1))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[1617, 7592, 7575])).
% 2.02/2.21 tff(7594,plain,
% 2.02/2.21 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(elem!1)))),
% 2.02/2.21 inference(monotonicity,[status(thm)],[7593])).
% 2.02/2.21 tff(7595,plain,
% 2.02/2.21 (b(s(s(z)), s(s(elem!1)))),
% 2.02/2.21 inference(modus_ponens,[status(thm)],[964, 7594])).
% 2.02/2.21 tff(7596,plain,
% 2.02/2.21 (~b(elem!1, s(s(s(s(z)))))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[1438, 287, 578, 1391])).
% 2.02/2.21 tff(7597,plain,
% 2.02/2.21 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 2.02/2.21 inference(symmetry,[status(thm)],[2268])).
% 2.02/2.21 tff(7598,plain,
% 2.02/2.21 (b(elem!1, s(s(s(s(z)))))),
% 2.02/2.21 inference(modus_ponens,[status(thm)],[1619, 7597])).
% 2.02/2.21 tff(7599,plain,
% 2.02/2.21 ($false),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[6193, 7598])).
% 2.02/2.21 tff(7600,plain,((~(elem!1 = s(s(elem!1)))) | b(elem!1, s(s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.21 tff(7601,plain,
% 2.02/2.21 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[7600, 7593, 7596])).
% 2.02/2.21 tff(7602,plain,
% 2.02/2.21 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[1660, 7601, 1011])).
% 2.02/2.21 tff(7603,plain,
% 2.02/2.21 ((s(s(s(z))) = elem!1) <=> (s(s(s(z))) = s(s(elem!1)))),
% 2.02/2.21 inference(monotonicity,[status(thm)],[7593])).
% 2.02/2.21 tff(7604,plain,
% 2.02/2.21 ((s(s(s(z))) = elem!1) <=> (s(s(elem!1)) = s(s(s(z))))),
% 2.02/2.21 inference(transitivity,[status(thm)],[7603, 1909])).
% 2.02/2.21 tff(7605,plain,
% 2.02/2.21 ((~(s(s(s(z))) = elem!1)) <=> (~(s(s(elem!1)) = s(s(s(z)))))),
% 2.02/2.21 inference(monotonicity,[status(thm)],[7604])).
% 2.02/2.21 tff(7606,plain,
% 2.02/2.21 (~(s(s(s(z))) = elem!1)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[1612, 7593])).
% 2.02/2.21 tff(7607,plain,
% 2.02/2.21 (~(s(s(elem!1)) = s(s(s(z))))),
% 2.02/2.21 inference(modus_ponens,[status(thm)],[7606, 7605])).
% 2.02/2.21 tff(7608,plain,
% 2.02/2.21 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.02/2.21 inference(monotonicity,[status(thm)],[7593])).
% 2.02/2.21 tff(7609,plain,
% 2.02/2.21 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.02/2.21 inference(modus_ponens,[status(thm)],[287, 7608])).
% 2.02/2.21 tff(7610,plain,
% 2.02/2.21 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(elem!1)))),
% 2.02/2.21 inference(monotonicity,[status(thm)],[7593])).
% 2.02/2.21 tff(7611,plain,
% 2.02/2.21 (b(s(s(s(z))), elem!1)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[1115, 7606, 1710])).
% 2.02/2.21 tff(7612,plain,
% 2.02/2.21 (b(s(s(s(z))), s(s(elem!1)))),
% 2.02/2.21 inference(modus_ponens,[status(thm)],[7611, 7610])).
% 2.02/2.21 tff(7613,assumption,(b(s(s(z)), s(s(elem!1)))), introduced(assumption)).
% 2.02/2.21 tff(7614,assumption,(b(s(s(elem!1)), s(s(s(z))))), introduced(assumption)).
% 2.02/2.21 tff(7615,plain,
% 2.02/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.02/2.21 inference(rewrite,[status(thm)],[])).
% 2.02/2.21 tff(7616,plain,
% 2.02/2.21 (((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.02/2.21 inference(rewrite,[status(thm)],[])).
% 2.02/2.21 tff(7617,plain,
% 2.02/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), 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(X1, 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(s(s(z)))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))))),
% 2.02/2.21 inference(monotonicity,[status(thm)],[7616])).
% 2.02/2.21 tff(7618,plain,
% 2.02/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), 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(X1, 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(s(s(z)))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.02/2.21 inference(transitivity,[status(thm)],[7617, 7615])).
% 2.02/2.21 tff(7619,plain,
% 2.02/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.02/2.21 inference(quant_inst,[status(thm)],[])).
% 2.02/2.21 tff(7620,plain,
% 2.02/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 2.02/2.21 inference(modus_ponens,[status(thm)],[7619, 7618])).
% 2.02/2.21 tff(7621,plain,
% 2.02/2.21 ($false),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[7620, 75, 7614, 3628, 895, 7613, 5712])).
% 2.02/2.21 tff(7622,plain,((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.22 tff(7623,plain,
% 2.02/2.22 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[7622, 7612, 895, 7595, 7609])).
% 2.02/2.22 tff(7624,plain,
% 2.02/2.22 (r(s(s(elem!1)), s(s(s(z))))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[1936, 7623, 7607])).
% 2.02/2.22 tff(7625,plain,
% 2.02/2.22 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[4241, 7624, 7602])).
% 2.02/2.22 tff(7626,plain,
% 2.02/2.22 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[575, 7625])).
% 2.02/2.22 tff(7627,plain,
% 2.02/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.02/2.22 inference(rewrite,[status(thm)],[])).
% 2.02/2.22 tff(7628,plain,
% 2.02/2.22 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.02/2.22 inference(rewrite,[status(thm)],[])).
% 2.02/2.22 tff(7629,plain,
% 2.02/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(z))))))))),
% 2.02/2.22 inference(monotonicity,[status(thm)],[7628])).
% 2.02/2.22 tff(7630,plain,
% 2.02/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.02/2.22 inference(transitivity,[status(thm)],[7629, 7627])).
% 2.02/2.22 tff(7631,plain,
% 2.02/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.02/2.22 inference(quant_inst,[status(thm)],[])).
% 2.02/2.22 tff(7632,plain,
% 2.02/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(z))))))),
% 2.02/2.22 inference(modus_ponens,[status(thm)],[7631, 7630])).
% 2.02/2.22 tff(7633,plain,
% 2.02/2.22 (~b(s(s(z)), s(s(s(z))))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[7632, 75, 1457, 578, 7612, 7626, 895, 7595])).
% 2.02/2.22 tff(7634,plain,
% 2.02/2.22 (r(s(s(z)), s(s(s(z))))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[1559, 58, 1556, 7633])).
% 2.02/2.22 tff(7635,plain,
% 2.02/2.22 (b(elem!1, s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 2.02/2.22 inference(monotonicity,[status(thm)],[7593])).
% 2.02/2.22 tff(7636,plain,
% 2.02/2.22 ((~b(elem!1, s(s(z)))) <=> (~b(s(s(elem!1)), s(s(z))))),
% 2.02/2.22 inference(monotonicity,[status(thm)],[7635])).
% 2.02/2.22 tff(7637,plain,
% 2.02/2.22 (~b(elem!1, s(s(z)))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[2255, 964, 895, 287])).
% 2.02/2.22 tff(7638,plain,
% 2.02/2.22 (~b(s(s(elem!1)), s(s(z)))),
% 2.02/2.22 inference(modus_ponens,[status(thm)],[7637, 7636])).
% 2.02/2.22 tff(7639,plain,
% 2.02/2.22 (r(s(s(elem!1)), s(s(z)))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[1476, 7638, 266])).
% 2.02/2.22 tff(7640,plain,
% 2.02/2.22 (((~![X0: $i, 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(z)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.02/2.22 inference(rewrite,[status(thm)],[])).
% 2.02/2.22 tff(7641,plain,
% 2.02/2.22 (((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(z))))) <=> ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.02/2.22 inference(rewrite,[status(thm)],[])).
% 2.02/2.22 tff(7642,plain,
% 2.02/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(z)), s(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(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 2.02/2.22 inference(monotonicity,[status(thm)],[7641])).
% 2.02/2.22 tff(7643,plain,
% 2.02/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(z)), s(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(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.02/2.22 inference(transitivity,[status(thm)],[7642, 7640])).
% 2.02/2.22 tff(7644,plain,
% 2.02/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.02/2.22 inference(quant_inst,[status(thm)],[])).
% 2.02/2.22 tff(7645,plain,
% 2.02/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 2.02/2.22 inference(modus_ponens,[status(thm)],[7644, 7643])).
% 2.02/2.22 tff(7646,plain,
% 2.02/2.22 ($false),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[7645, 37, 7624, 7639, 7634])).
% 2.02/2.22 tff(7647,plain,((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (s(s(elem!1)) = s(s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (s(s(elem!1)) = s(s(s(s(z))))) | r(s(s(s(z))), elem!1) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.22 tff(7648,plain,
% 2.02/2.22 (~b(s(s(elem!1)), s(z))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[7647, 7545, 895, 266, 578, 7553, 1011, 7568, 372, 7557, 1391])).
% 2.02/2.22 tff(7649,plain,
% 2.02/2.22 (r(s(s(elem!1)), s(z))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[561, 7648])).
% 2.02/2.22 tff(7650,plain,
% 2.02/2.22 (~r(s(s(z)), s(s(elem!1)))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[2243, 37, 7649, 7567])).
% 2.02/2.22 tff(7651,plain,
% 2.02/2.22 (b(s(s(z)), s(s(elem!1)))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[6336, 58, 7650, 7548])).
% 2.02/2.22 tff(7652,plain,
% 2.02/2.22 (~r(s(s(elem!1)), s(s(z)))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[500, 37, 7649, 7567])).
% 2.02/2.22 tff(7653,plain,
% 2.02/2.22 (b(s(s(elem!1)), s(s(z)))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[1476, 7652, 266])).
% 2.02/2.22 tff(7654,assumption,(~(s(s(s(s(z)))) = s(s(elem!1)))), introduced(assumption)).
% 2.02/2.22 tff(7655,plain,
% 2.02/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.02/2.22 inference(rewrite,[status(thm)],[])).
% 2.02/2.22 tff(7656,plain,
% 2.02/2.22 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.02/2.22 inference(rewrite,[status(thm)],[])).
% 2.02/2.22 tff(7657,plain,
% 2.02/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))))),
% 2.02/2.22 inference(monotonicity,[status(thm)],[7656])).
% 2.02/2.22 tff(7658,plain,
% 2.02/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.02/2.22 inference(transitivity,[status(thm)],[7657, 7655])).
% 2.02/2.22 tff(7659,plain,
% 2.02/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.02/2.22 inference(quant_inst,[status(thm)],[])).
% 2.02/2.22 tff(7660,plain,
% 2.02/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 2.02/2.22 inference(modus_ponens,[status(thm)],[7659, 7658])).
% 2.02/2.22 tff(7661,plain,
% 2.02/2.22 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[7660, 75, 964, 1619, 287, 895, 7613])).
% 2.02/2.22 tff(7662,plain,
% 2.02/2.22 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[3876, 58, 7661, 7654])).
% 2.02/2.22 tff(7663,plain,
% 2.02/2.22 (~(elem!1 = s(s(elem!1)))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[7600, 1619, 7596])).
% 2.02/2.22 tff(7664,plain,
% 2.02/2.22 (~(s(s(elem!1)) = elem!1)),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[2555, 7663])).
% 2.02/2.22 tff(7665,plain,
% 2.02/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(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(X1, 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(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.02/2.22 inference(rewrite,[status(thm)],[])).
% 2.02/2.22 tff(7666,plain,
% 2.02/2.22 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~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(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.02/2.22 inference(rewrite,[status(thm)],[])).
% 2.02/2.22 tff(7667,plain,
% 2.02/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(s(s(s(z)))))) | (~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(X1, 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(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))))),
% 2.02/2.22 inference(monotonicity,[status(thm)],[7666])).
% 2.02/2.22 tff(7668,plain,
% 2.02/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(s(s(s(z)))))) | (~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(X1, 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(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.02/2.22 inference(transitivity,[status(thm)],[7667, 7665])).
% 2.02/2.22 tff(7669,plain,
% 2.02/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(s(s(s(z)))))) | (~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)))))),
% 2.02/2.22 inference(quant_inst,[status(thm)],[])).
% 2.02/2.22 tff(7670,plain,
% 2.02/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))),
% 2.02/2.22 inference(modus_ponens,[status(thm)],[7669, 7668])).
% 2.02/2.22 tff(7671,plain,
% 2.02/2.22 (~b(s(s(elem!1)), elem!1)),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[7670, 75, 1391, 964, 578, 1619, 895, 1283])).
% 2.02/2.22 tff(7672,plain,
% 2.02/2.22 (r(s(s(elem!1)), elem!1)),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[2673, 7671, 7664])).
% 2.02/2.22 tff(7673,plain,
% 2.02/2.22 (~b(elem!1, s(s(elem!1)))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[5690, 7672, 1391, 588])).
% 2.02/2.22 tff(7674,plain,
% 2.02/2.22 (r(elem!1, s(s(elem!1)))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[1617, 7673, 7663])).
% 2.02/2.22 tff(7675,plain,
% 2.02/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(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(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 2.02/2.22 inference(rewrite,[status(thm)],[])).
% 2.02/2.22 tff(7676,plain,
% 2.02/2.22 (((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 2.02/2.22 inference(rewrite,[status(thm)],[])).
% 2.02/2.22 tff(7677,plain,
% 2.02/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))))),
% 2.02/2.22 inference(monotonicity,[status(thm)],[7676])).
% 2.02/2.22 tff(7678,plain,
% 2.02/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 2.02/2.22 inference(transitivity,[status(thm)],[7677, 7675])).
% 2.02/2.22 tff(7679,plain,
% 2.02/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z)))))))),
% 2.02/2.22 inference(quant_inst,[status(thm)],[])).
% 2.02/2.22 tff(7680,plain,
% 2.02/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))),
% 2.02/2.22 inference(modus_ponens,[status(thm)],[7679, 7678])).
% 2.02/2.22 tff(7681,plain,
% 2.02/2.22 ($false),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[7680, 37, 7674, 3195, 7662])).
% 2.02/2.22 tff(7682,plain,((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (s(s(s(s(z)))) = s(s(elem!1))) | (~b(elem!1, s(z))) | (~r(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.22 tff(7683,plain,
% 2.02/2.22 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[7682, 7547, 5881, 1391, 7551, 7553, 578, 895, 7653, 7545, 7651])).
% 2.02/2.22 tff(7684,plain,
% 2.02/2.22 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[1660, 7683, 1011])).
% 2.02/2.22 tff(7685,plain,
% 2.02/2.22 (~r(elem!1, s(s(elem!1)))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[3811, 7684, 7547])).
% 2.02/2.22 tff(7686,plain,
% 2.02/2.22 (~b(elem!1, z)),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[7583, 75, 372, 7557, 1391])).
% 2.02/2.22 tff(7687,plain,
% 2.02/2.22 (r(elem!1, z)),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[387, 7686, 305])).
% 2.02/2.22 tff(7688,plain,
% 2.02/2.22 (((~![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)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), elem!1)))),
% 2.02/2.23 inference(rewrite,[status(thm)],[])).
% 2.02/2.23 tff(7689,plain,
% 2.02/2.23 (((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), elem!1)))),
% 2.02/2.23 inference(rewrite,[status(thm)],[])).
% 2.02/2.23 tff(7690,plain,
% 2.02/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(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(elem!1, z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), elem!1))))),
% 2.02/2.23 inference(monotonicity,[status(thm)],[7689])).
% 2.02/2.23 tff(7691,plain,
% 2.02/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(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(elem!1, z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), elem!1)))),
% 2.02/2.23 inference(transitivity,[status(thm)],[7690, 7688])).
% 2.02/2.23 tff(7692,plain,
% 2.02/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)))),
% 2.02/2.23 inference(quant_inst,[status(thm)],[])).
% 2.02/2.23 tff(7693,plain,
% 2.02/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), elem!1))),
% 2.02/2.23 inference(modus_ponens,[status(thm)],[7692, 7691])).
% 2.02/2.23 tff(7694,plain,
% 2.02/2.23 (~r(s(s(elem!1)), elem!1)),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[7693, 37, 7687, 7547, 7684])).
% 2.02/2.23 tff(7695,plain,
% 2.02/2.23 (~(s(s(elem!1)) = elem!1)),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[2555, 1630])).
% 2.02/2.23 tff(7696,plain,
% 2.02/2.23 (b(s(s(elem!1)), elem!1)),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[2673, 7695, 2668])).
% 2.02/2.23 tff(7697,plain,
% 2.02/2.23 (b(elem!1, s(s(elem!1)))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[1617, 1630, 2217])).
% 2.02/2.23 tff(7698,plain,
% 2.02/2.23 ($false),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[4718, 75, 7697, 964, 1283, 7696])).
% 2.02/2.23 tff(7699,plain,((elem!1 = s(s(elem!1))) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), s(s(z)))) | r(s(s(elem!1)), elem!1) | r(elem!1, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.23 tff(7700,plain,
% 2.02/2.23 (elem!1 = s(s(elem!1))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[7699, 7553, 7653, 7694, 7685])).
% 2.02/2.23 tff(7701,plain,
% 2.02/2.23 (b(elem!1, s(z)) <=> b(s(s(elem!1)), s(z))),
% 2.02/2.23 inference(monotonicity,[status(thm)],[7700])).
% 2.02/2.23 tff(7702,plain,
% 2.02/2.23 (b(s(s(elem!1)), s(z)) <=> b(elem!1, s(z))),
% 2.02/2.23 inference(symmetry,[status(thm)],[7701])).
% 2.02/2.23 tff(7703,plain,
% 2.02/2.23 ((~b(s(s(elem!1)), s(z))) <=> (~b(elem!1, s(z)))),
% 2.02/2.23 inference(monotonicity,[status(thm)],[7702])).
% 2.02/2.23 tff(7704,plain,
% 2.02/2.23 (~b(elem!1, s(z))),
% 2.02/2.23 inference(modus_ponens,[status(thm)],[7648, 7703])).
% 2.02/2.23 tff(7705,plain,
% 2.02/2.23 ($false),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[1391, 7704])).
% 2.02/2.23 tff(7706,plain,((s(s(s(s(z)))) = elem!1) | (~b(elem!1, s(z))) | (s(s(elem!1)) = s(s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (s(s(elem!1)) = s(s(z))) | (~b(z, s(z))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.23 tff(7707,plain,
% 2.02/2.23 (s(s(s(s(z)))) = elem!1),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[7706, 7543, 1011, 3657, 895, 266, 7542, 7155])).
% 2.02/2.23 tff(7708,plain,
% 2.02/2.23 ((s(s(elem!1)) = s(s(s(s(z))))) <=> (s(s(elem!1)) = elem!1)),
% 2.02/2.23 inference(monotonicity,[status(thm)],[7707])).
% 2.02/2.23 tff(7709,plain,
% 2.02/2.23 ((s(s(elem!1)) = s(s(s(s(z))))) <=> (elem!1 = s(s(elem!1)))),
% 2.02/2.23 inference(transitivity,[status(thm)],[7708, 3428])).
% 2.02/2.23 tff(7710,plain,
% 2.02/2.23 ((~(s(s(elem!1)) = s(s(s(s(z)))))) <=> (~(elem!1 = s(s(elem!1))))),
% 2.02/2.23 inference(monotonicity,[status(thm)],[7709])).
% 2.02/2.23 tff(7711,plain,
% 2.02/2.23 (~(elem!1 = s(s(elem!1)))),
% 2.02/2.23 inference(modus_ponens,[status(thm)],[1011, 7710])).
% 2.02/2.23 tff(7712,plain,
% 2.02/2.23 (~r(s(z), elem!1)),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[3664, 7707, 3656])).
% 2.02/2.23 tff(7713,plain,
% 2.02/2.23 (b(s(z), elem!1)),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[601, 7712, 7156])).
% 2.02/2.23 tff(7714,plain,
% 2.02/2.23 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(z)), elem!1)),
% 2.02/2.23 inference(monotonicity,[status(thm)],[7707])).
% 2.02/2.23 tff(7715,plain,
% 2.02/2.23 (b(s(s(z)), elem!1)),
% 2.02/2.23 inference(modus_ponens,[status(thm)],[895, 7714])).
% 2.02/2.23 tff(7716,plain,
% 2.02/2.23 (~b(s(s(elem!1)), s(z))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[1638, 1620, 1391, 107])).
% 2.02/2.23 tff(7717,plain,
% 2.02/2.23 (r(s(s(elem!1)), s(z))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[561, 7716])).
% 2.02/2.23 tff(7718,plain,
% 2.02/2.23 (~r(s(s(z)), s(s(elem!1)))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[2243, 37, 7717, 7473])).
% 2.02/2.23 tff(7719,plain,
% 2.02/2.23 (b(s(s(z)), s(s(elem!1)))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[6336, 58, 7718, 7548])).
% 2.02/2.23 tff(7720,plain,
% 2.02/2.23 (~r(s(s(elem!1)), s(s(z)))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[500, 37, 7717, 7473])).
% 2.02/2.23 tff(7721,plain,
% 2.02/2.23 (b(s(s(elem!1)), s(s(z)))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[1476, 7720, 266])).
% 2.02/2.23 tff(7722,plain,
% 2.02/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.02/2.23 inference(rewrite,[status(thm)],[])).
% 2.02/2.23 tff(7723,plain,
% 2.02/2.23 (((~b(s(s(z)), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), elem!1))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.02/2.23 inference(rewrite,[status(thm)],[])).
% 2.02/2.23 tff(7724,plain,
% 2.02/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1))))))),
% 2.02/2.23 inference(monotonicity,[status(thm)],[7723])).
% 2.02/2.23 tff(7725,plain,
% 2.02/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.02/2.23 inference(transitivity,[status(thm)],[7724, 7722])).
% 2.02/2.23 tff(7726,plain,
% 2.02/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), elem!1)))),
% 2.02/2.23 inference(quant_inst,[status(thm)],[])).
% 2.02/2.23 tff(7727,plain,
% 2.02/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1))))),
% 2.02/2.23 inference(modus_ponens,[status(thm)],[7726, 7725])).
% 2.02/2.23 tff(7728,plain,
% 2.02/2.23 ($false),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[7727, 75, 1620, 964, 7721, 7719])).
% 2.02/2.23 tff(7729,plain,((~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), elem!1)) | (s(s(elem!1)) = s(s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.23 tff(7730,plain,
% 2.02/2.23 (~b(elem!1, s(s(elem!1)))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[7729, 7715, 266, 7543, 7713])).
% 2.02/2.23 tff(7731,plain,
% 2.02/2.23 (r(elem!1, s(s(elem!1)))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[1617, 7730, 7711])).
% 2.02/2.23 tff(7732,plain,
% 2.02/2.23 (~r(z, s(s(elem!1)))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[2372, 7731, 7155])).
% 2.02/2.23 tff(7733,plain,
% 2.02/2.23 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[7485, 7715, 7543, 7713, 7707, 3657])).
% 2.02/2.23 tff(7734,plain,
% 2.02/2.23 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[575, 7733])).
% 2.02/2.23 tff(7735,plain,
% 2.02/2.23 (r(s(s(s(z))), elem!1)),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[6396, 7734, 7707])).
% 2.02/2.23 tff(7736,plain,
% 2.02/2.23 (~r(s(s(s(z))), z)),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[1330, 37, 7155, 7735])).
% 2.02/2.23 tff(7737,plain,
% 2.02/2.23 (b(s(s(s(z))), z)),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[1334, 58, 221, 7736])).
% 2.02/2.23 tff(7738,plain,
% 2.02/2.23 (r(s(s(s(s(z)))), z) <=> r(elem!1, z)),
% 2.02/2.23 inference(monotonicity,[status(thm)],[7707])).
% 2.02/2.23 tff(7739,plain,
% 2.02/2.23 (r(elem!1, z) <=> r(s(s(s(s(z)))), z)),
% 2.02/2.23 inference(symmetry,[status(thm)],[7738])).
% 2.02/2.23 tff(7740,plain,
% 2.02/2.23 (~b(elem!1, z)),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[2101, 75, 7542, 7713, 7543])).
% 2.02/2.23 tff(7741,plain,
% 2.02/2.23 (r(elem!1, z)),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[387, 7740, 305])).
% 2.02/2.23 tff(7742,plain,
% 2.02/2.23 (r(s(s(s(s(z)))), z)),
% 2.02/2.23 inference(modus_ponens,[status(thm)],[7741, 7739])).
% 2.02/2.23 tff(7743,plain,
% 2.02/2.23 (r(s(s(s(s(z)))), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.02/2.23 inference(monotonicity,[status(thm)],[7707])).
% 2.02/2.23 tff(7744,plain,
% 2.02/2.23 (r(elem!1, s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.02/2.23 inference(symmetry,[status(thm)],[7743])).
% 2.02/2.23 tff(7745,plain,
% 2.02/2.23 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.02/2.23 inference(modus_ponens,[status(thm)],[7731, 7744])).
% 2.02/2.23 tff(7746,plain,
% 2.02/2.23 (~r(s(s(elem!1)), z)),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[2707, 7745, 7742])).
% 2.02/2.23 tff(7747,plain,
% 2.02/2.23 (b(s(s(elem!1)), z)),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[2696, 7746])).
% 2.02/2.23 tff(7748,plain,
% 2.02/2.23 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[5576, 7747, 7737, 7732])).
% 2.02/2.23 tff(7749,plain,
% 2.02/2.23 (r(s(s(s(z))), s(s(elem!1)))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[62, 7748, 7158])).
% 2.02/2.23 tff(7750,plain,
% 2.02/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(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(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 2.02/2.23 inference(rewrite,[status(thm)],[])).
% 2.02/2.23 tff(7751,plain,
% 2.02/2.23 (((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 2.02/2.23 inference(rewrite,[status(thm)],[])).
% 2.02/2.23 tff(7752,plain,
% 2.02/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))))),
% 2.02/2.23 inference(monotonicity,[status(thm)],[7751])).
% 2.02/2.23 tff(7753,plain,
% 2.02/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 2.02/2.23 inference(transitivity,[status(thm)],[7752, 7750])).
% 2.02/2.23 tff(7754,plain,
% 2.02/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)))),
% 2.02/2.23 inference(quant_inst,[status(thm)],[])).
% 2.02/2.23 tff(7755,plain,
% 2.02/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))),
% 2.02/2.23 inference(modus_ponens,[status(thm)],[7754, 7753])).
% 2.02/2.23 tff(7756,plain,
% 2.02/2.23 ($false),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[7755, 37, 7741, 7731, 7735, 7749])).
% 2.02/2.23 tff(7757,plain,((s(s(elem!1)) = s(s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (s(s(elem!1)) = s(s(s(s(z))))) | r(s(z), s(s(s(s(z))))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.02/2.23 tff(7758,plain,
% 2.02/2.23 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[7757, 7154, 266, 285, 7130])).
% 2.02/2.23 tff(7759,plain,
% 2.02/2.23 (~b(s(s(z)), elem!1)),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[6139, 7758, 3285])).
% 2.02/2.23 tff(7760,plain,
% 2.02/2.23 (r(s(s(z)), elem!1)),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[104, 7759, 6325])).
% 2.02/2.23 tff(7761,plain,
% 2.02/2.23 (~r(s(s(elem!1)), s(s(z)))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[2661, 37, 7760, 2647])).
% 2.02/2.23 tff(7762,plain,
% 2.02/2.23 (b(s(s(elem!1)), s(s(z)))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[1476, 7761, 266])).
% 2.02/2.23 tff(7763,plain,
% 2.02/2.23 (~r(s(s(z)), z)),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[328, 7760, 300])).
% 2.02/2.23 tff(7764,plain,
% 2.02/2.23 (b(s(s(z)), z)),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[202, 7763])).
% 2.02/2.23 tff(7765,plain,
% 2.02/2.23 (~r(z, s(s(z)))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[339, 7760, 300])).
% 2.02/2.23 tff(7766,plain,
% 2.02/2.23 (b(z, s(s(z)))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[351, 7765])).
% 2.02/2.23 tff(7767,plain,
% 2.02/2.23 ($false),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[546, 75, 7766, 7764, 7762, 5177])).
% 2.02/2.23 tff(7768,plain,((~r(s(s(elem!1)), s(s(s(s(z)))))) | (s(s(elem!1)) = s(s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~(s(s(s(s(z)))) = elem!1)) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.02/2.23 tff(7769,plain,
% 2.02/2.23 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[7768, 2647, 266, 300, 3285, 285])).
% 2.02/2.23 tff(7770,plain,
% 2.02/2.23 ($false),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[7769, 4483])).
% 2.02/2.23 tff(7771,plain,((~r(s(s(elem!1)), elem!1)) | (~(s(s(s(s(z)))) = elem!1)) | (s(s(elem!1)) = s(s(z))) | (~r(z, elem!1)) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.02/2.23 tff(7772,plain,
% 2.02/2.23 (~r(s(s(elem!1)), elem!1)),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[7771, 3285, 266, 300, 285])).
% 2.02/2.23 tff(7773,plain,
% 2.02/2.23 (b(s(s(elem!1)), elem!1)),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[2673, 7772, 4477])).
% 2.02/2.23 tff(7774,plain,
% 2.02/2.23 (r(elem!1, s(z))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[89, 14, 112])).
% 2.02/2.23 tff(7775,plain,
% 2.02/2.23 (~r(elem!1, s(s(elem!1)))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[7265, 7774, 4464, 300])).
% 2.02/2.23 tff(7776,plain,
% 2.02/2.23 (~b(s(s(z)), s(z))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[425, 14, 300, 353, 99])).
% 2.02/2.23 tff(7777,plain,
% 2.02/2.23 (r(elem!1, s(z))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[89, 14, 95])).
% 2.02/2.23 tff(7778,plain,
% 2.02/2.23 (~r(s(s(z)), s(z))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[123, 7777, 106])).
% 2.02/2.23 tff(7779,plain,
% 2.02/2.23 ($false),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[153, 7778, 7776])).
% 2.02/2.23 tff(7780,plain,(b(elem!1, s(z)) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (elem!1 = z) | b(s(s(z)), elem!1) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.23 tff(7781,plain,
% 2.02/2.23 ($false),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[7780, 105, 99, 300, 353, 14, 95])).
% 2.02/2.23 tff(7782,plain,(b(s(s(z)), elem!1) | (~r(z, elem!1)) | (elem!1 = z) | b(elem!1, s(z)) | (elem!1 = s(z)) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.02/2.23 tff(7783,plain,
% 2.02/2.23 (b(s(s(z)), elem!1)),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[7782, 14, 353, 300, 112, 6325])).
% 2.02/2.23 tff(7784,plain,
% 2.02/2.23 (b(s(s(z)), s(s(s(s(z)))))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[6139, 7783, 3285])).
% 2.02/2.23 tff(7785,plain,
% 2.02/2.23 (r(s(z), s(s(s(s(z)))))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[7410, 7784, 4464, 7130, 266, 300, 108, 7774])).
% 2.02/2.23 tff(7786,plain,
% 2.02/2.23 ((s(s(z)) = s(s(s(s(s(s(z))))))) <=> (s(s(z)) = s(s(elem!1)))),
% 2.02/2.23 inference(monotonicity,[status(thm)],[4553])).
% 2.02/2.23 tff(7787,plain,
% 2.02/2.23 ((s(s(z)) = s(s(s(s(s(s(z))))))) <=> (s(s(elem!1)) = s(s(z)))),
% 2.02/2.23 inference(transitivity,[status(thm)],[7786, 2229])).
% 2.02/2.23 tff(7788,plain,
% 2.02/2.23 ((s(s(elem!1)) = s(s(z))) <=> (s(s(z)) = s(s(s(s(s(s(z)))))))),
% 2.02/2.23 inference(symmetry,[status(thm)],[7787])).
% 2.02/2.23 tff(7789,plain,
% 2.02/2.23 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(s(s(s(z))))))))),
% 2.02/2.23 inference(monotonicity,[status(thm)],[7788])).
% 2.02/2.23 tff(7790,plain,
% 2.02/2.23 ((s(s(s(s(z)))) = z) <=> (elem!1 = z)),
% 2.02/2.23 inference(monotonicity,[status(thm)],[4467])).
% 2.02/2.23 tff(7791,plain,
% 2.02/2.23 ((s(s(s(s(z)))) = z) <=> (z = elem!1)),
% 2.02/2.23 inference(transitivity,[status(thm)],[7790, 216])).
% 2.02/2.23 tff(7792,plain,
% 2.02/2.23 ((~(s(s(s(s(z)))) = z)) <=> (~(z = elem!1))),
% 2.02/2.23 inference(monotonicity,[status(thm)],[7791])).
% 2.02/2.23 tff(7793,plain,
% 2.02/2.23 (~(z = elem!1)),
% 2.02/2.23 inference(modus_ponens,[status(thm)],[1143, 7792])).
% 2.02/2.23 tff(7794,plain,
% 2.02/2.23 (~(s(s(elem!1)) = s(s(z)))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[237, 7793])).
% 2.02/2.23 tff(7795,plain,
% 2.02/2.23 (~(s(s(z)) = s(s(s(s(s(s(z)))))))),
% 2.02/2.23 inference(modus_ponens,[status(thm)],[7794, 7789])).
% 2.02/2.23 tff(7796,plain,
% 2.02/2.23 ((s(s(elem!1)) = s(s(s(s(z))))) <=> (s(s(elem!1)) = elem!1)),
% 2.02/2.23 inference(monotonicity,[status(thm)],[4467])).
% 2.02/2.23 tff(7797,plain,
% 2.02/2.23 ((s(s(elem!1)) = s(s(s(s(z))))) <=> (elem!1 = s(s(elem!1)))),
% 2.02/2.23 inference(transitivity,[status(thm)],[7796, 3428])).
% 2.02/2.23 tff(7798,plain,
% 2.02/2.23 ((~(s(s(elem!1)) = s(s(s(s(z)))))) <=> (~(elem!1 = s(s(elem!1))))),
% 2.02/2.23 inference(monotonicity,[status(thm)],[7797])).
% 2.02/2.23 tff(7799,plain,
% 2.02/2.23 (~(elem!1 = s(s(elem!1)))),
% 2.02/2.23 inference(modus_ponens,[status(thm)],[1011, 7798])).
% 2.02/2.23 tff(7800,plain,
% 2.02/2.23 (b(elem!1, s(s(elem!1)))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[1617, 7799, 2217])).
% 2.02/2.23 tff(7801,plain,
% 2.02/2.23 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 2.02/2.23 inference(modus_ponens,[status(thm)],[7800, 7369])).
% 2.02/2.23 tff(7802,plain,
% 2.02/2.23 ((~r(s(s(elem!1)), elem!1)) <=> (~r(s(s(elem!1)), s(s(s(s(z))))))),
% 2.02/2.23 inference(monotonicity,[status(thm)],[7272])).
% 2.02/2.23 tff(7803,plain,
% 2.02/2.23 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.02/2.23 inference(modus_ponens,[status(thm)],[2668, 7802])).
% 2.02/2.23 tff(7804,plain,
% 2.02/2.23 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[1660, 7803, 1011])).
% 2.02/2.23 tff(7805,plain,
% 2.02/2.23 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 2.02/2.23 inference(modus_ponens,[status(thm)],[7804, 7371])).
% 2.02/2.23 tff(7806,plain,
% 2.02/2.23 (r(z, elem!1)),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[298, 7793, 285])).
% 2.02/2.23 tff(7807,plain,
% 2.02/2.23 (~r(z, s(z))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[367, 7806, 114])).
% 2.02/2.23 tff(7808,plain,
% 2.02/2.23 (b(z, s(z))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[187, 7807])).
% 2.02/2.23 tff(7809,plain,
% 2.02/2.23 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(s(s(s(z)))))),
% 2.02/2.23 inference(monotonicity,[status(thm)],[270])).
% 2.02/2.23 tff(7810,plain,
% 2.02/2.23 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(z)), elem!1)),
% 2.02/2.24 inference(symmetry,[status(thm)],[7809])).
% 2.02/2.24 tff(7811,plain,
% 2.02/2.24 (r(s(s(z)), elem!1)),
% 2.02/2.24 inference(modus_ponens,[status(thm)],[467, 7810])).
% 2.02/2.24 tff(7812,plain,
% 2.02/2.24 (~b(z, s(s(z)))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[380, 1571, 371, 372])).
% 2.02/2.24 tff(7813,plain,
% 2.02/2.24 (r(z, s(s(z)))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[351, 7812])).
% 2.02/2.24 tff(7814,plain,
% 2.02/2.24 (~r(s(s(z)), elem!1)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[339, 7813, 300])).
% 2.02/2.24 tff(7815,plain,
% 2.02/2.24 ($false),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[7814, 7811])).
% 2.02/2.24 tff(7816,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~(elem!1 = s(s(s(s(z)))))) | (~r(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.24 tff(7817,plain,
% 2.02/2.24 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[7816, 270, 7806, 371, 7808, 468])).
% 2.02/2.24 tff(7818,plain,
% 2.02/2.24 (b(s(s(z)), s(s(s(s(z)))))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[465, 7817])).
% 2.02/2.24 tff(7819,plain,
% 2.02/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))))))))),
% 2.02/2.24 inference(rewrite,[status(thm)],[])).
% 2.02/2.24 tff(7820,plain,
% 2.02/2.24 (((~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(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(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)))))))))),
% 2.02/2.24 inference(rewrite,[status(thm)],[])).
% 2.02/2.24 tff(7821,plain,
% 2.02/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(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(X1, 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(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))))))))))),
% 2.02/2.24 inference(monotonicity,[status(thm)],[7820])).
% 2.02/2.24 tff(7822,plain,
% 2.02/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(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(X1, 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(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)))))))))),
% 2.02/2.24 inference(transitivity,[status(thm)],[7821, 7819])).
% 2.02/2.24 tff(7823,plain,
% 2.02/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.02/2.24 inference(quant_inst,[status(thm)],[])).
% 2.02/2.24 tff(7824,plain,
% 2.02/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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))))))))),
% 2.02/2.24 inference(modus_ponens,[status(thm)],[7823, 7822])).
% 2.02/2.24 tff(7825,plain,
% 2.02/2.24 (~b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[7824, 75, 7818, 7805, 7801])).
% 2.02/2.24 tff(7826,plain,
% 2.02/2.24 (((~![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))))))))),
% 2.02/2.24 inference(rewrite,[status(thm)],[])).
% 2.02/2.24 tff(7827,plain,
% 2.02/2.24 ((~![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))))))))),
% 2.02/2.24 inference(quant_inst,[status(thm)],[])).
% 2.02/2.24 tff(7828,plain,
% 2.02/2.24 ((~![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)))))))),
% 2.02/2.24 inference(modus_ponens,[status(thm)],[7827, 7826])).
% 2.02/2.24 tff(7829,plain,
% 2.02/2.24 ((s(s(z)) = s(s(s(s(s(s(z))))))) | r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[7828, 58, 7825])).
% 2.02/2.24 tff(7830,plain,
% 2.02/2.24 (r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[7829, 7795])).
% 2.02/2.24 tff(7831,plain,
% 2.02/2.24 (r(s(z), elem!1) <=> r(s(z), s(s(s(s(z)))))),
% 2.02/2.24 inference(monotonicity,[status(thm)],[270])).
% 2.02/2.24 tff(7832,plain,
% 2.02/2.24 (r(s(z), s(s(s(s(z))))) <=> r(s(z), elem!1)),
% 2.02/2.24 inference(symmetry,[status(thm)],[7831])).
% 2.02/2.24 tff(7833,plain,
% 2.02/2.24 (r(s(z), elem!1)),
% 2.02/2.24 inference(modus_ponens,[status(thm)],[468, 7832])).
% 2.02/2.24 tff(7834,plain,
% 2.02/2.24 (~r(s(s(s(z))), elem!1)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[1362, 7806, 7833])).
% 2.02/2.24 tff(7835,plain,
% 2.02/2.24 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[6396, 7834, 7268])).
% 2.02/2.24 tff(7836,plain,
% 2.02/2.24 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[575, 7835])).
% 2.02/2.24 tff(7837,plain,
% 2.02/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.02/2.24 inference(rewrite,[status(thm)],[])).
% 2.02/2.24 tff(7838,plain,
% 2.02/2.24 (((~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(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.02/2.24 inference(rewrite,[status(thm)],[])).
% 2.02/2.24 tff(7839,plain,
% 2.02/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 2.02/2.24 inference(monotonicity,[status(thm)],[7838])).
% 2.02/2.24 tff(7840,plain,
% 2.02/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.02/2.24 inference(transitivity,[status(thm)],[7839, 7837])).
% 2.02/2.24 tff(7841,plain,
% 2.02/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.02/2.24 inference(quant_inst,[status(thm)],[])).
% 2.02/2.24 tff(7842,plain,
% 2.02/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 2.02/2.24 inference(modus_ponens,[status(thm)],[7841, 7840])).
% 2.02/2.24 tff(7843,plain,
% 2.02/2.24 (~b(s(s(s(z))), s(s(z)))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[7842, 75, 7836, 7818, 7805, 7801])).
% 2.02/2.24 tff(7844,plain,
% 2.02/2.24 ((s(s(s(z))) = s(s(z))) | r(s(s(s(z))), s(s(z)))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[2173, 58, 7843])).
% 2.02/2.24 tff(7845,plain,
% 2.02/2.24 (r(s(s(s(z))), s(s(z)))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[7844, 2150])).
% 2.02/2.24 tff(7846,plain,
% 2.02/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.02/2.24 inference(rewrite,[status(thm)],[])).
% 2.02/2.24 tff(7847,plain,
% 2.02/2.24 (((~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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.02/2.24 inference(rewrite,[status(thm)],[])).
% 2.02/2.24 tff(7848,plain,
% 2.02/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 2.02/2.24 inference(monotonicity,[status(thm)],[7847])).
% 2.02/2.24 tff(7849,plain,
% 2.02/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.02/2.24 inference(transitivity,[status(thm)],[7848, 7846])).
% 2.02/2.24 tff(7850,plain,
% 2.02/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.02/2.24 inference(quant_inst,[status(thm)],[])).
% 2.02/2.24 tff(7851,plain,
% 2.02/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 2.02/2.24 inference(modus_ponens,[status(thm)],[7850, 7849])).
% 2.02/2.24 tff(7852,plain,
% 2.02/2.24 (~b(s(s(z)), s(s(s(z))))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[7851, 75, 7836, 7818, 7805, 7801])).
% 2.02/2.24 tff(7853,plain,
% 2.02/2.24 (r(s(s(z)), s(s(s(z))))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[1559, 58, 1556, 7852])).
% 2.02/2.24 tff(7854,plain,
% 2.02/2.24 (b(s(s(s(z))), s(s(s(s(s(s(z))))))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 2.02/2.24 inference(symmetry,[status(thm)],[6229])).
% 2.02/2.24 tff(7855,plain,
% 2.02/2.24 ((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) <=> (~b(s(s(s(z))), s(s(elem!1))))),
% 2.02/2.24 inference(monotonicity,[status(thm)],[7854])).
% 2.02/2.24 tff(7856,plain,
% 2.02/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(s(s(s(z)))))))),
% 2.02/2.24 inference(rewrite,[status(thm)],[])).
% 2.02/2.24 tff(7857,plain,
% 2.02/2.24 (((~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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 2.02/2.24 inference(rewrite,[status(thm)],[])).
% 2.02/2.24 tff(7858,plain,
% 2.02/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(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(X1, 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(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(s(s(s(z))))))))),
% 2.02/2.24 inference(monotonicity,[status(thm)],[7857])).
% 2.02/2.24 tff(7859,plain,
% 2.02/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(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(X1, 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(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(s(s(s(z)))))))),
% 2.02/2.24 inference(transitivity,[status(thm)],[7858, 7856])).
% 2.02/2.24 tff(7860,plain,
% 2.02/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.02/2.24 inference(quant_inst,[status(thm)],[])).
% 2.02/2.24 tff(7861,plain,
% 2.02/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(s(s(s(z))))))),
% 2.02/2.24 inference(modus_ponens,[status(thm)],[7860, 7859])).
% 2.02/2.24 tff(7862,plain,
% 2.02/2.24 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[7861, 75, 7836, 7805, 7801])).
% 2.02/2.24 tff(7863,plain,
% 2.02/2.24 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.02/2.24 inference(modus_ponens,[status(thm)],[7862, 7855])).
% 2.02/2.24 tff(7864,plain,
% 2.02/2.24 (r(s(s(s(z))), s(s(elem!1)))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[62, 7863, 16])).
% 2.02/2.24 tff(7865,plain,
% 2.02/2.24 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.02/2.24 inference(modus_ponens,[status(thm)],[7864, 4603])).
% 2.02/2.24 tff(7866,plain,
% 2.02/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(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(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.02/2.24 inference(rewrite,[status(thm)],[])).
% 2.02/2.24 tff(7867,plain,
% 2.02/2.24 (((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.02/2.24 inference(rewrite,[status(thm)],[])).
% 2.02/2.24 tff(7868,plain,
% 2.02/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 2.02/2.25 inference(monotonicity,[status(thm)],[7867])).
% 2.02/2.25 tff(7869,plain,
% 2.02/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.02/2.25 inference(transitivity,[status(thm)],[7868, 7866])).
% 2.02/2.25 tff(7870,plain,
% 2.02/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.02/2.25 inference(quant_inst,[status(thm)],[])).
% 2.02/2.25 tff(7871,plain,
% 2.02/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 2.02/2.25 inference(modus_ponens,[status(thm)],[7870, 7869])).
% 2.02/2.25 tff(7872,plain,
% 2.02/2.25 ($false),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[7871, 37, 7865, 7853, 7845, 7830])).
% 2.02/2.25 tff(7873,plain,((~(elem!1 = s(s(s(s(z)))))) | (~b(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (s(s(s(z))) = s(s(elem!1))) | (~r(elem!1, s(z))) | (s(s(elem!1)) = s(s(s(s(z))))) | r(elem!1, s(s(elem!1))) | b(z, elem!1) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.02/2.25 tff(7874,plain,
% 2.02/2.25 (~b(s(z), z)),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[7873, 7785, 4464, 6204, 7130, 7774, 7775, 285, 7772])).
% 2.02/2.25 tff(7875,plain,
% 2.02/2.25 (r(z, s(s(s(s(z))))) <=> r(z, elem!1)),
% 2.02/2.25 inference(monotonicity,[status(thm)],[4467])).
% 2.02/2.25 tff(7876,plain,
% 2.02/2.25 (r(z, elem!1) <=> r(z, s(s(s(s(z)))))),
% 2.02/2.25 inference(symmetry,[status(thm)],[7875])).
% 2.02/2.25 tff(7877,plain,
% 2.02/2.25 (r(z, s(s(s(s(z)))))),
% 2.02/2.25 inference(modus_ponens,[status(thm)],[7806, 7876])).
% 2.02/2.25 tff(7878,plain,
% 2.02/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), 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(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 2.02/2.25 inference(rewrite,[status(thm)],[])).
% 2.02/2.25 tff(7879,plain,
% 2.02/2.25 (((~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 2.02/2.25 inference(rewrite,[status(thm)],[])).
% 2.02/2.25 tff(7880,plain,
% 2.02/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))))),
% 2.02/2.25 inference(monotonicity,[status(thm)],[7879])).
% 2.02/2.25 tff(7881,plain,
% 2.02/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 2.02/2.25 inference(transitivity,[status(thm)],[7880, 7878])).
% 2.02/2.25 tff(7882,plain,
% 2.02/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), z)))),
% 2.02/2.25 inference(quant_inst,[status(thm)],[])).
% 2.02/2.25 tff(7883,plain,
% 2.02/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))),
% 2.02/2.25 inference(modus_ponens,[status(thm)],[7882, 7881])).
% 2.02/2.25 tff(7884,plain,
% 2.02/2.25 (~r(z, s(s(s(s(z)))))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[7883, 37, 1561, 468])).
% 2.02/2.25 tff(7885,plain,
% 2.02/2.25 ($false),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[7884, 7877])).
% 2.02/2.25 tff(7886,plain,((~(elem!1 = s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.02/2.25 tff(7887,plain,
% 2.02/2.25 (~r(s(z), z)),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[7886, 7785, 4464, 285])).
% 2.02/2.25 tff(7888,plain,
% 2.02/2.25 ($false),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[169, 7887, 7874])).
% 2.02/2.25 tff(7889,plain,(b(elem!1, s(z)) | b(z, elem!1) | (s(s(elem!1)) = s(s(z))) | (~r(z, elem!1)) | (s(z) = elem!1) | (~(s(s(s(s(z)))) = elem!1)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 2.02/2.25 tff(7890,plain,
% 2.02/2.25 (b(elem!1, s(z))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[7889, 3285, 266, 300, 108, 285, 353])).
% 2.02/2.25 tff(7891,plain,
% 2.02/2.25 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[7757, 3656, 266, 285, 7130])).
% 2.02/2.25 tff(7892,plain,
% 2.02/2.25 (~b(s(s(z)), elem!1)),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[6139, 7891, 3285])).
% 2.02/2.25 tff(7893,plain,
% 2.02/2.25 (r(s(s(z)), elem!1)),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[104, 7892, 6325])).
% 2.02/2.25 tff(7894,plain,
% 2.02/2.25 ((elem!1 = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.02/2.25 inference(monotonicity,[status(thm)],[3311])).
% 2.02/2.25 tff(7895,plain,
% 2.02/2.25 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.02/2.25 inference(transitivity,[status(thm)],[7894, 3278])).
% 2.02/2.25 tff(7896,plain,
% 2.02/2.25 ((s(s(s(s(s(s(s(z))))))) = elem!1) <=> (elem!1 = s(s(s(elem!1))))),
% 2.02/2.25 inference(symmetry,[status(thm)],[7895])).
% 2.02/2.25 tff(7897,plain,
% 2.02/2.25 ((s(s(s(s(s(s(s(z))))))) = elem!1) <=> (s(s(s(elem!1))) = elem!1)),
% 2.02/2.25 inference(transitivity,[status(thm)],[7896, 3277])).
% 2.02/2.25 tff(7898,plain,
% 2.02/2.25 ((~(s(s(s(s(s(s(s(z))))))) = elem!1)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 2.02/2.25 inference(monotonicity,[status(thm)],[7897])).
% 2.02/2.25 tff(7899,plain,
% 2.02/2.25 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[3298, 3285, 3262])).
% 2.02/2.25 tff(7900,plain,
% 2.02/2.25 (~(s(s(s(elem!1))) = elem!1)),
% 2.02/2.25 inference(modus_ponens,[status(thm)],[7899, 7898])).
% 2.02/2.25 tff(7901,plain,
% 2.02/2.25 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(s(s(s(z)))))) = s(s(s(elem!1))))),
% 2.02/2.25 inference(monotonicity,[status(thm)],[3288])).
% 2.02/2.25 tff(7902,plain,
% 2.02/2.25 ((~(s(s(elem!1)) = s(s(s(elem!1))))) <=> (~(s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))))),
% 2.02/2.25 inference(monotonicity,[status(thm)],[7901])).
% 2.02/2.25 tff(7903,plain,
% 2.02/2.25 ((~(s(s(s(s(s(s(s(z))))))) = elem!1)) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 2.02/2.25 inference(monotonicity,[status(thm)],[7896])).
% 2.02/2.25 tff(7904,plain,
% 2.02/2.25 (~(elem!1 = s(s(s(elem!1))))),
% 2.02/2.25 inference(modus_ponens,[status(thm)],[7899, 7903])).
% 2.02/2.25 tff(7905,plain,
% 2.02/2.25 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[5804, 7904])).
% 2.02/2.25 tff(7906,plain,
% 2.02/2.25 (~(s(s(s(s(s(s(z)))))) = s(s(s(elem!1))))),
% 2.02/2.25 inference(modus_ponens,[status(thm)],[7905, 7902])).
% 2.02/2.25 tff(7907,plain,
% 2.02/2.25 (~r(s(z), elem!1)),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[3664, 3656, 3285])).
% 2.02/2.25 tff(7908,plain,
% 2.02/2.25 (b(s(z), elem!1)),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[601, 7907, 108])).
% 2.02/2.25 tff(7909,plain,
% 2.02/2.25 ((s(z) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(z))),
% 2.02/2.25 inference(commutativity,[status(thm)],[])).
% 2.02/2.25 tff(7910,plain,
% 2.02/2.25 ((s(z) = s(s(s(elem!1)))) <=> (s(z) = s(s(s(s(s(s(s(z))))))))),
% 2.02/2.25 inference(monotonicity,[status(thm)],[3311])).
% 2.02/2.25 tff(7911,plain,
% 2.02/2.25 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(s(s(s(s(z))))))) = s(z))),
% 2.02/2.25 inference(transitivity,[status(thm)],[7910, 7909])).
% 2.02/2.25 tff(7912,plain,
% 2.02/2.25 ((s(s(s(s(s(s(s(z))))))) = s(z)) <=> (s(z) = s(s(s(elem!1))))),
% 2.02/2.25 inference(symmetry,[status(thm)],[7911])).
% 2.02/2.25 tff(7913,plain,
% 2.02/2.25 ((~(s(s(s(s(s(s(s(z))))))) = s(z))) <=> (~(s(z) = s(s(s(elem!1)))))),
% 2.02/2.25 inference(monotonicity,[status(thm)],[7912])).
% 2.02/2.25 tff(7914,plain,
% 2.02/2.25 (~(s(z) = s(s(s(elem!1))))),
% 2.02/2.25 inference(modus_ponens,[status(thm)],[1227, 7913])).
% 2.02/2.25 tff(7915,plain,
% 2.02/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 2.02/2.25 inference(rewrite,[status(thm)],[])).
% 2.02/2.25 tff(7916,plain,
% 2.02/2.25 (((~b(s(z), elem!1)) | (~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(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 2.02/2.25 inference(rewrite,[status(thm)],[])).
% 2.02/2.25 tff(7917,plain,
% 2.02/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1)))))))),
% 2.02/2.25 inference(monotonicity,[status(thm)],[7916])).
% 2.02/2.25 tff(7918,plain,
% 2.02/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 2.02/2.25 inference(transitivity,[status(thm)],[7917, 7915])).
% 2.02/2.25 tff(7919,plain,
% 2.02/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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))))))),
% 2.02/2.25 inference(quant_inst,[status(thm)],[])).
% 2.02/2.25 tff(7920,plain,
% 2.02/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1)))))),
% 2.02/2.25 inference(modus_ponens,[status(thm)],[7919, 7918])).
% 2.02/2.25 tff(7921,plain,
% 2.02/2.25 (~b(s(z), s(s(s(elem!1))))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[7920, 75, 107, 1391, 922])).
% 2.02/2.25 tff(7922,plain,
% 2.02/2.25 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1)))))),
% 2.02/2.25 inference(rewrite,[status(thm)],[])).
% 2.02/2.25 tff(7923,plain,
% 2.02/2.25 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1)))))),
% 2.02/2.25 inference(quant_inst,[status(thm)],[])).
% 2.02/2.25 tff(7924,plain,
% 2.02/2.25 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1))))),
% 2.02/2.25 inference(modus_ponens,[status(thm)],[7923, 7922])).
% 2.02/2.25 tff(7925,plain,
% 2.02/2.25 ((s(z) = s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1))))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[7924, 58, 7921])).
% 2.02/2.25 tff(7926,plain,
% 2.02/2.25 (r(s(z), s(s(s(elem!1))))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[7925, 7914])).
% 2.02/2.25 tff(7927,plain,
% 2.02/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 2.02/2.25 inference(rewrite,[status(thm)],[])).
% 2.02/2.25 tff(7928,plain,
% 2.02/2.25 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 2.02/2.25 inference(rewrite,[status(thm)],[])).
% 2.02/2.25 tff(7929,plain,
% 2.02/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z)))))),
% 2.02/2.25 inference(monotonicity,[status(thm)],[7928])).
% 2.02/2.25 tff(7930,plain,
% 2.02/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 2.02/2.25 inference(transitivity,[status(thm)],[7929, 7927])).
% 2.02/2.25 tff(7931,plain,
% 2.02/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 2.02/2.25 inference(quant_inst,[status(thm)],[])).
% 2.02/2.25 tff(7932,plain,
% 2.02/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z)))),
% 2.02/2.25 inference(modus_ponens,[status(thm)],[7931, 7930])).
% 2.02/2.25 tff(7933,plain,
% 2.02/2.25 (~b(s(s(s(elem!1))), s(z))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[7932, 75, 107, 1391, 922])).
% 2.02/2.25 tff(7934,plain,
% 2.02/2.25 ((s(s(s(elem!1))) = s(z)) | r(s(s(s(elem!1))), s(z))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[3400, 58, 7933])).
% 2.02/2.25 tff(7935,plain,
% 2.02/2.25 (r(s(s(s(elem!1))), s(z))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[7934, 4098])).
% 2.02/2.25 tff(7936,plain,
% 2.02/2.25 ((s(s(s(elem!1))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(s(s(elem!1))))),
% 2.02/2.25 inference(commutativity,[status(thm)],[])).
% 2.02/2.25 tff(7937,plain,
% 2.02/2.25 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(s(s(elem!1))) = s(s(s(s(s(s(z)))))))),
% 2.02/2.25 inference(monotonicity,[status(thm)],[3288])).
% 2.02/2.25 tff(7938,plain,
% 2.02/2.25 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(s(s(s(s(s(z)))))) = s(s(s(elem!1))))),
% 2.02/2.25 inference(transitivity,[status(thm)],[7937, 7936])).
% 2.02/2.25 tff(7939,plain,
% 2.02/2.25 ((s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 2.02/2.25 inference(symmetry,[status(thm)],[7938])).
% 2.02/2.25 tff(7940,plain,
% 2.02/2.25 ((~(s(s(s(s(s(s(z)))))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 2.02/2.26 inference(monotonicity,[status(thm)],[7939])).
% 2.02/2.26 tff(7941,assumption,(~(s(s(s(s(s(s(z)))))) = s(s(s(elem!1))))), introduced(assumption)).
% 2.02/2.26 tff(7942,plain,
% 2.02/2.26 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.02/2.26 inference(modus_ponens,[status(thm)],[7941, 7940])).
% 2.02/2.26 tff(7943,plain,
% 2.02/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(s(z), 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(X1, 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(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.02/2.26 inference(rewrite,[status(thm)],[])).
% 2.02/2.26 tff(7944,plain,
% 2.02/2.26 (((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~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(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.02/2.26 inference(rewrite,[status(thm)],[])).
% 2.02/2.26 tff(7945,plain,
% 2.02/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~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(X1, 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(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 2.02/2.26 inference(monotonicity,[status(thm)],[7944])).
% 2.02/2.26 tff(7946,plain,
% 2.02/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~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(X1, 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(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.02/2.26 inference(transitivity,[status(thm)],[7945, 7943])).
% 2.02/2.26 tff(7947,plain,
% 2.02/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~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)))))),
% 2.02/2.26 inference(quant_inst,[status(thm)],[])).
% 2.02/2.26 tff(7948,plain,
% 2.02/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 2.02/2.26 inference(modus_ponens,[status(thm)],[7947, 7946])).
% 2.02/2.26 tff(7949,plain,
% 2.02/2.26 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[7948, 75, 107, 1391, 707, 922])).
% 2.02/2.26 tff(7950,plain,
% 2.02/2.26 (((~![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))))),
% 2.02/2.26 inference(rewrite,[status(thm)],[])).
% 2.02/2.26 tff(7951,plain,
% 2.02/2.26 ((~![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))))),
% 2.02/2.26 inference(quant_inst,[status(thm)],[])).
% 2.02/2.26 tff(7952,plain,
% 2.02/2.26 ((~![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)))),
% 2.02/2.26 inference(modus_ponens,[status(thm)],[7951, 7950])).
% 2.02/2.26 tff(7953,plain,
% 2.02/2.26 ((s(s(s(elem!1))) = s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[7952, 58, 7949])).
% 2.02/2.26 tff(7954,plain,
% 2.02/2.26 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[7953, 7942])).
% 2.02/2.26 tff(7955,plain,
% 2.02/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))))),
% 2.02/2.26 inference(rewrite,[status(thm)],[])).
% 2.02/2.26 tff(7956,plain,
% 2.02/2.26 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))))),
% 2.02/2.26 inference(rewrite,[status(thm)],[])).
% 2.02/2.26 tff(7957,plain,
% 2.02/2.26 (((~![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))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1)))))))),
% 2.02/2.26 inference(monotonicity,[status(thm)],[7956])).
% 2.02/2.26 tff(7958,plain,
% 2.02/2.26 (((~![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))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))))),
% 2.02/2.26 inference(transitivity,[status(thm)],[7957, 7955])).
% 2.02/2.26 tff(7959,plain,
% 2.02/2.26 ((~![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))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))))),
% 2.02/2.26 inference(quant_inst,[status(thm)],[])).
% 2.02/2.26 tff(7960,plain,
% 2.02/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1)))))),
% 2.02/2.26 inference(modus_ponens,[status(thm)],[7959, 7958])).
% 2.02/2.26 tff(7961,plain,
% 2.02/2.26 ($false),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[7960, 37, 6901, 7954, 7935, 7926])).
% 2.02/2.26 tff(7962,plain,((~b(elem!1, s(z))) | (~(s(s(s(s(z)))) = elem!1)) | (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.26 tff(7963,plain,
% 2.02/2.26 (~b(s(s(s(elem!1))), elem!1)),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[7962, 7908, 3285, 7906, 1391, 7773])).
% 2.02/2.26 tff(7964,plain,
% 2.02/2.26 (r(s(s(s(elem!1))), elem!1)),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[3370, 7963, 7900])).
% 2.02/2.26 tff(7965,plain,
% 2.02/2.26 (~r(s(s(s(elem!1))), z)),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[944, 37, 300, 624])).
% 2.02/2.26 tff(7966,plain,
% 2.02/2.26 (b(s(s(s(elem!1))), z)),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[948, 58, 662, 7965])).
% 2.02/2.26 tff(7967,plain,
% 2.02/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.02/2.26 inference(rewrite,[status(thm)],[])).
% 2.02/2.26 tff(7968,plain,
% 2.02/2.26 (((~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.02/2.26 inference(rewrite,[status(thm)],[])).
% 2.02/2.26 tff(7969,plain,
% 2.02/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 2.02/2.26 inference(monotonicity,[status(thm)],[7968])).
% 2.02/2.26 tff(7970,plain,
% 2.02/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.02/2.26 inference(transitivity,[status(thm)],[7969, 7967])).
% 2.02/2.26 tff(7971,plain,
% 2.02/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.02/2.26 inference(quant_inst,[status(thm)],[])).
% 2.02/2.26 tff(7972,plain,
% 2.02/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 2.02/2.26 inference(modus_ponens,[status(thm)],[7971, 7970])).
% 2.02/2.26 tff(7973,plain,
% 2.02/2.26 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[7972, 75, 678, 2073, 7966])).
% 2.02/2.26 tff(7974,plain,
% 2.02/2.26 ($false),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[3361, 7973, 3316])).
% 2.02/2.26 tff(7975,plain,((~r(s(s(s(elem!1))), elem!1)) | (~(s(s(s(s(z)))) = elem!1)) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.26 tff(7976,plain,
% 2.02/2.26 ($false),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[7975, 7964, 7893, 300, 3285])).
% 2.02/2.26 tff(7977,plain,(r(s(z), s(s(s(s(z))))) | (~r(z, elem!1)) | (~(s(s(s(s(z)))) = elem!1)) | (~b(elem!1, s(z))) | (s(z) = elem!1) | (s(s(elem!1)) = s(s(z))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.02/2.26 tff(7978,plain,
% 2.02/2.26 (r(s(z), s(s(s(s(z)))))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[7977, 3285, 300, 7890, 108, 266, 285])).
% 2.02/2.26 tff(7979,plain,
% 2.02/2.26 (r(s(z), elem!1)),
% 2.02/2.26 inference(modus_ponens,[status(thm)],[7978, 3660])).
% 2.02/2.26 tff(7980,plain,
% 2.02/2.26 (~r(s(s(z)), elem!1)),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[2086, 7979, 300])).
% 2.02/2.26 tff(7981,plain,
% 2.02/2.26 (b(s(s(z)), elem!1)),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[104, 7980, 6325])).
% 2.02/2.26 tff(7982,plain,
% 2.02/2.26 (~r(s(z), z)),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[7886, 7978, 4464, 285])).
% 2.02/2.26 tff(7983,plain,
% 2.02/2.26 (b(s(z), z)),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[169, 7982])).
% 2.02/2.26 tff(7984,plain,
% 2.02/2.26 (~r(z, s(z))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[1358, 7979, 300])).
% 2.02/2.26 tff(7985,plain,
% 2.02/2.26 (b(z, s(z))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[187, 7984])).
% 2.02/2.26 tff(7986,plain,
% 2.02/2.26 (~b(s(s(z)), s(z))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[7565, 7985, 7890, 7983, 7981])).
% 2.02/2.26 tff(7987,plain,
% 2.02/2.26 (r(s(s(z)), s(z))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[153, 7986])).
% 2.02/2.26 tff(7988,plain,
% 2.02/2.26 (~b(elem!1, z)),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[7583, 75, 7985, 7983, 7890])).
% 2.02/2.26 tff(7989,plain,
% 2.02/2.26 (r(elem!1, z)),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[387, 7988, 353])).
% 2.02/2.26 tff(7990,plain,
% 2.02/2.26 (r(s(s(s(s(z)))), z)),
% 2.02/2.26 inference(modus_ponens,[status(thm)],[7989, 4743])).
% 2.02/2.26 tff(7991,plain,
% 2.02/2.26 (~r(s(s(s(z))), elem!1)),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[1362, 7979, 300])).
% 2.02/2.26 tff(7992,plain,
% 2.02/2.26 (b(s(s(s(z))), elem!1)),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[1115, 7991, 6405])).
% 2.02/2.26 tff(7993,plain,
% 2.02/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~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(X1, 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)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))))),
% 2.02/2.26 inference(rewrite,[status(thm)],[])).
% 2.02/2.26 tff(7994,plain,
% 2.02/2.26 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))))),
% 2.02/2.26 inference(rewrite,[status(thm)],[])).
% 2.02/2.26 tff(7995,plain,
% 2.02/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~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(X1, 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)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z)))))))),
% 2.02/2.26 inference(monotonicity,[status(thm)],[7994])).
% 2.02/2.26 tff(7996,plain,
% 2.02/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~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(X1, 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)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))))),
% 2.02/2.26 inference(transitivity,[status(thm)],[7995, 7993])).
% 2.02/2.26 tff(7997,plain,
% 2.02/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))))),
% 2.02/2.26 inference(quant_inst,[status(thm)],[])).
% 2.02/2.26 tff(7998,plain,
% 2.02/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z)))))),
% 2.02/2.26 inference(modus_ponens,[status(thm)],[7997, 7996])).
% 2.02/2.26 tff(7999,plain,
% 2.02/2.26 (~b(s(s(z)), s(s(s(z))))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[7998, 75, 1620, 964, 1119, 707])).
% 2.02/2.26 tff(8000,plain,
% 2.02/2.26 (r(s(s(z)), s(s(s(z))))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[1559, 58, 1556, 7999])).
% 2.02/2.26 tff(8001,assumption,(~(s(s(z)) = s(s(elem!1)))), introduced(assumption)).
% 2.02/2.26 tff(8002,plain,
% 2.02/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.02/2.26 inference(rewrite,[status(thm)],[])).
% 2.02/2.26 tff(8003,plain,
% 2.02/2.26 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.02/2.26 inference(rewrite,[status(thm)],[])).
% 2.02/2.26 tff(8004,plain,
% 2.02/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1))))))),
% 2.02/2.26 inference(monotonicity,[status(thm)],[8003])).
% 2.02/2.26 tff(8005,plain,
% 2.02/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.02/2.26 inference(transitivity,[status(thm)],[8004, 8002])).
% 2.02/2.26 tff(8006,plain,
% 2.02/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.02/2.26 inference(quant_inst,[status(thm)],[])).
% 2.02/2.26 tff(8007,plain,
% 2.02/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1))))),
% 2.02/2.26 inference(modus_ponens,[status(thm)],[8006, 8005])).
% 2.02/2.26 tff(8008,plain,
% 2.02/2.26 (~b(s(s(z)), s(s(elem!1)))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[8007, 75, 1620, 964, 707])).
% 2.02/2.26 tff(8009,plain,
% 2.02/2.26 (r(s(s(z)), s(s(elem!1)))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[6336, 58, 8008, 8001])).
% 2.02/2.26 tff(8010,plain,
% 2.02/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.02/2.27 inference(rewrite,[status(thm)],[])).
% 2.02/2.27 tff(8011,plain,
% 2.02/2.27 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.02/2.27 inference(rewrite,[status(thm)],[])).
% 2.02/2.27 tff(8012,plain,
% 2.02/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 2.02/2.27 inference(monotonicity,[status(thm)],[8011])).
% 2.02/2.27 tff(8013,plain,
% 2.02/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.02/2.27 inference(transitivity,[status(thm)],[8012, 8010])).
% 2.02/2.27 tff(8014,plain,
% 2.02/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.02/2.27 inference(quant_inst,[status(thm)],[])).
% 2.02/2.27 tff(8015,plain,
% 2.02/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(elem!1))))),
% 2.02/2.27 inference(modus_ponens,[status(thm)],[8014, 8013])).
% 2.02/2.27 tff(8016,plain,
% 2.02/2.27 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[8015, 75, 1620, 1119, 707])).
% 2.02/2.27 tff(8017,plain,
% 2.02/2.27 (r(s(s(s(z))), s(s(elem!1)))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[62, 8016, 16])).
% 2.02/2.27 tff(8018,plain,
% 2.02/2.27 (((~![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(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.02/2.27 inference(rewrite,[status(thm)],[])).
% 2.02/2.27 tff(8019,plain,
% 2.02/2.27 (((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.02/2.27 inference(rewrite,[status(thm)],[])).
% 2.02/2.27 tff(8020,plain,
% 2.02/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(z)))))))),
% 2.02/2.27 inference(monotonicity,[status(thm)],[8019])).
% 2.02/2.27 tff(8021,plain,
% 2.02/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.02/2.27 inference(transitivity,[status(thm)],[8020, 8018])).
% 2.02/2.27 tff(8022,plain,
% 2.02/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.02/2.27 inference(quant_inst,[status(thm)],[])).
% 2.02/2.27 tff(8023,plain,
% 2.02/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(z)))))),
% 2.02/2.27 inference(modus_ponens,[status(thm)],[8022, 8021])).
% 2.02/2.27 tff(8024,plain,
% 2.02/2.27 ($false),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[8023, 37, 8017, 8009, 8000])).
% 2.02/2.27 tff(8025,plain,((~b(elem!1, s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | (s(s(s(z))) = s(s(elem!1))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.27 tff(8026,plain,
% 2.02/2.27 (~b(elem!1, s(s(elem!1)))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[8025, 7992, 6204, 7548, 7773, 7981])).
% 2.02/2.27 tff(8027,plain,
% 2.02/2.27 (r(elem!1, s(s(elem!1)))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[1617, 8026, 4476])).
% 2.02/2.27 tff(8028,plain,
% 2.02/2.27 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.02/2.27 inference(modus_ponens,[status(thm)],[8027, 4740])).
% 2.02/2.27 tff(8029,plain,
% 2.02/2.27 (~r(s(s(elem!1)), z)),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[2707, 8028, 7990])).
% 2.02/2.27 tff(8030,plain,
% 2.02/2.27 (b(s(s(elem!1)), z)),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[2696, 8029])).
% 2.02/2.27 tff(8031,plain,
% 2.02/2.27 (~b(s(s(elem!1)), s(z))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[4754, 7985, 7983, 8030])).
% 2.02/2.27 tff(8032,plain,
% 2.02/2.27 (r(s(s(elem!1)), s(z))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[561, 8031])).
% 2.02/2.27 tff(8033,plain,
% 2.02/2.27 (~r(s(s(z)), s(s(elem!1)))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[2243, 37, 8032, 7987])).
% 2.02/2.27 tff(8034,plain,
% 2.02/2.27 (b(s(s(z)), s(s(elem!1)))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[6336, 58, 8033, 7548])).
% 2.02/2.27 tff(8035,plain,
% 2.02/2.27 (~r(s(s(elem!1)), s(s(z)))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[500, 37, 8032, 7987])).
% 2.02/2.27 tff(8036,plain,
% 2.02/2.27 (b(s(s(elem!1)), s(s(z)))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[1476, 8035, 266])).
% 2.02/2.27 tff(8037,plain,
% 2.02/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(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(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(elem!1)))))),
% 2.02/2.27 inference(rewrite,[status(thm)],[])).
% 2.02/2.27 tff(8038,plain,
% 2.02/2.27 (((~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(elem!1)))))),
% 2.02/2.27 inference(rewrite,[status(thm)],[])).
% 2.02/2.27 tff(8039,plain,
% 2.02/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(elem!1))))))),
% 2.02/2.27 inference(monotonicity,[status(thm)],[8038])).
% 2.02/2.27 tff(8040,plain,
% 2.02/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(elem!1)))))),
% 2.02/2.27 inference(transitivity,[status(thm)],[8039, 8037])).
% 2.02/2.27 tff(8041,plain,
% 2.02/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(s(z))))))),
% 2.02/2.27 inference(quant_inst,[status(thm)],[])).
% 2.02/2.27 tff(8042,plain,
% 2.02/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(elem!1))))),
% 2.02/2.27 inference(modus_ponens,[status(thm)],[8041, 8040])).
% 2.02/2.27 tff(8043,plain,
% 2.02/2.27 (~r(elem!1, s(s(s(z))))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[8042, 37, 1490, 27])).
% 2.02/2.27 tff(8044,plain,
% 2.02/2.27 (b(elem!1, s(s(s(z))))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[1279, 8043, 1305])).
% 2.02/2.27 tff(8045,plain,
% 2.02/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(elem!1, 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(X1, 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(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.02/2.27 inference(rewrite,[status(thm)],[])).
% 2.02/2.27 tff(8046,plain,
% 2.02/2.27 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.02/2.27 inference(rewrite,[status(thm)],[])).
% 2.02/2.27 tff(8047,plain,
% 2.02/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 2.02/2.27 inference(monotonicity,[status(thm)],[8046])).
% 2.02/2.27 tff(8048,plain,
% 2.02/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.02/2.27 inference(transitivity,[status(thm)],[8047, 8045])).
% 2.02/2.27 tff(8049,plain,
% 2.02/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))))),
% 2.02/2.27 inference(quant_inst,[status(thm)],[])).
% 2.02/2.27 tff(8050,plain,
% 2.02/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))),
% 2.02/2.27 inference(modus_ponens,[status(thm)],[8049, 8048])).
% 2.02/2.27 tff(8051,plain,
% 2.02/2.27 (~b(s(s(z)), s(s(s(z))))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[8050, 75, 964, 1119, 8044])).
% 2.02/2.27 tff(8052,plain,
% 2.02/2.27 (r(s(s(z)), s(s(s(z))))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[1559, 58, 1556, 8051])).
% 2.02/2.27 tff(8053,plain,
% 2.02/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))))),
% 2.02/2.27 inference(rewrite,[status(thm)],[])).
% 2.02/2.27 tff(8054,plain,
% 2.02/2.27 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))))),
% 2.02/2.27 inference(rewrite,[status(thm)],[])).
% 2.02/2.27 tff(8055,plain,
% 2.02/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(elem!1, s(s(s(z)))))))),
% 2.02/2.27 inference(monotonicity,[status(thm)],[8054])).
% 2.02/2.27 tff(8056,plain,
% 2.02/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))))),
% 2.02/2.27 inference(transitivity,[status(thm)],[8055, 8053])).
% 2.02/2.27 tff(8057,plain,
% 2.02/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.02/2.27 inference(quant_inst,[status(thm)],[])).
% 2.02/2.27 tff(8058,plain,
% 2.02/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(elem!1, s(s(s(z)))))),
% 2.02/2.27 inference(modus_ponens,[status(thm)],[8057, 8056])).
% 2.02/2.27 tff(8059,plain,
% 2.02/2.27 (~b(s(s(z)), s(s(elem!1)))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[8058, 75, 964, 1119, 8044, 707])).
% 2.02/2.27 tff(8060,plain,
% 2.02/2.27 (r(s(s(z)), s(s(elem!1)))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[6336, 58, 8059, 8001])).
% 2.02/2.27 tff(8061,plain,
% 2.02/2.27 ($false),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[8023, 37, 27, 8060, 8052])).
% 2.02/2.27 tff(8062,plain,((~r(s(s(s(z))), s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (elem!1 = s(s(s(z)))) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.27 tff(8063,plain,
% 2.02/2.27 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[8062, 7981, 7548, 7992, 7773, 6426, 8027])).
% 2.02/2.27 tff(8064,plain,
% 2.02/2.27 (b(s(s(s(z))), s(s(elem!1)))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[62, 8063, 6204])).
% 2.02/2.27 tff(8065,plain,
% 2.02/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), elem!1)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), elem!1)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.02/2.27 inference(rewrite,[status(thm)],[])).
% 2.02/2.27 tff(8066,plain,
% 2.02/2.27 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.02/2.27 inference(rewrite,[status(thm)],[])).
% 2.02/2.27 tff(8067,plain,
% 2.02/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), elem!1)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 2.02/2.27 inference(monotonicity,[status(thm)],[8066])).
% 2.02/2.27 tff(8068,plain,
% 2.02/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), elem!1)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.02/2.27 inference(transitivity,[status(thm)],[8067, 8065])).
% 2.02/2.27 tff(8069,plain,
% 2.02/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.02/2.27 inference(quant_inst,[status(thm)],[])).
% 2.02/2.27 tff(8070,plain,
% 2.02/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), elem!1)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 2.02/2.28 inference(modus_ponens,[status(thm)],[8069, 8068])).
% 2.02/2.28 tff(8071,plain,
% 2.02/2.28 (~b(s(s(s(z))), s(s(z)))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[8070, 75, 7992, 8064, 8036, 8034, 7773])).
% 2.02/2.28 tff(8072,plain,
% 2.02/2.28 ((s(s(s(z))) = s(s(z))) | r(s(s(s(z))), s(s(z)))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[2173, 58, 8071])).
% 2.02/2.28 tff(8073,plain,
% 2.02/2.28 (r(s(s(s(z))), s(s(z)))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[8072, 2150])).
% 2.02/2.28 tff(8074,plain,
% 2.02/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))))),
% 2.02/2.28 inference(rewrite,[status(thm)],[])).
% 2.02/2.28 tff(8075,plain,
% 2.02/2.28 (((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))))),
% 2.02/2.28 inference(rewrite,[status(thm)],[])).
% 2.02/2.28 tff(8076,plain,
% 2.02/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(z), z)) | (~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(X1, 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(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z)))))),
% 2.02/2.28 inference(monotonicity,[status(thm)],[8075])).
% 2.02/2.28 tff(8077,plain,
% 2.02/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(z), z)) | (~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(X1, 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(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))))),
% 2.02/2.28 inference(transitivity,[status(thm)],[8076, 8074])).
% 2.02/2.28 tff(8078,plain,
% 2.02/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 2.02/2.28 inference(quant_inst,[status(thm)],[])).
% 2.02/2.28 tff(8079,plain,
% 2.02/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z)))),
% 2.02/2.28 inference(modus_ponens,[status(thm)],[8078, 8077])).
% 2.02/2.28 tff(8080,plain,
% 2.02/2.28 ($false),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[8079, 75, 372, 371, 1391, 1119, 984])).
% 2.02/2.28 tff(8081,plain,((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.28 tff(8082,plain,
% 2.02/2.28 (~b(s(s(s(z))), s(z))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[8081, 7985, 7983, 7890, 7992])).
% 2.02/2.28 tff(8083,plain,
% 2.02/2.28 (r(s(s(s(z))), s(z))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[1081, 8082])).
% 2.02/2.28 tff(8084,plain,
% 2.02/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.02/2.28 inference(rewrite,[status(thm)],[])).
% 2.02/2.28 tff(8085,plain,
% 2.02/2.28 (((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.02/2.28 inference(rewrite,[status(thm)],[])).
% 2.02/2.28 tff(8086,plain,
% 2.02/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z))))))),
% 2.02/2.28 inference(monotonicity,[status(thm)],[8085])).
% 2.02/2.28 tff(8087,plain,
% 2.02/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.02/2.28 inference(transitivity,[status(thm)],[8086, 8084])).
% 2.02/2.28 tff(8088,plain,
% 2.02/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.02/2.28 inference(quant_inst,[status(thm)],[])).
% 2.02/2.28 tff(8089,plain,
% 2.02/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z))))),
% 2.02/2.28 inference(modus_ponens,[status(thm)],[8088, 8087])).
% 2.02/2.28 tff(8090,plain,
% 2.02/2.28 ($false),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[8089, 37, 7987, 8083, 8073])).
% 2.02/2.28 tff(8091,plain,((~(s(s(s(s(z)))) = elem!1)) | (s(s(elem!1)) = s(s(z))) | (elem!1 = z) | (~r(z, elem!1)) | b(z, elem!1) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.02/2.28 tff(8092,plain,
% 2.02/2.28 (~(s(s(s(s(z)))) = elem!1)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[8091, 7125, 7108, 7124, 285, 7123])).
% 2.02/2.28 tff(8093,plain,
% 2.02/2.28 (b(s(s(s(s(z)))), elem!1)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[283, 8092, 12])).
% 2.02/2.28 tff(8094,plain,
% 2.02/2.28 (~r(s(z), elem!1)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[1358, 506, 7108])).
% 2.02/2.28 tff(8095,plain,
% 2.02/2.28 (b(s(z), elem!1)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[601, 7124, 8094])).
% 2.02/2.28 tff(8096,plain,
% 2.02/2.28 (~b(s(s(s(s(z)))), s(z))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[1402, 75, 8095, 7121, 8093])).
% 2.02/2.28 tff(8097,plain,
% 2.02/2.28 (r(s(s(s(s(z)))), s(z))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[1406, 58, 8096, 483])).
% 2.02/2.28 tff(8098,plain,
% 2.02/2.28 (~r(s(s(s(s(z)))), z)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[1417, 8097, 506])).
% 2.02/2.28 tff(8099,plain,
% 2.02/2.28 (b(s(s(s(s(z)))), z)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[1421, 58, 1143, 8098])).
% 2.02/2.28 tff(8100,plain,
% 2.02/2.28 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[6517, 8093, 1])).
% 2.02/2.28 tff(8101,plain,
% 2.02/2.28 (~(s(s(z)) = elem!1)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[1013, 8100])).
% 2.02/2.28 tff(8102,plain,
% 2.02/2.28 (r(s(s(z)), elem!1)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[104, 8101, 99])).
% 2.02/2.28 tff(8103,plain,
% 2.02/2.28 (~r(s(s(z)), z)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[328, 8102, 7108])).
% 2.02/2.28 tff(8104,plain,
% 2.02/2.28 (b(s(s(z)), z)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[202, 8103])).
% 2.02/2.28 tff(8105,plain,
% 2.02/2.28 (~r(z, s(s(z)))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[339, 8102, 7108])).
% 2.02/2.28 tff(8106,plain,
% 2.02/2.28 (b(z, s(s(z)))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[351, 8105])).
% 2.02/2.28 tff(8107,plain,
% 2.02/2.28 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[1670, 75, 8106, 8104, 8099])).
% 2.02/2.28 tff(8108,plain,
% 2.02/2.28 (r(s(s(z)), s(s(s(s(z)))))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[465, 8107])).
% 2.02/2.28 tff(8109,plain,
% 2.02/2.28 (r(elem!1, s(s(s(s(z)))))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[3193, 8092, 12, 99, 7125])).
% 2.02/2.28 tff(8110,plain,
% 2.02/2.28 ($false),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[6555, 37, 8102, 8109, 8108])).
% 2.02/2.28 tff(8111,plain,(b(s(s(elem!1)), elem!1) | (~r(z, s(z))) | b(s(s(z)), elem!1) | r(s(s(s(s(z)))), elem!1) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.02/2.28 tff(8112,plain,
% 2.02/2.28 (~r(z, s(z))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[8111, 1, 99, 12, 285])).
% 2.02/2.28 tff(8113,plain,
% 2.02/2.28 (b(z, s(z))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[187, 8112])).
% 2.02/2.28 tff(8114,plain,
% 2.02/2.28 (~(s(z) = elem!1)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[2093, 8113, 285])).
% 2.02/2.28 tff(8115,plain,
% 2.02/2.28 ((~b(elem!1, s(z))) <=> (~b(z, s(z)))),
% 2.02/2.28 inference(monotonicity,[status(thm)],[5496])).
% 2.02/2.28 tff(8116,plain,
% 2.02/2.28 (~b(z, s(z))),
% 2.02/2.28 inference(modus_ponens,[status(thm)],[14, 8115])).
% 2.02/2.28 tff(8117,plain,
% 2.02/2.28 ($false),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[372, 8116])).
% 2.02/2.28 tff(8118,plain,((~(z = elem!1)) | (~b(z, s(z))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.28 tff(8119,plain,
% 2.02/2.28 (~(z = elem!1)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[8118, 14, 372])).
% 2.02/2.28 tff(8120,plain,
% 2.02/2.28 (~(elem!1 = z)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[304, 8119])).
% 2.02/2.28 tff(8121,plain,
% 2.02/2.28 (~(s(s(elem!1)) = s(s(z)))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[237, 8119])).
% 2.02/2.28 tff(8122,plain,
% 2.02/2.28 (~(elem!1 = s(z))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[111, 2094])).
% 2.02/2.28 tff(8123,plain,
% 2.02/2.28 (r(elem!1, s(z))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[89, 14, 8122])).
% 2.02/2.28 tff(8124,plain,
% 2.02/2.28 (~b(s(z), s(s(s(s(z)))))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[7428, 114, 300, 3195])).
% 2.02/2.28 tff(8125,plain,
% 2.02/2.28 (~r(s(z), s(s(s(s(z)))))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[3203, 114, 3195])).
% 2.02/2.28 tff(8126,plain,
% 2.02/2.28 ($false),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[489, 8125, 8124])).
% 2.02/2.28 tff(8127,plain,((~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.28 tff(8128,plain,
% 2.02/2.28 (~r(elem!1, s(s(s(s(z)))))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[8127, 8123, 7108])).
% 2.02/2.28 tff(8129,plain,
% 2.02/2.28 (s(s(s(s(z)))) = elem!1),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[3193, 8128, 12, 99, 8121])).
% 2.02/2.28 tff(8130,plain,
% 2.02/2.28 ($false),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[8091, 8129, 8121, 7108, 2094, 285, 8120])).
% 2.02/2.28 tff(8131,plain,(b(elem!1, s(z)) | b(z, elem!1) | r(s(s(s(s(z)))), elem!1) | b(s(s(z)), elem!1) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.28 tff(8132,plain,
% 2.02/2.28 (b(elem!1, s(z))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[8131, 8113, 12, 99, 285])).
% 2.02/2.28 tff(8133,plain,
% 2.02/2.28 (~(z = elem!1)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[6116, 8132, 12])).
% 2.02/2.28 tff(8134,plain,
% 2.02/2.28 (~(elem!1 = z)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[304, 8133])).
% 2.02/2.28 tff(8135,plain,
% 2.02/2.28 (~(s(s(elem!1)) = s(s(z)))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[237, 8133])).
% 2.02/2.28 tff(8136,plain,
% 2.02/2.28 (~(s(s(s(s(z)))) = elem!1)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[8091, 8135, 7108, 8114, 285, 8134])).
% 2.02/2.28 tff(8137,plain,
% 2.02/2.28 (b(s(s(s(s(z)))), elem!1)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[283, 8136, 12])).
% 2.02/2.28 tff(8138,plain,
% 2.02/2.28 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[6517, 8137, 1])).
% 2.02/2.28 tff(8139,plain,
% 2.02/2.28 (~(s(s(z)) = elem!1)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[1013, 8138])).
% 2.02/2.28 tff(8140,plain,
% 2.02/2.28 (r(s(s(z)), elem!1)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[104, 8139, 99])).
% 2.02/2.28 tff(8141,plain,
% 2.02/2.28 (~r(s(z), elem!1)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[2086, 8140, 7108])).
% 2.02/2.28 tff(8142,plain,
% 2.02/2.28 (b(s(z), elem!1)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[601, 8141, 8114])).
% 2.02/2.28 tff(8143,plain,
% 2.02/2.28 (~b(s(z), s(s(s(s(z)))))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[5527, 8142, 8132, 8137])).
% 2.02/2.28 tff(8144,plain,
% 2.02/2.28 (r(s(z), s(s(s(s(z)))))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[489, 8143])).
% 2.02/2.28 tff(8145,plain,
% 2.02/2.28 (~b(elem!1, z)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[2101, 75, 8113, 8142, 8132])).
% 2.02/2.28 tff(8146,plain,
% 2.02/2.28 (r(elem!1, z)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[387, 8145, 8134])).
% 2.02/2.28 tff(8147,plain,
% 2.02/2.28 (~b(s(s(z)), s(z))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[1792, 8142, 8113, 8133, 8132, 8140])).
% 2.02/2.28 tff(8148,plain,
% 2.02/2.28 (r(s(s(z)), s(z))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[153, 8147])).
% 2.02/2.28 tff(8149,plain,
% 2.02/2.28 (~r(s(s(z)), z)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[328, 8140, 7108])).
% 2.02/2.28 tff(8150,plain,
% 2.02/2.28 (b(s(s(z)), z)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[202, 8149])).
% 2.02/2.28 tff(8151,plain,
% 2.02/2.28 (~r(z, s(s(z)))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[339, 8140, 7108])).
% 2.02/2.28 tff(8152,plain,
% 2.02/2.28 (b(z, s(s(z)))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[351, 8151])).
% 2.02/2.28 tff(8153,plain,
% 2.02/2.28 (((~![X0: $i, 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)))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), elem!1)))),
% 2.02/2.28 inference(rewrite,[status(thm)],[])).
% 2.02/2.28 tff(8154,plain,
% 2.02/2.28 (((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), elem!1)) | (~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)))) | (~r(s(s(z)), elem!1)))),
% 2.02/2.28 inference(rewrite,[status(thm)],[])).
% 2.02/2.28 tff(8155,plain,
% 2.02/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~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)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), elem!1))))),
% 2.02/2.28 inference(monotonicity,[status(thm)],[8154])).
% 2.02/2.28 tff(8156,plain,
% 2.02/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~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)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), elem!1)))),
% 2.02/2.28 inference(transitivity,[status(thm)],[8155, 8153])).
% 2.02/2.28 tff(8157,plain,
% 2.02/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.02/2.28 inference(quant_inst,[status(thm)],[])).
% 2.02/2.28 tff(8158,plain,
% 2.02/2.28 ((~![X0: $i, 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)))) | (~r(s(s(z)), elem!1))),
% 2.02/2.28 inference(modus_ponens,[status(thm)],[8157, 8156])).
% 2.02/2.28 tff(8159,plain,
% 2.02/2.28 (~r(s(s(elem!1)), s(s(z)))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[8158, 37, 494, 106, 115])).
% 2.02/2.28 tff(8160,plain,
% 2.02/2.28 (~(elem!1 = s(s(elem!1)))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[2258, 494, 468, 287, 266, 115])).
% 2.02/2.28 tff(8161,plain,
% 2.02/2.28 (~(s(s(elem!1)) = elem!1)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[2555, 8160])).
% 2.02/2.28 tff(8162,plain,
% 2.02/2.28 (r(s(s(elem!1)), elem!1)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[2673, 8161, 1])).
% 2.02/2.28 tff(8163,plain,
% 2.02/2.28 (~r(s(s(elem!1)), z)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[4774, 8162, 155])).
% 2.02/2.28 tff(8164,plain,
% 2.02/2.28 (b(s(s(elem!1)), z)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[2696, 8163])).
% 2.02/2.28 tff(8165,plain,
% 2.02/2.28 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[476, 468, 115])).
% 2.02/2.28 tff(8166,plain,
% 2.02/2.28 (b(s(s(z)), s(s(s(s(z)))))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[465, 8165])).
% 2.02/2.28 tff(8167,plain,
% 2.02/2.28 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[6517, 287, 1])).
% 2.02/2.28 tff(8168,plain,
% 2.02/2.28 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[1660, 2354, 8167])).
% 2.02/2.28 tff(8169,plain,
% 2.02/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.02/2.28 inference(rewrite,[status(thm)],[])).
% 2.02/2.28 tff(8170,plain,
% 2.02/2.28 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(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(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.02/2.28 inference(rewrite,[status(thm)],[])).
% 2.02/2.28 tff(8171,plain,
% 2.02/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(elem!1)), s(s(s(s(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(X1, 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(z)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 2.02/2.28 inference(monotonicity,[status(thm)],[8170])).
% 2.02/2.28 tff(8172,plain,
% 2.02/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(elem!1)), s(s(s(s(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(X1, 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(z)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.02/2.28 inference(transitivity,[status(thm)],[8171, 8169])).
% 2.02/2.28 tff(8173,plain,
% 2.02/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(elem!1)), s(s(s(s(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)))))),
% 2.02/2.28 inference(quant_inst,[status(thm)],[])).
% 2.02/2.28 tff(8174,plain,
% 2.02/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 2.02/2.28 inference(modus_ponens,[status(thm)],[8173, 8172])).
% 2.02/2.28 tff(8175,plain,
% 2.02/2.28 (~b(s(s(elem!1)), s(s(z)))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[8174, 75, 370, 401, 8168, 8166, 8164])).
% 2.02/2.28 tff(8176,plain,
% 2.02/2.28 ($false),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[1476, 8175, 8159, 266])).
% 2.02/2.28 tff(8177,plain,((~r(s(s(elem!1)), s(z))) | (s(s(elem!1)) = s(s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))) | (~r(elem!1, z)) | b(s(s(elem!1)), elem!1) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.28 tff(8178,plain,
% 2.02/2.28 (~r(s(s(elem!1)), s(z))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[8177, 8135, 8152, 8150, 8140, 8148, 8146, 1, 8144, 8137])).
% 2.02/2.29 tff(8179,plain,
% 2.02/2.29 (b(s(s(elem!1)), s(z))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[561, 8178])).
% 2.02/2.29 tff(8180,plain,
% 2.02/2.29 (~b(elem!1, s(s(elem!1)))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[1638, 8179, 8132, 8142])).
% 2.02/2.29 tff(8181,plain,
% 2.02/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 2.02/2.29 inference(rewrite,[status(thm)],[])).
% 2.02/2.29 tff(8182,plain,
% 2.02/2.29 (((~b(elem!1, s(z))) | (~b(s(s(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(z, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 2.02/2.29 inference(rewrite,[status(thm)],[])).
% 2.02/2.29 tff(8183,plain,
% 2.02/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))))),
% 2.02/2.29 inference(monotonicity,[status(thm)],[8182])).
% 2.02/2.29 tff(8184,plain,
% 2.02/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 2.02/2.29 inference(transitivity,[status(thm)],[8183, 8181])).
% 2.02/2.29 tff(8185,plain,
% 2.02/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))))),
% 2.02/2.29 inference(quant_inst,[status(thm)],[])).
% 2.02/2.29 tff(8186,plain,
% 2.02/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))),
% 2.02/2.29 inference(modus_ponens,[status(thm)],[8185, 8184])).
% 2.02/2.29 tff(8187,plain,
% 2.02/2.29 (~b(z, s(s(elem!1)))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[8186, 75, 8179, 8113, 8142, 8132])).
% 2.02/2.29 tff(8188,plain,
% 2.02/2.29 (r(z, s(s(elem!1)))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[6314, 8187])).
% 2.02/2.29 tff(8189,plain,
% 2.02/2.29 (~r(elem!1, s(s(elem!1)))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[2372, 8188, 7108])).
% 2.02/2.29 tff(8190,plain,
% 2.02/2.29 (elem!1 = s(s(elem!1))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[1617, 8189, 8180])).
% 2.02/2.29 tff(8191,plain,
% 2.02/2.29 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(s(elem!1)))),
% 2.02/2.29 inference(monotonicity,[status(thm)],[8190])).
% 2.02/2.29 tff(8192,plain,
% 2.02/2.29 (r(s(s(z)), s(s(elem!1)))),
% 2.02/2.29 inference(modus_ponens,[status(thm)],[8140, 8191])).
% 2.02/2.29 tff(8193,plain,
% 2.02/2.29 (~(s(s(z)) = s(elem!1))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[3261, 8114])).
% 2.02/2.29 tff(8194,plain,
% 2.02/2.29 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[4541, 8193])).
% 2.02/2.29 tff(8195,plain,
% 2.02/2.29 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.02/2.29 inference(monotonicity,[status(thm)],[8190])).
% 2.02/2.29 tff(8196,plain,
% 2.02/2.29 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.02/2.29 inference(modus_ponens,[status(thm)],[8137, 8195])).
% 2.02/2.29 tff(8197,plain,
% 2.02/2.29 (b(s(z), s(s(elem!1)))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[2329, 8190, 8142])).
% 2.02/2.29 tff(8198,plain,
% 2.02/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.02/2.29 inference(rewrite,[status(thm)],[])).
% 2.02/2.29 tff(8199,plain,
% 2.02/2.29 (((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.02/2.29 inference(rewrite,[status(thm)],[])).
% 2.02/2.29 tff(8200,plain,
% 2.02/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1))))))),
% 2.02/2.29 inference(monotonicity,[status(thm)],[8199])).
% 2.02/2.29 tff(8201,plain,
% 2.02/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.02/2.29 inference(transitivity,[status(thm)],[8200, 8198])).
% 2.02/2.29 tff(8202,plain,
% 2.02/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.02/2.29 inference(quant_inst,[status(thm)],[])).
% 2.02/2.29 tff(8203,plain,
% 2.02/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 2.02/2.29 inference(modus_ponens,[status(thm)],[8202, 8201])).
% 2.02/2.29 tff(8204,plain,
% 2.02/2.29 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[8203, 75, 1457, 1894, 3628, 5712])).
% 2.02/2.29 tff(8205,plain,
% 2.02/2.29 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[575, 8204])).
% 2.02/2.29 tff(8206,plain,
% 2.02/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.02/2.29 inference(rewrite,[status(thm)],[])).
% 2.02/2.29 tff(8207,plain,
% 2.02/2.29 (((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.02/2.29 inference(rewrite,[status(thm)],[])).
% 2.02/2.29 tff(8208,plain,
% 2.02/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 2.02/2.29 inference(monotonicity,[status(thm)],[8207])).
% 2.02/2.29 tff(8209,plain,
% 2.02/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.02/2.29 inference(transitivity,[status(thm)],[8208, 8206])).
% 2.02/2.29 tff(8210,plain,
% 2.02/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))))),
% 2.02/2.29 inference(quant_inst,[status(thm)],[])).
% 2.02/2.29 tff(8211,plain,
% 2.02/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 2.02/2.29 inference(modus_ponens,[status(thm)],[8210, 8209])).
% 2.02/2.29 tff(8212,plain,
% 2.02/2.29 (~b(s(z), s(s(s(z))))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[8211, 75, 1457, 1894, 3628])).
% 2.02/2.29 tff(8213,plain,
% 2.02/2.29 (r(s(z), s(s(s(z))))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[1263, 8212])).
% 2.02/2.29 tff(8214,plain,
% 2.02/2.29 ($false),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[1316, 8213, 8205, 468])).
% 2.02/2.29 tff(8215,plain,((~b(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.29 tff(8216,plain,
% 2.02/2.29 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[8215, 8144, 8179, 8197, 8196])).
% 2.02/2.29 tff(8217,plain,
% 2.02/2.29 (r(s(s(s(z))), s(s(elem!1)))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[62, 8216, 8194])).
% 2.02/2.29 tff(8218,assumption,(b(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 2.02/2.29 tff(8219,plain,
% 2.02/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))),
% 2.02/2.29 inference(rewrite,[status(thm)],[])).
% 2.02/2.29 tff(8220,plain,
% 2.02/2.29 (((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))),
% 2.02/2.29 inference(rewrite,[status(thm)],[])).
% 2.02/2.29 tff(8221,plain,
% 2.02/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z))))),
% 2.02/2.29 inference(monotonicity,[status(thm)],[8220])).
% 2.02/2.29 tff(8222,plain,
% 2.02/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z)))),
% 2.02/2.29 inference(transitivity,[status(thm)],[8221, 8219])).
% 2.02/2.29 tff(8223,plain,
% 2.02/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)))),
% 2.02/2.29 inference(quant_inst,[status(thm)],[])).
% 2.02/2.29 tff(8224,plain,
% 2.02/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), z))),
% 2.02/2.29 inference(modus_ponens,[status(thm)],[8223, 8222])).
% 2.02/2.29 tff(8225,plain,
% 2.02/2.29 (~r(s(s(s(z))), z)),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[8224, 37, 27, 2364])).
% 2.02/2.29 tff(8226,plain,
% 2.02/2.29 (b(s(s(s(z))), z)),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[1334, 58, 221, 8225])).
% 2.02/2.29 tff(8227,assumption,(s(s(s(z))) = s(s(z))), introduced(assumption)).
% 2.02/2.29 tff(8228,plain,
% 2.02/2.29 (s(s(z)) = s(s(s(z)))),
% 2.02/2.29 inference(symmetry,[status(thm)],[8227])).
% 2.02/2.29 tff(8229,plain,
% 2.02/2.29 ($false),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[1556, 8228])).
% 2.02/2.29 tff(8230,plain,(~(s(s(s(z))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.29 tff(8231,assumption,(r(s(s(z)), s(s(elem!1)))), introduced(assumption)).
% 2.02/2.29 tff(8232,plain,
% 2.02/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.02/2.29 inference(rewrite,[status(thm)],[])).
% 2.02/2.29 tff(8233,plain,
% 2.02/2.29 (((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.02/2.29 inference(rewrite,[status(thm)],[])).
% 2.02/2.29 tff(8234,plain,
% 2.02/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1))))))),
% 2.02/2.29 inference(monotonicity,[status(thm)],[8233])).
% 2.02/2.29 tff(8235,plain,
% 2.02/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.02/2.29 inference(transitivity,[status(thm)],[8234, 8232])).
% 2.02/2.29 tff(8236,plain,
% 2.02/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.02/2.29 inference(quant_inst,[status(thm)],[])).
% 2.02/2.29 tff(8237,plain,
% 2.02/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1))))),
% 2.02/2.29 inference(modus_ponens,[status(thm)],[8236, 8235])).
% 2.02/2.29 tff(8238,plain,
% 2.02/2.29 (~r(s(s(s(z))), s(s(z)))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[8237, 37, 115, 27, 8231])).
% 2.02/2.29 tff(8239,plain,
% 2.02/2.29 (b(s(s(s(z))), s(s(z)))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[2173, 58, 8238, 8230])).
% 2.02/2.29 tff(8240,plain,
% 2.02/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), 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(X1, 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(z))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.02/2.29 inference(rewrite,[status(thm)],[])).
% 2.02/2.29 tff(8241,plain,
% 2.02/2.29 (((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.02/2.29 inference(rewrite,[status(thm)],[])).
% 2.02/2.29 tff(8242,plain,
% 2.02/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))))),
% 2.02/2.29 inference(monotonicity,[status(thm)],[8241])).
% 2.02/2.29 tff(8243,plain,
% 2.02/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.02/2.29 inference(transitivity,[status(thm)],[8242, 8240])).
% 2.02/2.29 tff(8244,plain,
% 2.02/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 2.02/2.29 inference(quant_inst,[status(thm)],[])).
% 2.02/2.29 tff(8245,plain,
% 2.02/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))),
% 2.12/2.30 inference(modus_ponens,[status(thm)],[8244, 8243])).
% 2.12/2.30 tff(8246,plain,
% 2.12/2.30 ($false),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[8245, 75, 370, 8239, 8226, 8218])).
% 2.12/2.30 tff(8247,plain,((~r(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.30 tff(8248,plain,
% 2.12/2.30 (~b(s(s(z)), s(s(s(z))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[8247, 8217, 8152, 8188, 8148, 8192])).
% 2.12/2.30 tff(8249,assumption,(~r(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 2.12/2.30 tff(8250,assumption,(~b(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 2.12/2.30 tff(8251,plain,
% 2.12/2.30 ($false),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[1559, 58, 1556, 8250, 8249])).
% 2.12/2.30 tff(8252,plain,(b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.30 tff(8253,plain,
% 2.12/2.30 (r(s(s(z)), s(s(s(z))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[8252, 8248])).
% 2.12/2.30 tff(8254,plain,
% 2.12/2.30 ($false),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[8023, 37, 8217, 8192, 8253])).
% 2.12/2.30 tff(8255,plain,(b(s(s(elem!1)), elem!1) | b(s(s(z)), elem!1) | r(s(s(s(s(z)))), elem!1) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.12/2.30 tff(8256,plain,
% 2.12/2.30 (b(s(s(elem!1)), elem!1)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[8255, 285, 12, 99])).
% 2.12/2.30 tff(8257,plain,
% 2.12/2.30 (~(z = elem!1)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[3652, 8256, 99])).
% 2.12/2.30 tff(8258,plain,
% 2.12/2.30 (~(elem!1 = z)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[304, 8257])).
% 2.12/2.30 tff(8259,plain,
% 2.12/2.30 (~(s(s(elem!1)) = s(s(z)))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[237, 8257])).
% 2.12/2.30 tff(8260,plain,
% 2.12/2.30 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 2.12/2.30 inference(monotonicity,[status(thm)],[1047])).
% 2.12/2.30 tff(8261,plain,
% 2.12/2.30 (b(s(s(s(s(z)))), elem!1)),
% 2.12/2.30 inference(modus_ponens,[status(thm)],[707, 8260])).
% 2.12/2.30 tff(8262,plain,
% 2.12/2.30 ((s(s(z)) = s(z)) <=> (elem!1 = s(z))),
% 2.12/2.30 inference(monotonicity,[status(thm)],[310])).
% 2.12/2.30 tff(8263,plain,
% 2.12/2.30 ((s(s(z)) = s(z)) <=> (s(z) = elem!1)),
% 2.12/2.30 inference(transitivity,[status(thm)],[8262, 91])).
% 2.12/2.30 tff(8264,plain,
% 2.12/2.30 ((s(s(z)) = s(z)) <=> (elem!1 = s(z))),
% 2.12/2.30 inference(transitivity,[status(thm)],[8263, 92])).
% 2.12/2.30 tff(8265,plain,
% 2.12/2.30 ((~(s(s(z)) = s(z))) <=> (~(elem!1 = s(z)))),
% 2.12/2.30 inference(monotonicity,[status(thm)],[8264])).
% 2.12/2.30 tff(8266,plain,
% 2.12/2.30 (~(elem!1 = s(z))),
% 2.12/2.30 inference(modus_ponens,[status(thm)],[148, 8265])).
% 2.12/2.30 tff(8267,plain,
% 2.12/2.30 ((s(s(z)) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(z)))))),
% 2.12/2.30 inference(monotonicity,[status(thm)],[310])).
% 2.12/2.30 tff(8268,plain,
% 2.12/2.30 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 2.12/2.30 inference(transitivity,[status(thm)],[8267, 240])).
% 2.12/2.30 tff(8269,plain,
% 2.12/2.30 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 2.12/2.30 inference(monotonicity,[status(thm)],[8268])).
% 2.12/2.30 tff(8270,plain,
% 2.12/2.30 (~(s(s(s(s(z)))) = elem!1)),
% 2.12/2.30 inference(modus_ponens,[status(thm)],[459, 8269])).
% 2.12/2.30 tff(8271,plain,
% 2.12/2.30 (r(elem!1, s(s(s(s(z)))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[3193, 8270, 12, 99, 3654])).
% 2.12/2.30 tff(8272,plain,
% 2.12/2.30 (~r(elem!1, s(z))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[8127, 8271, 7108])).
% 2.12/2.30 tff(8273,plain,
% 2.12/2.30 (b(elem!1, s(z))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[89, 8272, 8266])).
% 2.12/2.30 tff(8274,plain,
% 2.12/2.30 ((~(s(s(z)) = s(z))) <=> (~(s(z) = elem!1))),
% 2.12/2.30 inference(monotonicity,[status(thm)],[8263])).
% 2.12/2.30 tff(8275,plain,
% 2.12/2.30 (~(s(z) = elem!1)),
% 2.12/2.30 inference(modus_ponens,[status(thm)],[148, 8274])).
% 2.12/2.30 tff(8276,plain,
% 2.12/2.30 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(s(s(z)))))),
% 2.12/2.30 inference(monotonicity,[status(thm)],[1047])).
% 2.12/2.30 tff(8277,plain,
% 2.12/2.30 (r(elem!1, s(s(s(s(z))))) <=> r(elem!1, s(s(elem!1)))),
% 2.12/2.30 inference(symmetry,[status(thm)],[8276])).
% 2.12/2.30 tff(8278,plain,
% 2.12/2.30 (r(elem!1, s(s(elem!1)))),
% 2.12/2.30 inference(modus_ponens,[status(thm)],[8271, 8277])).
% 2.12/2.30 tff(8279,plain,
% 2.12/2.30 (~(elem!1 = z)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[304, 3653])).
% 2.12/2.30 tff(8280,plain,
% 2.12/2.30 (r(s(s(z)), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 2.12/2.30 inference(monotonicity,[status(thm)],[310])).
% 2.12/2.30 tff(8281,plain,
% 2.12/2.30 (r(elem!1, s(s(s(s(z))))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 2.12/2.30 inference(symmetry,[status(thm)],[8280])).
% 2.12/2.30 tff(8282,plain,
% 2.12/2.30 (r(s(s(z)), s(s(s(s(z)))))),
% 2.12/2.30 inference(modus_ponens,[status(thm)],[8271, 8281])).
% 2.12/2.30 tff(8283,plain,
% 2.12/2.30 (b(s(z), s(s(s(z)))) <=> b(s(z), s(elem!1))),
% 2.12/2.30 inference(monotonicity,[status(thm)],[1008])).
% 2.12/2.30 tff(8284,plain,
% 2.12/2.30 (b(s(z), elem!1)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[601, 1395, 8275])).
% 2.12/2.30 tff(8285,plain,
% 2.12/2.30 (~b(s(z), s(s(s(s(z)))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[5527, 8284, 1391, 8261])).
% 2.12/2.30 tff(8286,plain,
% 2.12/2.30 (r(s(z), s(s(s(s(z)))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[489, 8285])).
% 2.12/2.30 tff(8287,plain,
% 2.12/2.30 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 2.12/2.30 inference(monotonicity,[status(thm)],[1008])).
% 2.12/2.30 tff(8288,plain,
% 2.12/2.30 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 2.12/2.30 inference(symmetry,[status(thm)],[8287])).
% 2.12/2.30 tff(8289,plain,
% 2.12/2.30 ((~b(s(elem!1), s(s(s(s(z)))))) <=> (~b(s(s(s(z))), s(s(s(s(z))))))),
% 2.12/2.30 inference(monotonicity,[status(thm)],[8288])).
% 2.12/2.30 tff(8290,plain,
% 2.12/2.30 (r(s(s(elem!1)), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 2.12/2.30 inference(monotonicity,[status(thm)],[1047])).
% 2.12/2.30 tff(8291,plain,
% 2.12/2.30 (b(s(s(z)), s(z))),
% 2.12/2.30 inference(modus_ponens,[status(thm)],[1391, 312])).
% 2.12/2.30 tff(8292,plain,
% 2.12/2.30 (b(s(s(elem!1)), s(s(z))) <=> b(s(s(elem!1)), elem!1)),
% 2.12/2.30 inference(monotonicity,[status(thm)],[310])).
% 2.12/2.30 tff(8293,plain,
% 2.12/2.30 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(s(z)))),
% 2.12/2.30 inference(symmetry,[status(thm)],[8292])).
% 2.12/2.30 tff(8294,plain,
% 2.12/2.30 (b(s(s(elem!1)), s(s(z)))),
% 2.12/2.30 inference(modus_ponens,[status(thm)],[707, 8293])).
% 2.12/2.30 tff(8295,plain,
% 2.12/2.30 (~b(s(s(elem!1)), s(z))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[1465, 8284, 8294, 1391, 8291])).
% 2.12/2.30 tff(8296,plain,
% 2.12/2.30 (r(s(s(elem!1)), s(z))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[561, 8295])).
% 2.12/2.30 tff(8297,plain,
% 2.12/2.30 (r(s(s(s(s(z)))), s(z))),
% 2.12/2.30 inference(modus_ponens,[status(thm)],[8296, 8290])).
% 2.12/2.30 tff(8298,plain,
% 2.12/2.30 (~r(z, s(s(s(s(z)))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[1511, 37, 506, 8297])).
% 2.12/2.30 tff(8299,plain,
% 2.12/2.30 ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z)))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[1515, 58, 8298])).
% 2.12/2.30 tff(8300,plain,
% 2.12/2.30 (b(z, s(s(s(s(z)))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[8299, 1503])).
% 2.12/2.30 tff(8301,plain,
% 2.12/2.30 (~r(s(s(s(s(z)))), z)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[1415, 37, 506, 8297])).
% 2.12/2.30 tff(8302,plain,
% 2.12/2.30 (b(s(s(s(s(z)))), z)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[1421, 58, 1143, 8301])).
% 2.12/2.30 tff(8303,plain,
% 2.12/2.30 (~b(elem!1, z)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[1966, 8296, 707, 506])).
% 2.12/2.30 tff(8304,plain,
% 2.12/2.30 (r(elem!1, z)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[387, 8303, 353])).
% 2.12/2.30 tff(8305,plain,
% 2.12/2.30 ((s(s(z)) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 2.12/2.30 inference(monotonicity,[status(thm)],[310])).
% 2.12/2.30 tff(8306,plain,
% 2.12/2.30 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 2.12/2.30 inference(transitivity,[status(thm)],[8305, 1028])).
% 2.12/2.30 tff(8307,plain,
% 2.12/2.30 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = elem!1))),
% 2.12/2.30 inference(monotonicity,[status(thm)],[8306])).
% 2.12/2.30 tff(8308,plain,
% 2.12/2.30 (~(s(s(s(z))) = elem!1)),
% 2.12/2.30 inference(modus_ponens,[status(thm)],[1556, 8307])).
% 2.12/2.30 tff(8309,plain,
% 2.12/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.12/2.30 inference(rewrite,[status(thm)],[])).
% 2.12/2.30 tff(8310,plain,
% 2.12/2.30 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.12/2.30 inference(rewrite,[status(thm)],[])).
% 2.12/2.30 tff(8311,plain,
% 2.12/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 2.12/2.30 inference(monotonicity,[status(thm)],[8310])).
% 2.12/2.30 tff(8312,plain,
% 2.12/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.12/2.30 inference(transitivity,[status(thm)],[8311, 8309])).
% 2.12/2.30 tff(8313,plain,
% 2.12/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), z)))),
% 2.12/2.30 inference(quant_inst,[status(thm)],[])).
% 2.12/2.30 tff(8314,plain,
% 2.12/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 2.12/2.30 inference(modus_ponens,[status(thm)],[8313, 8312])).
% 2.12/2.30 tff(8315,plain,
% 2.12/2.30 (~b(s(elem!1), z)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[8314, 75, 1423, 3862, 1582])).
% 2.12/2.30 tff(8316,plain,
% 2.12/2.30 (r(s(elem!1), z)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[766, 8315])).
% 2.12/2.30 tff(8317,plain,
% 2.12/2.30 (~r(s(elem!1), elem!1)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[2988, 8316, 155])).
% 2.12/2.30 tff(8318,plain,
% 2.12/2.30 (r(s(elem!1), elem!1) <=> r(s(s(s(z))), elem!1)),
% 2.12/2.30 inference(monotonicity,[status(thm)],[1127])).
% 2.12/2.30 tff(8319,plain,
% 2.12/2.30 (r(s(s(s(z))), elem!1) <=> r(s(elem!1), elem!1)),
% 2.12/2.30 inference(symmetry,[status(thm)],[8318])).
% 2.12/2.30 tff(8320,plain,
% 2.12/2.30 (r(s(elem!1), elem!1)),
% 2.12/2.30 inference(modus_ponens,[status(thm)],[1061, 8319])).
% 2.12/2.30 tff(8321,plain,
% 2.12/2.30 ($false),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[1974, 8320])).
% 2.12/2.30 tff(8322,plain,((~r(s(s(s(z))), elem!1)) | r(s(elem!1), elem!1) | (~(s(s(z)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.30 tff(8323,plain,
% 2.12/2.30 (~r(s(s(s(z))), elem!1)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[8322, 8317, 310])).
% 2.12/2.30 tff(8324,plain,
% 2.12/2.30 (b(s(s(s(z))), elem!1)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[1115, 8323, 8308])).
% 2.12/2.30 tff(8325,plain,
% 2.12/2.30 (b(s(elem!1), elem!1)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[1122, 8324, 1047])).
% 2.12/2.30 tff(8326,plain,
% 2.12/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(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(X1, 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(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.12/2.30 inference(rewrite,[status(thm)],[])).
% 2.12/2.30 tff(8327,plain,
% 2.12/2.30 (((~b(s(z), elem!1)) | (~b(s(s(s(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(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.12/2.30 inference(rewrite,[status(thm)],[])).
% 2.12/2.30 tff(8328,plain,
% 2.12/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 2.12/2.30 inference(monotonicity,[status(thm)],[8327])).
% 2.12/2.30 tff(8329,plain,
% 2.12/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.12/2.30 inference(transitivity,[status(thm)],[8328, 8326])).
% 2.12/2.30 tff(8330,plain,
% 2.12/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))))))),
% 2.12/2.30 inference(quant_inst,[status(thm)],[])).
% 2.12/2.30 tff(8331,plain,
% 2.12/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(z))))))),
% 2.12/2.30 inference(modus_ponens,[status(thm)],[8330, 8329])).
% 2.12/2.30 tff(8332,plain,
% 2.12/2.30 ($false),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[8331, 75, 107, 1391, 287, 8325, 3862])).
% 2.12/2.30 tff(8333,plain,((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~(s(s(z)) = elem!1)) | (~r(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.30 tff(8334,plain,
% 2.12/2.30 (~b(s(elem!1), s(s(s(s(z)))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[8333, 8284, 1391, 8261, 310, 8304, 8302, 8300])).
% 2.12/2.30 tff(8335,plain,
% 2.12/2.30 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.12/2.30 inference(modus_ponens,[status(thm)],[8334, 8289])).
% 2.12/2.30 tff(8336,plain,
% 2.12/2.30 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[575, 8335])).
% 2.12/2.30 tff(8337,plain,
% 2.12/2.30 (~r(s(z), s(s(s(z))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[1316, 8336, 8286])).
% 2.12/2.30 tff(8338,plain,
% 2.12/2.30 (b(s(z), s(s(s(z))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[1263, 8337])).
% 2.12/2.30 tff(8339,plain,
% 2.12/2.30 (b(s(z), s(elem!1))),
% 2.12/2.30 inference(modus_ponens,[status(thm)],[8338, 8283])).
% 2.12/2.30 tff(8340,plain,
% 2.12/2.30 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(z))))),
% 2.12/2.30 inference(monotonicity,[status(thm)],[1127])).
% 2.12/2.30 tff(8341,plain,
% 2.12/2.30 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(elem!1))),
% 2.12/2.30 inference(symmetry,[status(thm)],[8340])).
% 2.12/2.30 tff(8342,plain,
% 2.12/2.30 (b(s(s(z)), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 2.12/2.30 inference(monotonicity,[status(thm)],[310])).
% 2.12/2.30 tff(8343,plain,
% 2.12/2.30 (b(s(s(z)), s(s(s(z)))) <=> b(elem!1, s(elem!1))),
% 2.12/2.30 inference(transitivity,[status(thm)],[8342, 8341])).
% 2.12/2.30 tff(8344,plain,
% 2.12/2.30 (b(elem!1, s(s(s(z)))) <=> b(s(s(z)), s(s(s(z))))),
% 2.12/2.30 inference(symmetry,[status(thm)],[8342])).
% 2.12/2.30 tff(8345,plain,
% 2.12/2.30 ((s(s(z)) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 2.12/2.30 inference(transitivity,[status(thm)],[8306, 3425])).
% 2.12/2.30 tff(8346,plain,
% 2.12/2.30 ((~(s(s(z)) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(z)))))),
% 2.12/2.30 inference(monotonicity,[status(thm)],[8345])).
% 2.12/2.30 tff(8347,plain,
% 2.12/2.30 (~(elem!1 = s(s(s(z))))),
% 2.12/2.30 inference(modus_ponens,[status(thm)],[1556, 8346])).
% 2.12/2.30 tff(8348,plain,
% 2.12/2.30 (r(s(s(s(z))), z) <=> r(s(elem!1), z)),
% 2.12/2.30 inference(monotonicity,[status(thm)],[1008])).
% 2.12/2.30 tff(8349,plain,
% 2.12/2.30 (r(s(elem!1), z) <=> r(s(s(s(z))), z)),
% 2.12/2.30 inference(symmetry,[status(thm)],[8348])).
% 2.12/2.30 tff(8350,plain,
% 2.12/2.30 (r(s(s(z)), s(s(s(z))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[8252, 8250])).
% 2.12/2.30 tff(8351,plain,
% 2.12/2.30 ($false),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[1548, 37, 1308, 467, 6494])).
% 2.12/2.30 tff(8352,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.30 tff(8353,plain,
% 2.12/2.30 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[8352, 8350, 467])).
% 2.12/2.30 tff(8354,plain,
% 2.12/2.30 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[575, 8353])).
% 2.12/2.30 tff(8355,plain,
% 2.12/2.30 (b(s(elem!1), s(s(s(s(z)))))),
% 2.12/2.30 inference(modus_ponens,[status(thm)],[8354, 8287])).
% 2.12/2.30 tff(8356,plain,
% 2.12/2.30 (~b(s(elem!1), z)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[8314, 75, 1423, 8355, 1582])).
% 2.12/2.30 tff(8357,plain,
% 2.12/2.30 (r(s(elem!1), z)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[766, 8356])).
% 2.12/2.30 tff(8358,plain,
% 2.12/2.30 (r(s(s(s(z))), z)),
% 2.12/2.30 inference(modus_ponens,[status(thm)],[8357, 8349])).
% 2.12/2.30 tff(8359,plain,
% 2.12/2.30 (~r(elem!1, s(s(s(z))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[6474, 8358, 155])).
% 2.12/2.30 tff(8360,plain,
% 2.12/2.30 (b(elem!1, s(s(s(z))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[1279, 8359, 8347])).
% 2.12/2.30 tff(8361,plain,
% 2.12/2.30 (b(s(s(z)), s(s(s(z))))),
% 2.12/2.30 inference(modus_ponens,[status(thm)],[8360, 8344])).
% 2.12/2.30 tff(8362,plain,
% 2.12/2.30 ($false),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[8250, 8361])).
% 2.12/2.30 tff(8363,plain,(b(s(s(z)), s(s(s(z)))) | (~(s(s(z)) = elem!1)) | (~r(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.30 tff(8364,plain,
% 2.12/2.30 (b(s(s(z)), s(s(s(z))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[8363, 8304, 310, 8302, 8300, 467])).
% 2.12/2.30 tff(8365,plain,
% 2.12/2.30 (b(elem!1, s(elem!1))),
% 2.12/2.30 inference(modus_ponens,[status(thm)],[8364, 8343])).
% 2.12/2.30 tff(8366,plain,
% 2.12/2.30 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 2.12/2.30 inference(commutativity,[status(thm)],[])).
% 2.12/2.30 tff(8367,plain,
% 2.12/2.30 ((s(elem!1) = s(s(elem!1))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 2.12/2.30 inference(monotonicity,[status(thm)],[1047])).
% 2.12/2.30 tff(8368,plain,
% 2.12/2.30 ((s(elem!1) = s(s(elem!1))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 2.12/2.30 inference(transitivity,[status(thm)],[8367, 8366])).
% 2.12/2.30 tff(8369,plain,
% 2.12/2.30 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(elem!1) = s(s(elem!1)))),
% 2.12/2.30 inference(symmetry,[status(thm)],[8368])).
% 2.12/2.30 tff(8370,plain,
% 2.12/2.30 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 2.12/2.30 inference(monotonicity,[status(thm)],[1127])).
% 2.12/2.30 tff(8371,plain,
% 2.12/2.30 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 2.12/2.30 inference(symmetry,[status(thm)],[8370])).
% 2.12/2.30 tff(8372,plain,
% 2.12/2.30 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(elem!1) = s(s(elem!1)))),
% 2.12/2.30 inference(transitivity,[status(thm)],[8371, 8369])).
% 2.12/2.30 tff(8373,plain,
% 2.12/2.30 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 2.12/2.30 inference(monotonicity,[status(thm)],[8372])).
% 2.12/2.30 tff(8374,plain,
% 2.12/2.30 (~(s(elem!1) = s(s(elem!1)))),
% 2.12/2.30 inference(modus_ponens,[status(thm)],[264, 8373])).
% 2.12/2.30 tff(8375,plain,
% 2.12/2.30 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 2.12/2.30 inference(monotonicity,[status(thm)],[1047])).
% 2.12/2.30 tff(8376,plain,
% 2.12/2.30 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.12/2.30 inference(symmetry,[status(thm)],[8375])).
% 2.12/2.30 tff(8377,plain,
% 2.12/2.31 ((~b(s(elem!1), s(s(s(s(z)))))) <=> (~b(s(elem!1), s(s(elem!1))))),
% 2.12/2.31 inference(monotonicity,[status(thm)],[8376])).
% 2.12/2.31 tff(8378,plain,
% 2.12/2.31 (~b(s(elem!1), s(s(elem!1)))),
% 2.12/2.31 inference(modus_ponens,[status(thm)],[8334, 8377])).
% 2.12/2.31 tff(8379,plain,
% 2.12/2.31 (r(s(elem!1), s(s(elem!1)))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[1851, 8378, 8374])).
% 2.12/2.31 tff(8380,plain,
% 2.12/2.31 (~r(s(elem!1), elem!1)),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[1950, 8379, 1490, 8304])).
% 2.12/2.31 tff(8381,plain,
% 2.12/2.31 (~r(s(s(s(z))), elem!1)),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[8322, 8380, 310])).
% 2.12/2.31 tff(8382,plain,
% 2.12/2.31 (b(s(s(s(z))), elem!1)),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[1115, 8381, 8308])).
% 2.12/2.31 tff(8383,plain,
% 2.12/2.31 (b(s(elem!1), elem!1)),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[1122, 8382, 1047])).
% 2.12/2.31 tff(8384,plain,
% 2.12/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))),
% 2.12/2.31 inference(rewrite,[status(thm)],[])).
% 2.12/2.31 tff(8385,plain,
% 2.12/2.31 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1))) <=> ((~b(s(z), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))),
% 2.12/2.31 inference(rewrite,[status(thm)],[])).
% 2.12/2.31 tff(8386,plain,
% 2.12/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~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(X1, 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), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1)))))),
% 2.12/2.31 inference(monotonicity,[status(thm)],[8385])).
% 2.12/2.31 tff(8387,plain,
% 2.12/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~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(X1, 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), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))))),
% 2.12/2.31 inference(transitivity,[status(thm)],[8386, 8384])).
% 2.12/2.31 tff(8388,plain,
% 2.12/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))),
% 2.12/2.31 inference(quant_inst,[status(thm)],[])).
% 2.12/2.31 tff(8389,plain,
% 2.12/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1)))),
% 2.12/2.31 inference(modus_ponens,[status(thm)],[8388, 8387])).
% 2.12/2.31 tff(8390,plain,
% 2.12/2.31 ($false),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[8389, 75, 8284, 8383, 8365, 8339])).
% 2.12/2.31 tff(8391,plain,((~r(z, s(z))) | (~(s(s(z)) = elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (elem!1 = z) | (~b(s(s(elem!1)), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.31 tff(8392,plain,
% 2.12/2.31 (~r(z, s(z))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[8391, 310, 8278, 8273, 8282, 8279, 707, 7108])).
% 2.12/2.31 tff(8393,plain,
% 2.12/2.31 (b(z, s(z))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[187, 8392])).
% 2.12/2.31 tff(8394,plain,
% 2.12/2.31 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(elem!1))),
% 2.12/2.31 inference(monotonicity,[status(thm)],[1008])).
% 2.12/2.31 tff(8395,plain,
% 2.12/2.31 (r(s(s(z)), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 2.12/2.31 inference(monotonicity,[status(thm)],[310])).
% 2.12/2.31 tff(8396,plain,
% 2.12/2.31 (r(s(s(z)), s(s(s(z)))) <=> r(elem!1, s(elem!1))),
% 2.12/2.31 inference(transitivity,[status(thm)],[8395, 8394])).
% 2.12/2.31 tff(8397,plain,
% 2.12/2.31 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(elem!1 = s(s(s(s(z))))))),
% 2.12/2.31 inference(monotonicity,[status(thm)],[8267])).
% 2.12/2.31 tff(8398,plain,
% 2.12/2.31 (~(elem!1 = s(s(s(s(z)))))),
% 2.12/2.31 inference(modus_ponens,[status(thm)],[459, 8397])).
% 2.12/2.31 tff(8399,plain,
% 2.12/2.31 (b(s(s(s(z))), elem!1)),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[2499, 588, 300, 99, 372, 8398])).
% 2.12/2.31 tff(8400,plain,
% 2.12/2.31 (b(s(s(s(z))), s(s(z)))),
% 2.12/2.31 inference(modus_ponens,[status(thm)],[8399, 1152])).
% 2.12/2.31 tff(8401,plain,
% 2.12/2.31 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(z)))), s(s(z)))),
% 2.12/2.31 inference(transitivity,[status(thm)],[8260, 1149])).
% 2.12/2.31 tff(8402,plain,
% 2.12/2.31 (b(s(s(s(s(z)))), s(s(z)))),
% 2.12/2.31 inference(modus_ponens,[status(thm)],[707, 8401])).
% 2.12/2.31 tff(8403,plain,
% 2.12/2.31 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(elem!1))),
% 2.12/2.31 inference(monotonicity,[status(thm)],[1008])).
% 2.12/2.31 tff(8404,plain,
% 2.12/2.31 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 2.12/2.31 inference(symmetry,[status(thm)],[8403])).
% 2.12/2.31 tff(8405,plain,
% 2.12/2.31 ((~r(s(s(s(s(z)))), s(elem!1))) <=> (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 2.12/2.31 inference(monotonicity,[status(thm)],[8404])).
% 2.12/2.31 tff(8406,plain,
% 2.12/2.31 (r(s(elem!1), s(z)) <=> r(s(s(s(z))), s(z))),
% 2.12/2.31 inference(monotonicity,[status(thm)],[1127])).
% 2.12/2.31 tff(8407,plain,
% 2.12/2.31 (r(s(s(s(z))), s(z)) <=> r(s(elem!1), s(z))),
% 2.12/2.31 inference(symmetry,[status(thm)],[8406])).
% 2.12/2.31 tff(8408,plain,
% 2.12/2.31 (~r(s(z), z)),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[7555, 588, 300])).
% 2.12/2.31 tff(8409,plain,
% 2.12/2.31 (b(s(z), z)),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[169, 8408])).
% 2.12/2.31 tff(8410,plain,
% 2.12/2.31 (~b(s(s(s(z))), s(z))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[8081, 8409, 372, 1391, 8399])).
% 2.12/2.31 tff(8411,plain,
% 2.12/2.31 (r(s(s(s(z))), s(z))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[1081, 8410])).
% 2.12/2.31 tff(8412,plain,
% 2.12/2.31 (r(s(elem!1), s(z))),
% 2.12/2.31 inference(modus_ponens,[status(thm)],[8411, 8407])).
% 2.12/2.31 tff(8413,plain,
% 2.12/2.31 (~r(s(z), s(s(elem!1)))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[6974, 588, 1490])).
% 2.12/2.31 tff(8414,plain,
% 2.12/2.31 (b(s(z), s(s(elem!1)))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[1890, 8413])).
% 2.12/2.31 tff(8415,plain,
% 2.12/2.31 (~b(s(s(elem!1)), s(z))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[7089, 8414, 707, 1391])).
% 2.12/2.31 tff(8416,plain,
% 2.12/2.31 (r(s(s(elem!1)), s(z))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[561, 8415])).
% 2.12/2.31 tff(8417,plain,
% 2.12/2.31 (r(s(s(s(s(z)))), s(z))),
% 2.12/2.31 inference(modus_ponens,[status(thm)],[8416, 8290])).
% 2.12/2.31 tff(8418,plain,
% 2.12/2.31 (((~![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(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(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 2.12/2.31 inference(rewrite,[status(thm)],[])).
% 2.12/2.31 tff(8419,plain,
% 2.12/2.31 (((~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(elem!1)))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 2.12/2.31 inference(rewrite,[status(thm)],[])).
% 2.12/2.31 tff(8420,plain,
% 2.12/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(elem!1)))))),
% 2.12/2.31 inference(monotonicity,[status(thm)],[8419])).
% 2.12/2.31 tff(8421,plain,
% 2.12/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 2.12/2.31 inference(transitivity,[status(thm)],[8420, 8418])).
% 2.12/2.31 tff(8422,plain,
% 2.12/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 2.12/2.31 inference(quant_inst,[status(thm)],[])).
% 2.12/2.31 tff(8423,plain,
% 2.12/2.31 ((~![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(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 2.12/2.31 inference(modus_ponens,[status(thm)],[8422, 8421])).
% 2.12/2.31 tff(8424,plain,
% 2.12/2.31 ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[8423, 37, 8417])).
% 2.12/2.31 tff(8425,plain,
% 2.12/2.31 (~r(s(s(s(s(z)))), s(elem!1))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[8424, 8412])).
% 2.12/2.31 tff(8426,plain,
% 2.12/2.31 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.12/2.31 inference(modus_ponens,[status(thm)],[8425, 8405])).
% 2.12/2.31 tff(8427,plain,
% 2.12/2.31 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[2898, 8426])).
% 2.12/2.31 tff(8428,plain,
% 2.12/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.12/2.31 inference(rewrite,[status(thm)],[])).
% 2.12/2.31 tff(8429,plain,
% 2.12/2.31 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(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(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.12/2.31 inference(rewrite,[status(thm)],[])).
% 2.12/2.31 tff(8430,plain,
% 2.12/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(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(X1, 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(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.12/2.31 inference(monotonicity,[status(thm)],[8429])).
% 2.12/2.31 tff(8431,plain,
% 2.12/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(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(X1, 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(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.12/2.31 inference(transitivity,[status(thm)],[8430, 8428])).
% 2.12/2.31 tff(8432,plain,
% 2.12/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.12/2.31 inference(quant_inst,[status(thm)],[])).
% 2.12/2.31 tff(8433,plain,
% 2.12/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.12/2.31 inference(modus_ponens,[status(thm)],[8432, 8431])).
% 2.12/2.31 tff(8434,plain,
% 2.12/2.31 ($false),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[8433, 75, 2390, 1155, 1154, 8218])).
% 2.12/2.31 tff(8435,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.31 tff(8436,plain,
% 2.12/2.31 (~b(s(s(z)), s(s(s(z))))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[8435, 8427, 8402, 8400])).
% 2.12/2.31 tff(8437,plain,
% 2.12/2.31 (r(s(s(z)), s(s(s(z))))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[8252, 8436])).
% 2.12/2.31 tff(8438,plain,
% 2.12/2.31 (r(elem!1, s(elem!1))),
% 2.12/2.31 inference(modus_ponens,[status(thm)],[8437, 8396])).
% 2.12/2.31 tff(8439,assumption,(s(z) = s(elem!1)), introduced(assumption)).
% 2.12/2.31 tff(8440,plain,
% 2.12/2.31 (s(elem!1) = s(z)),
% 2.12/2.31 inference(symmetry,[status(thm)],[8439])).
% 2.12/2.31 tff(8441,plain,
% 2.12/2.31 (s(s(s(z))) = s(z)),
% 2.12/2.31 inference(transitivity,[status(thm)],[1008, 8440])).
% 2.12/2.31 tff(8442,plain,
% 2.12/2.31 ($false),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[457, 8441])).
% 2.12/2.31 tff(8443,plain,((~(s(z) = s(elem!1))) | (~(s(s(z)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.31 tff(8444,plain,
% 2.12/2.31 (~(s(z) = s(elem!1))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[8443, 310])).
% 2.12/2.31 tff(8445,plain,
% 2.12/2.31 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 2.12/2.31 inference(monotonicity,[status(thm)],[8371])).
% 2.12/2.31 tff(8446,plain,
% 2.12/2.31 (~(s(s(s(s(z)))) = s(elem!1))),
% 2.12/2.31 inference(modus_ponens,[status(thm)],[264, 8445])).
% 2.12/2.31 tff(8447,plain,
% 2.12/2.31 (b(s(s(s(s(z)))), s(elem!1))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[4263, 58, 8446, 8425])).
% 2.12/2.31 tff(8448,plain,
% 2.12/2.31 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 2.12/2.31 inference(monotonicity,[status(thm)],[1047])).
% 2.12/2.31 tff(8449,plain,
% 2.12/2.31 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 2.12/2.31 inference(transitivity,[status(thm)],[8448, 8287])).
% 2.12/2.31 tff(8450,plain,
% 2.12/2.31 ((s(s(elem!1)) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 2.12/2.31 inference(symmetry,[status(thm)],[1909])).
% 2.12/2.31 tff(8451,plain,
% 2.12/2.31 ((s(s(elem!1)) = s(s(s(z)))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 2.12/2.31 inference(monotonicity,[status(thm)],[1047])).
% 2.12/2.31 tff(8452,plain,
% 2.12/2.31 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 2.12/2.31 inference(symmetry,[status(thm)],[8451])).
% 2.12/2.31 tff(8453,plain,
% 2.12/2.31 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 2.12/2.31 inference(transitivity,[status(thm)],[8452, 8450])).
% 2.12/2.31 tff(8454,plain,
% 2.12/2.31 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(elem!1))))),
% 2.12/2.31 inference(monotonicity,[status(thm)],[8453])).
% 2.12/2.31 tff(8455,plain,
% 2.12/2.31 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.12/2.31 inference(modus_ponens,[status(thm)],[264, 8454])).
% 2.12/2.31 tff(8456,plain,
% 2.12/2.31 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 2.12/2.31 inference(monotonicity,[status(thm)],[1047])).
% 2.12/2.31 tff(8457,plain,
% 2.12/2.31 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 2.12/2.31 inference(symmetry,[status(thm)],[8456])).
% 2.12/2.31 tff(8458,plain,
% 2.12/2.31 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 2.12/2.31 inference(symmetry,[status(thm)],[1147])).
% 2.12/2.31 tff(8459,plain,
% 2.12/2.31 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 2.12/2.31 inference(transitivity,[status(thm)],[8458, 8457])).
% 2.12/2.31 tff(8460,plain,
% 2.12/2.31 ((~r(s(elem!1), s(s(s(s(z)))))) <=> (~r(s(s(s(z))), s(s(elem!1))))),
% 2.12/2.31 inference(monotonicity,[status(thm)],[8459])).
% 2.12/2.31 tff(8461,plain,
% 2.12/2.31 (((~![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(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)))))))),
% 2.12/2.31 inference(rewrite,[status(thm)],[])).
% 2.12/2.31 tff(8462,plain,
% 2.12/2.31 (((~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)))))))),
% 2.12/2.31 inference(rewrite,[status(thm)],[])).
% 2.12/2.31 tff(8463,plain,
% 2.12/2.31 (((~![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(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))))))))),
% 2.12/2.31 inference(monotonicity,[status(thm)],[8462])).
% 2.12/2.31 tff(8464,plain,
% 2.12/2.31 (((~![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(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)))))))),
% 2.12/2.31 inference(transitivity,[status(thm)],[8463, 8461])).
% 2.12/2.31 tff(8465,plain,
% 2.12/2.31 ((~![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(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.12/2.31 inference(quant_inst,[status(thm)],[])).
% 2.12/2.31 tff(8466,plain,
% 2.12/2.31 ((~![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(elem!1), s(z))) | (~r(s(elem!1), s(s(s(s(z))))))),
% 2.12/2.31 inference(modus_ponens,[status(thm)],[8465, 8464])).
% 2.12/2.31 tff(8467,plain,
% 2.12/2.31 ((~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(s(z))))))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[8466, 37, 8417])).
% 2.12/2.31 tff(8468,plain,
% 2.12/2.31 (~r(s(elem!1), s(s(s(s(z)))))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[8467, 8412])).
% 2.12/2.31 tff(8469,plain,
% 2.12/2.31 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.12/2.31 inference(modus_ponens,[status(thm)],[8468, 8460])).
% 2.12/2.31 tff(8470,plain,
% 2.12/2.31 (b(s(s(s(z))), s(s(elem!1)))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[62, 8469, 8455])).
% 2.12/2.31 tff(8471,plain,
% 2.12/2.31 (b(s(elem!1), s(s(s(s(z)))))),
% 2.12/2.31 inference(modus_ponens,[status(thm)],[8470, 8449])).
% 2.12/2.31 tff(8472,plain,
% 2.12/2.31 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(s(z)))))),
% 2.12/2.31 inference(monotonicity,[status(thm)],[1047])).
% 2.12/2.31 tff(8473,plain,
% 2.12/2.31 (b(s(z), s(s(s(s(z)))))),
% 2.12/2.31 inference(modus_ponens,[status(thm)],[8414, 8472])).
% 2.12/2.31 tff(8474,plain,
% 2.12/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))))) | (~b(s(s(s(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(X1, 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(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.12/2.31 inference(rewrite,[status(thm)],[])).
% 2.12/2.31 tff(8475,plain,
% 2.12/2.31 (((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~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(elem!1))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.12/2.31 inference(rewrite,[status(thm)],[])).
% 2.12/2.31 tff(8476,plain,
% 2.12/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(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(X1, 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(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[8475])).
% 2.12/2.32 tff(8477,plain,
% 2.12/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(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(X1, 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(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.12/2.32 inference(transitivity,[status(thm)],[8476, 8474])).
% 2.12/2.32 tff(8478,plain,
% 2.12/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(elem!1))))),
% 2.12/2.32 inference(quant_inst,[status(thm)],[])).
% 2.12/2.32 tff(8479,plain,
% 2.12/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 2.12/2.32 inference(modus_ponens,[status(thm)],[8478, 8477])).
% 2.12/2.32 tff(8480,plain,
% 2.12/2.32 (~b(s(z), s(elem!1))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[8479, 75, 8473, 8471, 8447])).
% 2.12/2.32 tff(8481,plain,
% 2.12/2.32 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1)))),
% 2.12/2.32 inference(rewrite,[status(thm)],[])).
% 2.12/2.32 tff(8482,plain,
% 2.12/2.32 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1)))),
% 2.12/2.32 inference(quant_inst,[status(thm)],[])).
% 2.12/2.32 tff(8483,plain,
% 2.12/2.32 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1))),
% 2.12/2.32 inference(modus_ponens,[status(thm)],[8482, 8481])).
% 2.12/2.32 tff(8484,plain,
% 2.12/2.32 (r(s(z), s(elem!1))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[8483, 58, 8480, 8444])).
% 2.12/2.32 tff(8485,assumption,(r(elem!1, s(elem!1))), introduced(assumption)).
% 2.12/2.32 tff(8486,plain,
% 2.12/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))))),
% 2.12/2.32 inference(rewrite,[status(thm)],[])).
% 2.12/2.32 tff(8487,plain,
% 2.12/2.32 (((~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(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))))),
% 2.12/2.32 inference(rewrite,[status(thm)],[])).
% 2.12/2.32 tff(8488,plain,
% 2.12/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(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(s(z), s(elem!1))) | (~r(elem!1, s(elem!1)))))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[8487])).
% 2.12/2.32 tff(8489,plain,
% 2.12/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(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(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))))),
% 2.12/2.32 inference(transitivity,[status(thm)],[8488, 8486])).
% 2.12/2.32 tff(8490,plain,
% 2.12/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)))),
% 2.12/2.32 inference(quant_inst,[status(thm)],[])).
% 2.12/2.32 tff(8491,plain,
% 2.12/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(elem!1)))),
% 2.12/2.32 inference(modus_ponens,[status(thm)],[8490, 8489])).
% 2.12/2.32 tff(8492,plain,
% 2.12/2.32 ($false),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[8491, 37, 588, 8485, 1753])).
% 2.12/2.32 tff(8493,plain,((~r(elem!1, s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.32 tff(8494,plain,
% 2.12/2.32 (~r(elem!1, s(elem!1))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[8493, 588, 8484])).
% 2.12/2.32 tff(8495,plain,
% 2.12/2.32 ($false),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[8494, 8438])).
% 2.12/2.32 tff(8496,plain,((~r(s(z), elem!1)) | (~(s(s(z)) = elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | b(s(s(z)), elem!1) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.32 tff(8497,plain,
% 2.12/2.32 (~r(s(z), elem!1)),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[8496, 310, 8393, 8273, 707, 7108, 99, 8278])).
% 2.12/2.32 tff(8498,plain,
% 2.12/2.32 (b(s(z), elem!1)),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[601, 8497, 8275])).
% 2.12/2.32 tff(8499,plain,
% 2.12/2.32 (~b(s(z), s(s(s(s(z)))))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[5527, 8498, 8273, 8261])).
% 2.12/2.32 tff(8500,plain,
% 2.12/2.32 (r(s(z), s(s(s(s(z)))))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[489, 8499])).
% 2.12/2.32 tff(8501,assumption,(~b(s(s(s(s(s(s(s(z))))))), s(z))), introduced(assumption)).
% 2.12/2.32 tff(8502,plain,
% 2.12/2.32 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[1230, 58, 1227, 8501])).
% 2.12/2.32 tff(8503,plain,
% 2.12/2.32 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[2045, 75, 107, 1391, 287, 1168])).
% 2.12/2.32 tff(8504,plain,
% 2.12/2.32 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[1179, 58, 1176, 8503])).
% 2.12/2.32 tff(8505,assumption,(s(z) = s(s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 2.12/2.32 tff(8506,plain,
% 2.12/2.32 (s(s(s(s(s(s(s(z))))))) = s(z)),
% 2.12/2.32 inference(symmetry,[status(thm)],[8505])).
% 2.12/2.32 tff(8507,plain,
% 2.12/2.32 ($false),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[1227, 8506])).
% 2.12/2.32 tff(8508,plain,(~(s(z) = s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.32 tff(8509,plain,
% 2.12/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.32 inference(rewrite,[status(thm)],[])).
% 2.12/2.32 tff(8510,plain,
% 2.12/2.32 (((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.32 inference(rewrite,[status(thm)],[])).
% 2.12/2.32 tff(8511,plain,
% 2.12/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[8510])).
% 2.12/2.32 tff(8512,plain,
% 2.12/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.32 inference(transitivity,[status(thm)],[8511, 8509])).
% 2.12/2.32 tff(8513,plain,
% 2.12/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.32 inference(quant_inst,[status(thm)],[])).
% 2.12/2.32 tff(8514,plain,
% 2.12/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.12/2.32 inference(modus_ponens,[status(thm)],[8513, 8512])).
% 2.12/2.32 tff(8515,plain,
% 2.12/2.32 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[8514, 75, 107, 1391, 1168])).
% 2.12/2.32 tff(8516,plain,
% 2.12/2.32 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(s(s(z)))))))) | b(s(z), s(s(s(s(s(s(s(z)))))))) | r(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(s(s(z)))))))) | b(s(z), s(s(s(s(s(s(s(z)))))))) | r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.12/2.32 inference(rewrite,[status(thm)],[])).
% 2.12/2.32 tff(8517,plain,
% 2.12/2.32 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(s(s(z)))))))) | b(s(z), s(s(s(s(s(s(s(z)))))))) | r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.12/2.32 inference(quant_inst,[status(thm)],[])).
% 2.12/2.32 tff(8518,plain,
% 2.12/2.32 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(s(s(z)))))))) | b(s(z), s(s(s(s(s(s(s(z)))))))) | r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.32 inference(modus_ponens,[status(thm)],[8517, 8516])).
% 2.12/2.32 tff(8519,plain,
% 2.12/2.32 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[8518, 58, 8515, 8508])).
% 2.12/2.32 tff(8520,plain,
% 2.12/2.32 (((~![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(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(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(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.12/2.32 inference(rewrite,[status(thm)],[])).
% 2.12/2.32 tff(8521,plain,
% 2.12/2.32 (((~r(s(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(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.12/2.32 inference(rewrite,[status(thm)],[])).
% 2.12/2.32 tff(8522,plain,
% 2.12/2.32 (((~![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(s(z))))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(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(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[8521])).
% 2.12/2.32 tff(8523,plain,
% 2.12/2.32 (((~![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(s(z))))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(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(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.12/2.32 inference(transitivity,[status(thm)],[8522, 8520])).
% 2.12/2.32 tff(8524,plain,
% 2.12/2.32 ((~![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(s(z))))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.32 inference(quant_inst,[status(thm)],[])).
% 2.12/2.32 tff(8525,plain,
% 2.12/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 2.12/2.32 inference(modus_ponens,[status(thm)],[8524, 8523])).
% 2.12/2.32 tff(8526,plain,
% 2.12/2.32 ($false),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[8525, 37, 6530, 8519, 8504, 8502])).
% 2.12/2.32 tff(8527,plain,((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(s(z))))))), s(z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.32 tff(8528,plain,
% 2.12/2.32 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[8527, 1168, 1176, 107, 1391, 287])).
% 2.12/2.32 tff(8529,plain,
% 2.12/2.32 ($false),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[2037, 75, 107, 1391, 1168, 8528])).
% 2.12/2.32 tff(8530,plain,((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.32 tff(8531,plain,
% 2.12/2.32 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[8530, 8498, 8273, 1135, 8261])).
% 2.12/2.32 tff(8532,plain,
% 2.12/2.32 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[813, 8531, 1046])).
% 2.12/2.32 tff(8533,plain,
% 2.12/2.32 (~r(s(elem!1), elem!1)),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[808, 8532, 7108, 1146])).
% 2.12/2.32 tff(8534,plain,
% 2.12/2.32 (~r(s(s(s(z))), elem!1)),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[8322, 8533, 310])).
% 2.12/2.32 tff(8535,plain,
% 2.12/2.32 (b(s(s(s(z))), elem!1)),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[1115, 8534, 8308])).
% 2.12/2.32 tff(8536,plain,
% 2.12/2.32 (b(s(elem!1), elem!1)),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[1122, 8535, 1047])).
% 2.12/2.32 tff(8537,plain,
% 2.12/2.32 ($false),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[8331, 75, 107, 1391, 287, 921, 3862])).
% 2.12/2.32 tff(8538,plain,((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.32 tff(8539,plain,
% 2.12/2.32 (~b(s(elem!1), s(s(s(s(z)))))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[8538, 8536, 8273, 8261, 8498])).
% 2.12/2.32 tff(8540,plain,
% 2.12/2.32 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.12/2.32 inference(modus_ponens,[status(thm)],[8539, 8289])).
% 2.12/2.32 tff(8541,plain,
% 2.12/2.32 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[575, 8540])).
% 2.12/2.32 tff(8542,plain,
% 2.12/2.32 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(z))))),
% 2.12/2.32 inference(symmetry,[status(thm)],[8283])).
% 2.12/2.32 tff(8543,plain,
% 2.12/2.32 ((~b(s(z), s(elem!1))) <=> (~b(s(z), s(s(s(z)))))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[8542])).
% 2.12/2.32 tff(8544,plain,
% 2.12/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)))),
% 2.12/2.32 inference(rewrite,[status(thm)],[])).
% 2.12/2.32 tff(8545,plain,
% 2.12/2.32 (((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1)))) <=> ((~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)))),
% 2.12/2.32 inference(rewrite,[status(thm)],[])).
% 2.12/2.32 tff(8546,plain,
% 2.12/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1))))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[8545])).
% 2.12/2.32 tff(8547,plain,
% 2.12/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)))),
% 2.12/2.32 inference(transitivity,[status(thm)],[8546, 8544])).
% 2.12/2.32 tff(8548,plain,
% 2.12/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))),
% 2.12/2.32 inference(quant_inst,[status(thm)],[])).
% 2.12/2.32 tff(8549,plain,
% 2.12/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1))),
% 2.12/2.32 inference(modus_ponens,[status(thm)],[8548, 8547])).
% 2.12/2.32 tff(8550,plain,
% 2.12/2.32 (~b(s(z), s(elem!1))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[8549, 75, 8498, 8273, 8536])).
% 2.12/2.32 tff(8551,plain,
% 2.12/2.32 (~b(s(z), s(s(s(z))))),
% 2.12/2.32 inference(modus_ponens,[status(thm)],[8550, 8543])).
% 2.12/2.32 tff(8552,plain,
% 2.12/2.32 (r(s(z), s(s(s(z))))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[1263, 8551])).
% 2.12/2.32 tff(8553,plain,
% 2.12/2.32 ($false),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[1316, 8552, 8541, 8500])).
% 2.12/2.32 tff(8554,plain,((~(s(s(z)) = elem!1)) | (~b(s(s(elem!1)), elem!1)) | b(s(s(z)), elem!1) | r(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.12/2.32 tff(8555,plain,
% 2.12/2.32 (~(s(s(z)) = elem!1)),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[8554, 8256, 99, 12])).
% 2.12/2.32 tff(8556,plain,
% 2.12/2.32 (r(s(s(z)), elem!1)),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[104, 8555, 99])).
% 2.12/2.32 tff(8557,plain,
% 2.12/2.32 (elem!1 = s(z)),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[7780, 14, 7108, 8556, 99, 8258])).
% 2.12/2.32 tff(8558,plain,
% 2.12/2.32 (s(s(s(z))) = s(s(elem!1))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[84, 8557])).
% 2.12/2.32 tff(8559,plain,
% 2.12/2.32 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.12/2.33 inference(monotonicity,[status(thm)],[8558])).
% 2.12/2.33 tff(8560,plain,
% 2.12/2.33 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 2.12/2.33 inference(monotonicity,[status(thm)],[8559])).
% 2.12/2.33 tff(8561,plain,
% 2.12/2.33 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(z))),
% 2.12/2.33 inference(monotonicity,[status(thm)],[8557])).
% 2.12/2.33 tff(8562,plain,
% 2.12/2.33 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(elem!1))), s(z))),
% 2.12/2.33 inference(transitivity,[status(thm)],[8561, 8560])).
% 2.12/2.33 tff(8563,plain,
% 2.12/2.33 ((elem!1 = s(s(s(s(z))))) <=> (s(z) = s(s(s(s(z)))))),
% 2.12/2.33 inference(monotonicity,[status(thm)],[8557])).
% 2.12/2.33 tff(8564,plain,
% 2.12/2.33 ((s(z) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(z)))))),
% 2.12/2.33 inference(symmetry,[status(thm)],[8563])).
% 2.12/2.33 tff(8565,plain,
% 2.12/2.33 ((s(z) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 2.12/2.33 inference(transitivity,[status(thm)],[8564, 240])).
% 2.12/2.33 tff(8566,plain,
% 2.12/2.33 ((~(s(z) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 2.12/2.33 inference(monotonicity,[status(thm)],[8565])).
% 2.12/2.33 tff(8567,plain,
% 2.12/2.33 (~(s(s(s(s(z)))) = elem!1)),
% 2.12/2.33 inference(modus_ponens,[status(thm)],[484, 8566])).
% 2.12/2.33 tff(8568,plain,
% 2.12/2.33 (b(s(s(s(s(z)))), elem!1)),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[283, 8567, 12])).
% 2.12/2.33 tff(8569,plain,
% 2.12/2.33 (b(s(s(s(elem!1))), s(z))),
% 2.12/2.33 inference(modus_ponens,[status(thm)],[8568, 8562])).
% 2.12/2.33 tff(8570,plain,
% 2.12/2.33 (b(elem!1, s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 2.12/2.33 inference(monotonicity,[status(thm)],[8557])).
% 2.12/2.33 tff(8571,plain,
% 2.12/2.33 (~b(z, s(z))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[8131, 14, 12, 99, 285])).
% 2.12/2.33 tff(8572,plain,
% 2.12/2.33 (r(z, s(z))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[187, 8571])).
% 2.12/2.33 tff(8573,plain,
% 2.12/2.33 (~b(s(s(z)), s(z))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[425, 14, 7108, 8258, 99])).
% 2.12/2.33 tff(8574,plain,
% 2.12/2.33 (r(s(s(z)), s(z))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[153, 8573])).
% 2.12/2.33 tff(8575,plain,
% 2.12/2.33 (~r(s(s(elem!1)), s(z))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[548, 8574, 7108, 8572, 8259])).
% 2.12/2.33 tff(8576,plain,
% 2.12/2.33 (b(s(s(elem!1)), s(z))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[561, 8575])).
% 2.12/2.33 tff(8577,plain,
% 2.12/2.33 (b(elem!1, s(z)) <=> b(s(s(elem!1)), s(z))),
% 2.12/2.33 inference(monotonicity,[status(thm)],[1602])).
% 2.12/2.33 tff(8578,plain,
% 2.12/2.33 (b(s(s(elem!1)), s(z)) <=> b(elem!1, s(z))),
% 2.12/2.33 inference(symmetry,[status(thm)],[8577])).
% 2.12/2.33 tff(8579,plain,
% 2.12/2.33 (b(elem!1, s(z))),
% 2.12/2.33 inference(modus_ponens,[status(thm)],[1457, 8578])).
% 2.12/2.33 tff(8580,plain,
% 2.12/2.33 ($false),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[14, 8579])).
% 2.12/2.33 tff(8581,plain,((~(elem!1 = s(s(elem!1)))) | b(elem!1, s(z)) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.33 tff(8582,plain,
% 2.12/2.33 (~(elem!1 = s(s(elem!1)))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[8581, 8576, 14])).
% 2.12/2.33 tff(8583,plain,
% 2.12/2.33 (r(elem!1, s(s(s(s(z)))))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[3193, 8567, 12, 99, 8259])).
% 2.12/2.33 tff(8584,plain,
% 2.12/2.33 (s(z) = elem!1),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[111, 8557])).
% 2.12/2.33 tff(8585,plain,
% 2.12/2.33 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.12/2.33 inference(symmetry,[status(thm)],[8559])).
% 2.12/2.33 tff(8586,plain,
% 2.12/2.33 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 2.12/2.33 inference(monotonicity,[status(thm)],[8585])).
% 2.12/2.33 tff(8587,plain,
% 2.12/2.33 ((s(s(elem!1)) = s(s(s(s(z))))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 2.12/2.33 inference(symmetry,[status(thm)],[8586])).
% 2.12/2.33 tff(8588,plain,
% 2.12/2.33 ((~(s(s(elem!1)) = s(s(s(s(z)))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 2.12/2.33 inference(monotonicity,[status(thm)],[8587])).
% 2.12/2.33 tff(8589,plain,
% 2.12/2.33 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[1425, 8555])).
% 2.12/2.33 tff(8590,plain,
% 2.12/2.33 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.12/2.33 inference(modus_ponens,[status(thm)],[8589, 8588])).
% 2.12/2.33 tff(8591,plain,
% 2.12/2.33 (b(s(s(s(s(s(s(s(z))))))), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.12/2.33 inference(monotonicity,[status(thm)],[8557])).
% 2.12/2.33 tff(8592,plain,
% 2.12/2.33 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[719, 8584])).
% 2.12/2.33 tff(8593,plain,
% 2.12/2.33 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[736, 8584])).
% 2.12/2.33 tff(8594,plain,
% 2.12/2.33 (s(elem!1) = s(s(z))),
% 2.12/2.33 inference(monotonicity,[status(thm)],[8557])).
% 2.12/2.33 tff(8595,plain,
% 2.12/2.33 (r(s(elem!1), elem!1) <=> r(s(s(z)), s(z))),
% 2.12/2.33 inference(monotonicity,[status(thm)],[8594, 8557])).
% 2.12/2.33 tff(8596,plain,
% 2.12/2.33 (r(s(s(z)), s(z)) <=> r(s(elem!1), elem!1)),
% 2.12/2.33 inference(symmetry,[status(thm)],[8595])).
% 2.12/2.33 tff(8597,plain,
% 2.12/2.33 (r(s(elem!1), elem!1)),
% 2.12/2.33 inference(modus_ponens,[status(thm)],[8574, 8596])).
% 2.12/2.33 tff(8598,plain,
% 2.12/2.33 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[808, 8597, 7108, 8593])).
% 2.12/2.33 tff(8599,plain,
% 2.12/2.33 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[813, 8598, 8592])).
% 2.12/2.33 tff(8600,plain,
% 2.12/2.33 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.12/2.33 inference(modus_ponens,[status(thm)],[8599, 8591])).
% 2.12/2.33 tff(8601,plain,
% 2.12/2.33 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.12/2.33 inference(monotonicity,[status(thm)],[7111])).
% 2.12/2.33 tff(8602,plain,
% 2.12/2.33 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.12/2.33 inference(symmetry,[status(thm)],[8601])).
% 2.12/2.33 tff(8603,plain,
% 2.12/2.33 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.12/2.33 inference(monotonicity,[status(thm)],[8602])).
% 2.12/2.33 tff(8604,plain,
% 2.12/2.33 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.12/2.33 inference(symmetry,[status(thm)],[8603])).
% 2.12/2.33 tff(8605,plain,
% 2.12/2.33 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.12/2.33 inference(monotonicity,[status(thm)],[7111])).
% 2.12/2.33 tff(8606,plain,
% 2.12/2.33 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.12/2.33 inference(transitivity,[status(thm)],[8605, 8604])).
% 2.12/2.33 tff(8607,plain,
% 2.12/2.33 (s(z) = elem!1),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[111, 17])).
% 2.12/2.33 tff(8608,plain,
% 2.12/2.33 (r(elem!1, s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 2.12/2.33 inference(monotonicity,[status(thm)],[17])).
% 2.12/2.33 tff(8609,plain,
% 2.12/2.33 (r(s(z), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.12/2.33 inference(symmetry,[status(thm)],[8608])).
% 2.12/2.33 tff(8610,assumption,(b(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 2.12/2.33 tff(8611,plain,
% 2.12/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(X1, 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))))),
% 2.12/2.33 inference(rewrite,[status(thm)],[])).
% 2.12/2.33 tff(8612,plain,
% 2.12/2.33 (((~b(s(s(elem!1)), s(z))) | (~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(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))))),
% 2.12/2.33 inference(rewrite,[status(thm)],[])).
% 2.12/2.33 tff(8613,plain,
% 2.12/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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)))))),
% 2.12/2.33 inference(monotonicity,[status(thm)],[8612])).
% 2.12/2.33 tff(8614,plain,
% 2.12/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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))))),
% 2.12/2.33 inference(transitivity,[status(thm)],[8613, 8611])).
% 2.12/2.33 tff(8615,plain,
% 2.12/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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))))))),
% 2.12/2.33 inference(quant_inst,[status(thm)],[])).
% 2.12/2.33 tff(8616,plain,
% 2.12/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))),
% 2.12/2.33 inference(modus_ponens,[status(thm)],[8615, 8614])).
% 2.12/2.33 tff(8617,plain,
% 2.12/2.33 ($false),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[8616, 75, 1457, 1894, 5071, 8610])).
% 2.12/2.33 tff(8618,plain,((~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)))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.33 tff(8619,plain,
% 2.12/2.33 (~b(s(z), s(s(elem!1)))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[8618, 5071, 8610, 1457])).
% 2.12/2.33 tff(8620,plain,
% 2.12/2.33 (r(s(z), s(s(elem!1)))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[1890, 8619])).
% 2.12/2.33 tff(8621,plain,
% 2.12/2.33 (r(elem!1, s(s(elem!1)))),
% 2.12/2.33 inference(modus_ponens,[status(thm)],[8620, 8609])).
% 2.12/2.33 tff(8622,plain,
% 2.12/2.33 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[5049, 8621, 8607, 3195])).
% 2.12/2.33 tff(8623,plain,
% 2.12/2.33 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[2898, 8622])).
% 2.12/2.33 tff(8624,plain,
% 2.12/2.33 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.12/2.33 inference(modus_ponens,[status(thm)],[8623, 8606])).
% 2.12/2.33 tff(8625,plain,
% 2.12/2.33 (~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[836, 8607])).
% 2.12/2.33 tff(8626,plain,
% 2.12/2.33 (r(s(z), s(s(s(z)))) <=> r(s(z), s(s(elem!1)))),
% 2.12/2.33 inference(monotonicity,[status(thm)],[7111])).
% 2.12/2.33 tff(8627,plain,
% 2.12/2.33 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(z))))),
% 2.12/2.33 inference(symmetry,[status(thm)],[8626])).
% 2.12/2.33 tff(8628,plain,
% 2.12/2.33 (r(s(z), s(s(s(z))))),
% 2.12/2.33 inference(modus_ponens,[status(thm)],[8620, 8627])).
% 2.12/2.33 tff(8629,assumption,(b(s(s(s(s(s(s(s(z))))))), s(z))), introduced(assumption)).
% 2.12/2.33 tff(8630,assumption,(b(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 2.12/2.33 tff(8631,assumption,(b(s(z), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 2.12/2.33 tff(8632,plain,
% 2.12/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.12/2.33 inference(rewrite,[status(thm)],[])).
% 2.12/2.33 tff(8633,plain,
% 2.12/2.33 (((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(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(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.12/2.33 inference(rewrite,[status(thm)],[])).
% 2.12/2.33 tff(8634,plain,
% 2.12/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(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(X1, 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(s(s(s(z))))))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(z)))))),
% 2.12/2.33 inference(monotonicity,[status(thm)],[8633])).
% 2.12/2.33 tff(8635,plain,
% 2.12/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(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(X1, 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(s(s(s(z))))))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.12/2.33 inference(transitivity,[status(thm)],[8634, 8632])).
% 2.12/2.33 tff(8636,plain,
% 2.12/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(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)))))),
% 2.12/2.33 inference(quant_inst,[status(thm)],[])).
% 2.12/2.33 tff(8637,plain,
% 2.12/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(z)))),
% 2.12/2.33 inference(modus_ponens,[status(thm)],[8636, 8635])).
% 2.12/2.33 tff(8638,plain,
% 2.12/2.33 ($false),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[8637, 75, 1457, 8629, 8631, 8610, 8630])).
% 2.12/2.33 tff(8639,plain,((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.33 tff(8640,plain,
% 2.12/2.33 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[8639, 8624, 8629, 8610, 1457])).
% 2.12/2.33 tff(8641,assumption,(~b(s(z), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 2.12/2.33 tff(8642,assumption,(~r(s(z), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 2.12/2.33 tff(8643,plain,
% 2.12/2.33 ($false),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[8518, 58, 8642, 8641, 8508])).
% 2.12/2.33 tff(8644,plain,(r(s(z), s(s(s(s(s(s(s(z)))))))) | b(s(z), s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.33 tff(8645,plain,
% 2.12/2.33 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[8644, 8640])).
% 2.12/2.33 tff(8646,assumption,(r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))), introduced(assumption)).
% 2.12/2.33 tff(8647,assumption,(r(s(z), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 2.12/2.33 tff(8648,plain,
% 2.12/2.33 (((~![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(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.12/2.33 inference(rewrite,[status(thm)],[])).
% 2.12/2.33 tff(8649,plain,
% 2.12/2.33 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.12/2.33 inference(rewrite,[status(thm)],[])).
% 2.12/2.33 tff(8650,plain,
% 2.12/2.33 (((~![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(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(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(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))))),
% 2.12/2.33 inference(monotonicity,[status(thm)],[8649])).
% 2.12/2.33 tff(8651,plain,
% 2.12/2.33 (((~![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(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(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(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.12/2.33 inference(transitivity,[status(thm)],[8650, 8648])).
% 2.12/2.33 tff(8652,plain,
% 2.12/2.33 ((~![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(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.33 inference(quant_inst,[status(thm)],[])).
% 2.12/2.33 tff(8653,plain,
% 2.12/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 2.12/2.33 inference(modus_ponens,[status(thm)],[8652, 8651])).
% 2.12/2.33 tff(8654,plain,
% 2.12/2.33 ($false),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[8653, 37, 1265, 8647, 8646])).
% 2.12/2.33 tff(8655,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.33 tff(8656,plain,
% 2.12/2.33 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[8655, 8645, 8628])).
% 2.12/2.33 tff(8657,plain,
% 2.12/2.33 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.12/2.33 inference(monotonicity,[status(thm)],[4860])).
% 2.12/2.33 tff(8658,plain,
% 2.12/2.33 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.12/2.33 inference(symmetry,[status(thm)],[8657])).
% 2.12/2.33 tff(8659,plain,
% 2.12/2.33 ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) <=> (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 2.12/2.33 inference(monotonicity,[status(thm)],[8658])).
% 2.12/2.33 tff(8660,assumption,(~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))), introduced(assumption)).
% 2.12/2.33 tff(8661,plain,
% 2.12/2.33 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.12/2.33 inference(modus_ponens,[status(thm)],[8660, 8659])).
% 2.12/2.33 tff(8662,assumption,(~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))), introduced(assumption)).
% 2.12/2.33 tff(8663,plain,
% 2.12/2.33 ((s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[6017, 58, 8662])).
% 2.12/2.33 tff(8664,plain,
% 2.12/2.33 ($false),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[8663, 8661, 6007])).
% 2.12/2.33 tff(8665,plain,(b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | (~(s(s(s(z))) = s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.33 tff(8666,plain,
% 2.12/2.33 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[8665, 8656, 8625, 7111])).
% 2.12/2.33 tff(8667,plain,
% 2.12/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(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(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(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(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.12/2.34 inference(rewrite,[status(thm)],[])).
% 2.12/2.34 tff(8668,plain,
% 2.12/2.34 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(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(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.12/2.34 inference(rewrite,[status(thm)],[])).
% 2.12/2.34 tff(8669,plain,
% 2.12/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(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(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(z)))))),
% 2.12/2.34 inference(monotonicity,[status(thm)],[8668])).
% 2.12/2.34 tff(8670,plain,
% 2.12/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(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(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.12/2.34 inference(transitivity,[status(thm)],[8669, 8667])).
% 2.12/2.34 tff(8671,plain,
% 2.12/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.34 inference(quant_inst,[status(thm)],[])).
% 2.12/2.34 tff(8672,plain,
% 2.12/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(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(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(z)))),
% 2.12/2.34 inference(modus_ponens,[status(thm)],[8671, 8670])).
% 2.12/2.34 tff(8673,plain,
% 2.12/2.34 ((~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[8672, 75, 5071, 8629, 8610])).
% 2.12/2.34 tff(8674,plain,
% 2.12/2.34 (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[8673, 8666, 8624])).
% 2.12/2.34 tff(8675,plain,
% 2.12/2.34 ((elem!1 = s(s(s(s(z))))) <=> (s(z) = s(s(s(s(z)))))),
% 2.12/2.34 inference(monotonicity,[status(thm)],[17])).
% 2.12/2.34 tff(8676,plain,
% 2.12/2.34 ((s(z) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(z)))))),
% 2.12/2.34 inference(symmetry,[status(thm)],[8675])).
% 2.12/2.34 tff(8677,plain,
% 2.12/2.34 ((~(s(z) = s(s(s(s(z)))))) <=> (~(elem!1 = s(s(s(s(z))))))),
% 2.12/2.34 inference(monotonicity,[status(thm)],[8676])).
% 2.12/2.34 tff(8678,plain,
% 2.12/2.34 (~(elem!1 = s(s(s(s(z)))))),
% 2.12/2.34 inference(modus_ponens,[status(thm)],[484, 8677])).
% 2.12/2.34 tff(8679,plain,
% 2.12/2.34 (~(s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[862, 8678])).
% 2.12/2.34 tff(8680,plain,
% 2.12/2.34 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[3083, 58, 8679, 8674])).
% 2.12/2.34 tff(8681,plain,
% 2.12/2.34 (r(elem!1, s(s(s(elem!1))))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[5308, 3195, 8607])).
% 2.12/2.34 tff(8682,plain,
% 2.12/2.34 (s(z) = elem!1),
% 2.12/2.34 inference(symmetry,[status(thm)],[17])).
% 2.12/2.34 tff(8683,plain,
% 2.12/2.34 (r(s(z), s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 2.12/2.34 inference(monotonicity,[status(thm)],[8682])).
% 2.12/2.34 tff(8684,plain,
% 2.12/2.34 (r(elem!1, s(s(s(elem!1)))) <=> r(s(z), s(s(s(elem!1))))),
% 2.12/2.34 inference(symmetry,[status(thm)],[8683])).
% 2.12/2.34 tff(8685,plain,
% 2.12/2.34 (r(s(z), s(s(s(elem!1))))),
% 2.12/2.34 inference(modus_ponens,[status(thm)],[5311, 8684])).
% 2.12/2.34 tff(8686,assumption,(~r(s(z), s(s(s(elem!1))))), introduced(assumption)).
% 2.12/2.34 tff(8687,plain,
% 2.12/2.34 ($false),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[8686, 8685])).
% 2.12/2.34 tff(8688,plain,(r(s(z), s(s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.34 tff(8689,plain,
% 2.12/2.34 (r(s(z), s(s(s(elem!1))))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[8688, 8681, 17])).
% 2.12/2.34 tff(8690,plain,
% 2.12/2.34 (((~![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(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(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(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(elem!1))))))),
% 2.12/2.34 inference(rewrite,[status(thm)],[])).
% 2.12/2.34 tff(8691,plain,
% 2.12/2.34 (((~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(elem!1))))))),
% 2.12/2.34 inference(rewrite,[status(thm)],[])).
% 2.12/2.34 tff(8692,plain,
% 2.12/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(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(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(elem!1)))))))),
% 2.12/2.34 inference(monotonicity,[status(thm)],[8691])).
% 2.12/2.34 tff(8693,plain,
% 2.12/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(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(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(elem!1))))))),
% 2.12/2.34 inference(transitivity,[status(thm)],[8692, 8690])).
% 2.12/2.34 tff(8694,plain,
% 2.12/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(elem!1))))))),
% 2.12/2.34 inference(quant_inst,[status(thm)],[])).
% 2.12/2.34 tff(8695,plain,
% 2.12/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(elem!1)))))),
% 2.12/2.34 inference(modus_ponens,[status(thm)],[8694, 8693])).
% 2.12/2.34 tff(8696,plain,
% 2.12/2.34 ($false),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[8695, 37, 8645, 8689, 8680])).
% 2.12/2.34 tff(8697,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(s(s(z)))))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.34 tff(8698,plain,
% 2.12/2.34 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[8697, 8600, 8569, 8576, 8583, 8557])).
% 2.12/2.34 tff(8699,plain,
% 2.12/2.34 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[5815, 58, 8698, 8590])).
% 2.12/2.34 tff(8700,plain,
% 2.12/2.34 (((~![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))))))),
% 2.12/2.34 inference(rewrite,[status(thm)],[])).
% 2.12/2.34 tff(8701,plain,
% 2.12/2.34 (((~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))))))),
% 2.12/2.34 inference(rewrite,[status(thm)],[])).
% 2.12/2.34 tff(8702,plain,
% 2.12/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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)))))))),
% 2.12/2.34 inference(monotonicity,[status(thm)],[8701])).
% 2.12/2.34 tff(8703,plain,
% 2.12/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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))))))),
% 2.12/2.34 inference(transitivity,[status(thm)],[8702, 8700])).
% 2.12/2.34 tff(8704,plain,
% 2.12/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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)))))),
% 2.12/2.34 inference(quant_inst,[status(thm)],[])).
% 2.12/2.34 tff(8705,plain,
% 2.12/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.12/2.34 inference(modus_ponens,[status(thm)],[8704, 8703])).
% 2.12/2.34 tff(8706,plain,
% 2.12/2.34 ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[8705, 37, 1490])).
% 2.12/2.34 tff(8707,plain,
% 2.12/2.34 ($false),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[8706, 5035, 876])).
% 2.12/2.34 tff(8708,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.34 tff(8709,plain,
% 2.12/2.34 (~r(elem!1, s(s(elem!1)))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[8708, 8699, 8584, 8583])).
% 2.12/2.34 tff(8710,plain,
% 2.12/2.34 (b(elem!1, s(s(elem!1)))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[1617, 8709, 8582])).
% 2.12/2.34 tff(8711,plain,
% 2.12/2.34 (b(s(z), s(s(elem!1)))),
% 2.12/2.34 inference(modus_ponens,[status(thm)],[8710, 8570])).
% 2.12/2.34 tff(8712,plain,
% 2.12/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(X1, 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))))),
% 2.12/2.34 inference(rewrite,[status(thm)],[])).
% 2.12/2.34 tff(8713,plain,
% 2.12/2.34 (((~b(s(s(elem!1)), s(z))) | (~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))))),
% 2.12/2.34 inference(rewrite,[status(thm)],[])).
% 2.12/2.34 tff(8714,plain,
% 2.12/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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)))))),
% 2.12/2.34 inference(monotonicity,[status(thm)],[8713])).
% 2.12/2.34 tff(8715,plain,
% 2.12/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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))))),
% 2.12/2.34 inference(transitivity,[status(thm)],[8714, 8712])).
% 2.12/2.34 tff(8716,plain,
% 2.12/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))))),
% 2.12/2.34 inference(quant_inst,[status(thm)],[])).
% 2.12/2.34 tff(8717,plain,
% 2.12/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))),
% 2.12/2.34 inference(modus_ponens,[status(thm)],[8716, 8715])).
% 2.12/2.34 tff(8718,plain,
% 2.12/2.34 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[8717, 75, 8576, 8711, 8569])).
% 2.12/2.34 tff(8719,plain,
% 2.12/2.34 (~r(s(s(s(elem!1))), elem!1)),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[694, 8584, 7108, 8556])).
% 2.12/2.34 tff(8720,plain,
% 2.12/2.34 ((elem!1 = s(s(s(elem!1)))) <=> (s(z) = s(s(s(s(z)))))),
% 2.12/2.34 inference(monotonicity,[status(thm)],[8557, 8585])).
% 2.12/2.34 tff(8721,plain,
% 2.12/2.34 ((s(z) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(elem!1))))),
% 2.12/2.34 inference(symmetry,[status(thm)],[8720])).
% 2.12/2.34 tff(8722,plain,
% 2.12/2.34 ((s(z) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = elem!1)),
% 2.12/2.34 inference(transitivity,[status(thm)],[8721, 3277])).
% 2.12/2.34 tff(8723,plain,
% 2.12/2.34 ((~(s(z) = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 2.12/2.34 inference(monotonicity,[status(thm)],[8722])).
% 2.12/2.34 tff(8724,plain,
% 2.12/2.34 (~(s(s(s(elem!1))) = elem!1)),
% 2.12/2.34 inference(modus_ponens,[status(thm)],[484, 8723])).
% 2.12/2.34 tff(8725,plain,
% 2.12/2.34 (b(s(s(s(elem!1))), elem!1)),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[3370, 8724, 8719])).
% 2.12/2.34 tff(8726,plain,
% 2.12/2.34 (~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[836, 8584])).
% 2.12/2.34 tff(8727,plain,
% 2.12/2.34 ((~(s(z) = s(s(s(s(z)))))) <=> (~(elem!1 = s(s(s(s(z))))))),
% 2.12/2.34 inference(monotonicity,[status(thm)],[8564])).
% 2.12/2.34 tff(8728,plain,
% 2.12/2.34 (~(elem!1 = s(s(s(s(z)))))),
% 2.12/2.34 inference(modus_ponens,[status(thm)],[484, 8727])).
% 2.12/2.34 tff(8729,plain,
% 2.12/2.34 (~(s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[862, 8728])).
% 2.12/2.34 tff(8730,plain,
% 2.12/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.34 inference(rewrite,[status(thm)],[])).
% 2.12/2.34 tff(8731,plain,
% 2.12/2.34 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.34 inference(rewrite,[status(thm)],[])).
% 2.12/2.34 tff(8732,plain,
% 2.12/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))))),
% 2.12/2.34 inference(monotonicity,[status(thm)],[8731])).
% 2.12/2.34 tff(8733,plain,
% 2.12/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.34 inference(transitivity,[status(thm)],[8732, 8730])).
% 2.12/2.34 tff(8734,plain,
% 2.12/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.34 inference(quant_inst,[status(thm)],[])).
% 2.12/2.34 tff(8735,plain,
% 2.12/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))),
% 2.12/2.35 inference(modus_ponens,[status(thm)],[8734, 8733])).
% 2.12/2.35 tff(8736,plain,
% 2.12/2.35 (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[8735, 75, 1620, 1168, 707, 922])).
% 2.12/2.35 tff(8737,plain,
% 2.12/2.35 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[3083, 58, 868, 8736])).
% 2.12/2.35 tff(8738,plain,
% 2.12/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.12/2.35 inference(rewrite,[status(thm)],[])).
% 2.12/2.35 tff(8739,plain,
% 2.12/2.35 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.12/2.35 inference(rewrite,[status(thm)],[])).
% 2.12/2.35 tff(8740,plain,
% 2.12/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 2.12/2.35 inference(monotonicity,[status(thm)],[8739])).
% 2.12/2.35 tff(8741,plain,
% 2.12/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.12/2.35 inference(transitivity,[status(thm)],[8740, 8738])).
% 2.12/2.35 tff(8742,plain,
% 2.12/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.35 inference(quant_inst,[status(thm)],[])).
% 2.12/2.35 tff(8743,plain,
% 2.12/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.12/2.35 inference(modus_ponens,[status(thm)],[8742, 8741])).
% 2.12/2.35 tff(8744,plain,
% 2.12/2.35 (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[8743, 75, 1620, 1168, 707])).
% 2.12/2.35 tff(8745,plain,
% 2.12/2.35 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[840, 58, 3067, 8744])).
% 2.12/2.35 tff(8746,assumption,(r(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 2.12/2.35 tff(8747,plain,
% 2.12/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.35 inference(rewrite,[status(thm)],[])).
% 2.12/2.35 tff(8748,plain,
% 2.12/2.35 (((~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.35 inference(rewrite,[status(thm)],[])).
% 2.12/2.35 tff(8749,plain,
% 2.12/2.35 (((~![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(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(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(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))))),
% 2.12/2.35 inference(monotonicity,[status(thm)],[8748])).
% 2.12/2.35 tff(8750,plain,
% 2.12/2.35 (((~![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(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(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(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.35 inference(transitivity,[status(thm)],[8749, 8747])).
% 2.12/2.35 tff(8751,plain,
% 2.12/2.35 ((~![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(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.12/2.35 inference(quant_inst,[status(thm)],[])).
% 2.12/2.35 tff(8752,plain,
% 2.12/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))),
% 2.12/2.35 inference(modus_ponens,[status(thm)],[8751, 8750])).
% 2.12/2.35 tff(8753,plain,
% 2.12/2.35 ($false),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[8752, 37, 8746, 8745, 8737])).
% 2.12/2.35 tff(8754,plain,((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))) | (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.35 tff(8755,plain,
% 2.12/2.35 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[8754, 8710, 8256, 8729, 8726, 8725, 8599])).
% 2.12/2.35 tff(8756,plain,
% 2.12/2.35 (s(s(s(elem!1))) = s(s(elem!1))),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[7952, 58, 8755, 8718])).
% 2.12/2.35 tff(8757,plain,
% 2.12/2.35 (s(s(elem!1)) = s(s(s(elem!1)))),
% 2.12/2.35 inference(symmetry,[status(thm)],[8756])).
% 2.12/2.35 tff(8758,plain,
% 2.12/2.35 ($false),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[8590, 8757])).
% 2.12/2.35 tff(8759,plain,(b(elem!1, s(z)) | r(s(s(s(s(z)))), elem!1) | b(s(s(z)), elem!1) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.12/2.35 tff(8760,plain,
% 2.12/2.35 (b(elem!1, s(z))),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[8759, 285, 99, 12])).
% 2.12/2.35 tff(8761,plain,
% 2.12/2.35 (~(s(z) = elem!1)),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[1393, 8760])).
% 2.12/2.35 tff(8762,plain,
% 2.12/2.35 (~(s(s(s(s(z)))) = elem!1)),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[8091, 8761, 7108, 8259, 285, 8258])).
% 2.12/2.35 tff(8763,plain,
% 2.12/2.35 (b(s(s(s(s(z)))), elem!1)),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[283, 8762, 12])).
% 2.12/2.35 tff(8764,plain,
% 2.12/2.35 (~r(s(z), elem!1)),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[2086, 8556, 7108])).
% 2.12/2.35 tff(8765,plain,
% 2.12/2.35 (b(s(z), elem!1)),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[601, 8761, 8764])).
% 2.12/2.35 tff(8766,plain,
% 2.12/2.35 (~b(s(z), s(s(s(s(z)))))),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[5527, 8765, 8760, 8763])).
% 2.12/2.35 tff(8767,plain,
% 2.12/2.35 (r(s(z), s(s(s(s(z)))))),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[489, 8766])).
% 2.12/2.35 tff(8768,plain,
% 2.12/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 2.12/2.35 inference(rewrite,[status(thm)],[])).
% 2.12/2.35 tff(8769,plain,
% 2.12/2.35 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 2.12/2.35 inference(rewrite,[status(thm)],[])).
% 2.12/2.35 tff(8770,plain,
% 2.12/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))))),
% 2.12/2.35 inference(monotonicity,[status(thm)],[8769])).
% 2.12/2.35 tff(8771,plain,
% 2.12/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 2.12/2.35 inference(transitivity,[status(thm)],[8770, 8768])).
% 2.12/2.35 tff(8772,plain,
% 2.12/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 2.12/2.35 inference(quant_inst,[status(thm)],[])).
% 2.12/2.35 tff(8773,plain,
% 2.12/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))),
% 2.12/2.35 inference(modus_ponens,[status(thm)],[8772, 8771])).
% 2.12/2.35 tff(8774,plain,
% 2.12/2.35 (~b(s(s(elem!1)), s(z))),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[8773, 75, 8765, 8760, 8256])).
% 2.12/2.35 tff(8775,plain,
% 2.12/2.35 (r(s(s(elem!1)), s(z))),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[561, 8774])).
% 2.12/2.35 tff(8776,plain,
% 2.12/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.12/2.35 inference(rewrite,[status(thm)],[])).
% 2.12/2.35 tff(8777,plain,
% 2.12/2.35 (((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.12/2.35 inference(rewrite,[status(thm)],[])).
% 2.12/2.35 tff(8778,plain,
% 2.12/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 2.12/2.35 inference(monotonicity,[status(thm)],[8777])).
% 2.12/2.35 tff(8779,plain,
% 2.12/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.12/2.35 inference(transitivity,[status(thm)],[8778, 8776])).
% 2.12/2.35 tff(8780,plain,
% 2.12/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.12/2.35 inference(quant_inst,[status(thm)],[])).
% 2.12/2.35 tff(8781,plain,
% 2.12/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 2.12/2.35 inference(modus_ponens,[status(thm)],[8780, 8779])).
% 2.12/2.35 tff(8782,plain,
% 2.12/2.35 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[8781, 75, 8765, 8760, 8763, 8256])).
% 2.12/2.35 tff(8783,plain,
% 2.12/2.35 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[1660, 8782, 8589])).
% 2.12/2.35 tff(8784,plain,
% 2.12/2.35 ($false),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[1655, 8783, 8775, 8767])).
% 2.12/2.35 tff(8785,plain,(b(z, elem!1) | r(s(s(s(s(z)))), elem!1) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.12/2.35 tff(8786,plain,
% 2.12/2.35 (b(z, elem!1)),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[8785, 99, 12])).
% 2.12/2.35 tff(8787,plain,
% 2.12/2.35 ((s(s(s(s(z)))) = z) <=> (elem!1 = z)),
% 2.12/2.35 inference(monotonicity,[status(thm)],[3285])).
% 2.12/2.35 tff(8788,plain,
% 2.12/2.35 ((s(s(s(s(z)))) = z) <=> (z = elem!1)),
% 2.12/2.35 inference(transitivity,[status(thm)],[8787, 216])).
% 2.12/2.35 tff(8789,plain,
% 2.12/2.35 ((s(s(s(s(z)))) = z) <=> (elem!1 = z)),
% 2.12/2.35 inference(transitivity,[status(thm)],[8788, 1939])).
% 2.12/2.35 tff(8790,plain,
% 2.12/2.35 ((~(s(s(s(s(z)))) = z)) <=> (~(elem!1 = z))),
% 2.12/2.35 inference(monotonicity,[status(thm)],[8789])).
% 2.12/2.35 tff(8791,plain,
% 2.12/2.35 (~(elem!1 = z)),
% 2.12/2.35 inference(modus_ponens,[status(thm)],[1143, 8790])).
% 2.12/2.35 tff(8792,plain,
% 2.12/2.35 ((s(z) = s(s(s(s(z))))) <=> (elem!1 = s(z))),
% 2.12/2.35 inference(transitivity,[status(thm)],[3658, 92])).
% 2.12/2.35 tff(8793,plain,
% 2.12/2.35 ((~(s(z) = s(s(s(s(z)))))) <=> (~(elem!1 = s(z)))),
% 2.12/2.35 inference(monotonicity,[status(thm)],[8792])).
% 2.12/2.35 tff(8794,plain,
% 2.12/2.35 (~(elem!1 = s(z))),
% 2.12/2.35 inference(modus_ponens,[status(thm)],[484, 8793])).
% 2.12/2.35 tff(8795,plain,
% 2.12/2.35 ($false),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[7782, 7028, 8794, 300, 14, 8791, 99])).
% 2.12/2.35 tff(8796,plain,((~(s(s(s(s(z)))) = elem!1)) | (~r(z, elem!1)) | b(elem!1, s(z)) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.12/2.35 tff(8797,plain,
% 2.12/2.35 (~(s(s(s(s(z)))) = elem!1)),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[8796, 14, 7108, 99])).
% 2.12/2.35 tff(8798,plain,
% 2.12/2.35 (b(s(s(s(s(z)))), elem!1)),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[283, 8797, 12])).
% 2.12/2.35 tff(8799,plain,
% 2.12/2.35 (~b(s(s(elem!1)), elem!1)),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[8554, 310, 99, 12])).
% 2.12/2.35 tff(8800,plain,
% 2.12/2.35 ($false),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[6517, 8799, 1047, 287])).
% 2.12/2.35 tff(8801,plain,((~(s(s(z)) = elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | b(s(s(z)), elem!1) | r(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.12/2.35 tff(8802,plain,
% 2.12/2.35 (~(s(s(z)) = elem!1)),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[8801, 8798, 99, 12])).
% 2.12/2.35 tff(8803,plain,
% 2.12/2.35 (r(elem!1, s(z))),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[89, 95, 14])).
% 2.12/2.35 tff(8804,plain,
% 2.12/2.35 (~r(z, s(z))),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[367, 8803, 300])).
% 2.12/2.35 tff(8805,plain,
% 2.12/2.35 (elem!1 = z),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[7782, 95, 300, 14, 15, 99])).
% 2.12/2.35 tff(8806,plain,
% 2.12/2.35 (z = elem!1),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[304, 8805])).
% 2.12/2.35 tff(8807,plain,
% 2.12/2.35 (~b(z, s(z))),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[8118, 8806, 14])).
% 2.12/2.35 tff(8808,plain,
% 2.12/2.35 ($false),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[187, 8807, 8804])).
% 2.12/2.35 tff(8809,plain,((elem!1 = s(z)) | b(elem!1, s(z)) | (~r(z, elem!1)) | (s(s(z)) = elem!1) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.12/2.35 tff(8810,plain,
% 2.12/2.35 (elem!1 = s(z)),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[8809, 14, 7108, 8802, 99])).
% 2.12/2.35 tff(8811,plain,
% 2.12/2.35 (b(s(z), elem!1) <=> b(s(z), s(z))),
% 2.12/2.35 inference(monotonicity,[status(thm)],[8810])).
% 2.12/2.35 tff(8812,plain,
% 2.12/2.35 (b(s(z), s(z)) <=> b(s(z), elem!1)),
% 2.12/2.35 inference(symmetry,[status(thm)],[8811])).
% 2.12/2.35 tff(8813,plain,
% 2.12/2.35 ((~b(s(z), s(z))) <=> (~b(s(z), elem!1))),
% 2.12/2.35 inference(monotonicity,[status(thm)],[8812])).
% 2.12/2.35 tff(8814,plain,
% 2.12/2.35 (b(elem!1, elem!1) <=> b(s(z), s(z))),
% 2.12/2.35 inference(monotonicity,[status(thm)],[8810, 8810])).
% 2.12/2.35 tff(8815,plain,
% 2.12/2.35 ((~b(elem!1, elem!1)) <=> (~b(s(z), s(z)))),
% 2.12/2.35 inference(monotonicity,[status(thm)],[8814])).
% 2.12/2.35 tff(8816,plain,
% 2.12/2.35 (~b(s(z), s(z))),
% 2.12/2.35 inference(modus_ponens,[status(thm)],[1389, 8815])).
% 2.12/2.35 tff(8817,plain,
% 2.12/2.35 (~b(s(z), elem!1)),
% 2.12/2.35 inference(modus_ponens,[status(thm)],[8816, 8813])).
% 2.12/2.35 tff(8818,plain,
% 2.12/2.35 (~r(s(z), elem!1)),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[2086, 889, 7108])).
% 2.12/2.35 tff(8819,plain,
% 2.12/2.35 (s(z) = elem!1),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[601, 8818, 3627])).
% 2.12/2.35 tff(8820,plain,
% 2.12/2.35 (elem!1 = s(z)),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[97, 8819])).
% 2.12/2.35 tff(8821,plain,
% 2.12/2.35 (r(z, s(z)) <=> r(z, elem!1)),
% 2.12/2.35 inference(monotonicity,[status(thm)],[8819])).
% 2.12/2.35 tff(8822,plain,
% 2.12/2.35 (r(z, elem!1) <=> r(z, s(z))),
% 2.12/2.35 inference(symmetry,[status(thm)],[8821])).
% 2.12/2.35 tff(8823,plain,
% 2.12/2.35 (r(z, s(z))),
% 2.12/2.35 inference(modus_ponens,[status(thm)],[7108, 8822])).
% 2.12/2.35 tff(8824,plain,
% 2.12/2.35 (s(s(s(z))) = s(s(elem!1))),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[84, 8820])).
% 2.12/2.35 tff(8825,plain,
% 2.12/2.35 (~b(elem!1, z)),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[5223, 8824, 12, 8786, 15])).
% 2.12/2.35 tff(8826,plain,
% 2.12/2.35 (~(s(s(elem!1)) = s(s(z)))),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[4866, 8824])).
% 2.12/2.35 tff(8827,plain,
% 2.12/2.35 (~(z = elem!1)),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[293, 8826])).
% 2.12/2.35 tff(8828,plain,
% 2.12/2.35 (~(elem!1 = z)),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[304, 8827])).
% 2.12/2.36 tff(8829,plain,
% 2.12/2.36 (r(elem!1, z)),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[387, 8828, 8825])).
% 2.12/2.36 tff(8830,plain,
% 2.12/2.36 (b(z, s(z)) <=> b(z, elem!1)),
% 2.12/2.36 inference(monotonicity,[status(thm)],[8819])).
% 2.12/2.36 tff(8831,plain,
% 2.12/2.36 (b(z, elem!1) <=> b(z, s(z))),
% 2.12/2.36 inference(symmetry,[status(thm)],[8830])).
% 2.12/2.36 tff(8832,plain,
% 2.12/2.36 (b(z, s(z))),
% 2.12/2.36 inference(modus_ponens,[status(thm)],[8786, 8831])).
% 2.12/2.36 tff(8833,plain,
% 2.12/2.36 (~b(s(s(elem!1)), elem!1)),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[5349, 8832, 8786, 287, 8824, 8829])).
% 2.12/2.36 tff(8834,plain,
% 2.12/2.36 ($false),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[7119, 8833, 8823, 7108, 8820, 99])).
% 2.12/2.36 tff(8835,plain,((s(s(z)) = elem!1) | b(s(s(z)), elem!1) | (~b(s(s(s(s(z)))), elem!1)) | r(s(s(s(s(z)))), elem!1) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.12/2.36 tff(8836,plain,
% 2.12/2.36 (b(s(z), elem!1)),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[8835, 8802, 8798, 12, 99])).
% 2.12/2.36 tff(8837,plain,
% 2.12/2.36 ($false),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[8836, 8817])).
% 2.12/2.36 tff(8838,plain,(b(elem!1, s(z)) | b(s(s(z)), elem!1) | r(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.12/2.36 tff(8839,plain,
% 2.12/2.36 (b(elem!1, s(z))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[8838, 99, 12])).
% 2.12/2.36 tff(8840,plain,
% 2.12/2.36 (~b(s(s(elem!1)), elem!1)),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[7076, 8839, 12, 99, 8786])).
% 2.12/2.36 tff(8841,plain,
% 2.12/2.36 (~r(s(z), elem!1)),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[2086, 106, 7108])).
% 2.12/2.36 tff(8842,plain,
% 2.12/2.36 (b(s(z), elem!1)),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[601, 8841, 2478])).
% 2.12/2.36 tff(8843,plain,
% 2.12/2.36 (((~b(s(z), elem!1)) | (~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(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)))),
% 2.12/2.36 inference(rewrite,[status(thm)],[])).
% 2.12/2.36 tff(8844,plain,
% 2.12/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z, elem!1)) | (~b(s(z), elem!1))))),
% 2.12/2.36 inference(monotonicity,[status(thm)],[8843])).
% 2.12/2.36 tff(8845,plain,
% 2.12/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z, elem!1)) | (~b(s(z), elem!1)))),
% 2.12/2.36 inference(transitivity,[status(thm)],[8844, 1785])).
% 2.12/2.36 tff(8846,plain,
% 2.12/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 2.12/2.36 inference(quant_inst,[status(thm)],[])).
% 2.12/2.36 tff(8847,plain,
% 2.12/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, elem!1)) | (~b(s(z), elem!1))),
% 2.12/2.36 inference(modus_ponens,[status(thm)],[8846, 8845])).
% 2.12/2.36 tff(8848,plain,
% 2.12/2.36 (~b(z, s(z))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[8847, 75, 1518, 8842, 1391])).
% 2.12/2.36 tff(8849,plain,
% 2.12/2.36 (r(z, s(z))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[187, 8848])).
% 2.12/2.36 tff(8850,plain,
% 2.12/2.36 (~r(s(s(z)), z)),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[328, 106, 7108])).
% 2.12/2.36 tff(8851,plain,
% 2.12/2.36 (b(s(s(z)), z)),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[202, 8850])).
% 2.12/2.36 tff(8852,plain,
% 2.12/2.36 (~r(z, s(s(z)))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[339, 106, 7108])).
% 2.12/2.36 tff(8853,plain,
% 2.12/2.36 (b(z, s(s(z)))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[351, 8852])).
% 2.12/2.36 tff(8854,plain,
% 2.12/2.36 (~b(s(s(s(s(z)))), elem!1)),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[6533, 8842, 1518, 1391])).
% 2.12/2.36 tff(8855,plain,
% 2.12/2.36 (s(s(s(s(z)))) = elem!1),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[283, 8854, 12])).
% 2.12/2.36 tff(8856,plain,
% 2.12/2.36 (elem!1 = s(s(s(s(z))))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[4463, 8855])).
% 2.12/2.36 tff(8857,plain,
% 2.12/2.36 (~(elem!1 = s(s(elem!1)))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[4475, 8856, 7004])).
% 2.12/2.36 tff(8858,plain,
% 2.12/2.36 (~(s(s(elem!1)) = elem!1)),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[2555, 8857])).
% 2.12/2.36 tff(8859,plain,
% 2.12/2.36 (r(s(s(elem!1)), elem!1)),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[2673, 8858, 1])).
% 2.12/2.36 tff(8860,plain,
% 2.12/2.36 (~r(s(s(elem!1)), s(s(z)))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[2661, 37, 106, 8859])).
% 2.12/2.36 tff(8861,plain,
% 2.12/2.36 (b(s(s(elem!1)), s(s(z)))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[1476, 8860, 7004])).
% 2.12/2.36 tff(8862,plain,
% 2.12/2.36 (~b(s(s(z)), s(z))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[1471, 8861, 7108, 8853, 8851, 1391, 8849, 8842])).
% 2.12/2.36 tff(8863,plain,
% 2.12/2.36 (r(s(s(z)), s(z))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[153, 8862])).
% 2.12/2.36 tff(8864,plain,
% 2.12/2.36 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, elem!1)),
% 2.12/2.36 inference(monotonicity,[status(thm)],[8855])).
% 2.12/2.36 tff(8865,plain,
% 2.12/2.36 (b(elem!1, elem!1) <=> b(elem!1, s(s(s(s(z)))))),
% 2.12/2.36 inference(symmetry,[status(thm)],[8864])).
% 2.12/2.36 tff(8866,plain,
% 2.12/2.36 ((~b(elem!1, elem!1)) <=> (~b(elem!1, s(s(s(s(z))))))),
% 2.12/2.36 inference(monotonicity,[status(thm)],[8865])).
% 2.12/2.36 tff(8867,plain,
% 2.12/2.36 (~b(elem!1, s(s(s(s(z)))))),
% 2.12/2.36 inference(modus_ponens,[status(thm)],[1389, 8866])).
% 2.12/2.36 tff(8868,plain,
% 2.12/2.36 (r(s(z), s(s(s(s(z))))) <=> r(s(z), elem!1)),
% 2.12/2.36 inference(monotonicity,[status(thm)],[8855])).
% 2.12/2.36 tff(8869,plain,
% 2.12/2.36 (r(s(z), elem!1) <=> r(s(z), s(s(s(s(z)))))),
% 2.12/2.36 inference(symmetry,[status(thm)],[8868])).
% 2.12/2.36 tff(8870,plain,
% 2.12/2.36 ((~r(s(z), elem!1)) <=> (~r(s(z), s(s(s(s(z))))))),
% 2.12/2.36 inference(monotonicity,[status(thm)],[8869])).
% 2.12/2.36 tff(8871,plain,
% 2.12/2.36 (~r(s(z), s(s(s(s(z)))))),
% 2.12/2.36 inference(modus_ponens,[status(thm)],[8841, 8870])).
% 2.12/2.36 tff(8872,plain,
% 2.12/2.36 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(z)), elem!1)),
% 2.12/2.36 inference(monotonicity,[status(thm)],[8855])).
% 2.12/2.36 tff(8873,plain,
% 2.12/2.36 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(s(s(s(z)))))),
% 2.12/2.36 inference(symmetry,[status(thm)],[8872])).
% 2.12/2.36 tff(8874,plain,
% 2.12/2.36 (r(s(s(z)), s(s(s(s(z)))))),
% 2.12/2.36 inference(modus_ponens,[status(thm)],[106, 8873])).
% 2.12/2.36 tff(8875,plain,
% 2.12/2.36 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[4486, 8859, 8855])).
% 2.12/2.36 tff(8876,plain,
% 2.12/2.36 (~b(elem!1, s(s(elem!1)))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[6176, 8842, 1518, 1391])).
% 2.12/2.36 tff(8877,plain,
% 2.12/2.36 (r(elem!1, s(s(elem!1)))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[1617, 8857, 8876])).
% 2.12/2.36 tff(8878,plain,
% 2.12/2.36 (~b(s(s(elem!1)), s(z))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[6273, 8849, 1391, 7004, 1518, 8877, 8875, 2478, 8874, 8871, 8867])).
% 2.12/2.36 tff(8879,plain,
% 2.12/2.36 (r(s(s(elem!1)), s(z))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[561, 8878])).
% 2.12/2.36 tff(8880,plain,
% 2.12/2.36 ($false),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[548, 8879, 8863, 7108, 8849, 7004])).
% 2.12/2.36 tff(8881,plain,((~r(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | b(s(s(elem!1)), elem!1) | r(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.12/2.36 tff(8882,plain,
% 2.12/2.36 (~r(s(s(z)), elem!1)),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[8881, 8839, 8786, 8840, 12])).
% 2.12/2.36 tff(8883,plain,
% 2.12/2.36 (s(s(z)) = elem!1),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[104, 8882, 99])).
% 2.12/2.36 tff(8884,plain,
% 2.12/2.36 ((s(s(z)) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(z)))))),
% 2.12/2.36 inference(monotonicity,[status(thm)],[8883])).
% 2.12/2.36 tff(8885,plain,
% 2.12/2.36 ((elem!1 = s(s(s(s(z))))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 2.12/2.36 inference(symmetry,[status(thm)],[8884])).
% 2.12/2.36 tff(8886,plain,
% 2.12/2.36 (~b(s(s(s(s(z)))), elem!1)),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[8801, 8883, 99, 12])).
% 2.12/2.36 tff(8887,plain,
% 2.12/2.36 (s(s(s(s(z)))) = elem!1),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[283, 8886, 12])).
% 2.12/2.36 tff(8888,plain,
% 2.12/2.36 (elem!1 = s(s(s(s(z))))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[4463, 8887])).
% 2.12/2.36 tff(8889,plain,
% 2.12/2.36 (s(s(z)) = s(s(s(s(z))))),
% 2.12/2.36 inference(modus_ponens,[status(thm)],[8888, 8885])).
% 2.12/2.36 tff(8890,plain,
% 2.12/2.36 ($false),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[459, 8889])).
% 2.12/2.36 tff(8891,plain,(b(s(s(z)), elem!1) | r(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.12/2.36 tff(8892,plain,
% 2.12/2.36 (b(s(s(z)), elem!1)),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[8891, 12])).
% 2.12/2.36 tff(8893,plain,
% 2.12/2.36 (b(s(s(z)), elem!1) <=> b(elem!1, elem!1)),
% 2.12/2.36 inference(monotonicity,[status(thm)],[1058])).
% 2.12/2.36 tff(8894,plain,
% 2.12/2.36 (b(elem!1, elem!1) <=> b(s(s(z)), elem!1)),
% 2.12/2.36 inference(symmetry,[status(thm)],[8893])).
% 2.12/2.36 tff(8895,plain,
% 2.12/2.36 ((~b(elem!1, elem!1)) <=> (~b(s(s(z)), elem!1))),
% 2.12/2.36 inference(monotonicity,[status(thm)],[8894])).
% 2.12/2.36 tff(8896,plain,
% 2.12/2.36 (~b(s(s(z)), elem!1)),
% 2.12/2.36 inference(modus_ponens,[status(thm)],[1389, 8895])).
% 2.12/2.36 tff(8897,plain,
% 2.12/2.36 ($false),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[964, 8896])).
% 2.12/2.36 tff(8898,plain,((~(s(s(elem!1)) = s(s(s(s(z)))))) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.36 tff(8899,plain,
% 2.12/2.36 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[8898, 8892])).
% 2.12/2.36 tff(8900,plain,
% 2.12/2.36 (~(z = elem!1)),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[4314, 113, 12, 8892, 1011, 108])).
% 2.12/2.36 tff(8901,plain,
% 2.12/2.36 (~(s(s(elem!1)) = s(s(z)))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[237, 8900])).
% 2.12/2.36 tff(8902,plain,
% 2.12/2.36 ((~(s(z) = s(s(s(s(z)))))) <=> (~(s(z) = elem!1))),
% 2.12/2.36 inference(monotonicity,[status(thm)],[3658])).
% 2.12/2.36 tff(8903,plain,
% 2.12/2.36 (~(s(z) = elem!1)),
% 2.12/2.36 inference(modus_ponens,[status(thm)],[484, 8902])).
% 2.12/2.36 tff(8904,plain,
% 2.12/2.36 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[1425, 7028])).
% 2.12/2.36 tff(8905,plain,
% 2.12/2.36 (b(s(s(z)), s(s(s(s(z)))))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[6139, 3285, 964])).
% 2.12/2.36 tff(8906,plain,
% 2.12/2.36 ((~(s(s(s(s(z)))) = z)) <=> (~(z = elem!1))),
% 2.12/2.36 inference(monotonicity,[status(thm)],[8788])).
% 2.12/2.36 tff(8907,plain,
% 2.12/2.36 (~(z = elem!1)),
% 2.12/2.36 inference(modus_ponens,[status(thm)],[1143, 8906])).
% 2.12/2.36 tff(8908,plain,
% 2.12/2.36 (~(s(s(elem!1)) = s(s(z)))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[237, 8907])).
% 2.12/2.36 tff(8909,plain,
% 2.12/2.36 (r(s(z), s(s(s(s(z)))))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[7457, 8908, 300, 8905, 8904, 14, 8903])).
% 2.12/2.36 tff(8910,plain,
% 2.12/2.36 (r(s(z), elem!1)),
% 2.12/2.36 inference(modus_ponens,[status(thm)],[8909, 3660])).
% 2.12/2.36 tff(8911,plain,
% 2.12/2.36 (r(elem!1, s(z))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[89, 8794, 14])).
% 2.12/2.36 tff(8912,plain,
% 2.12/2.36 (b(z, elem!1)),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[7889, 8908, 300, 3285, 14, 8903, 8791])).
% 2.12/2.36 tff(8913,plain,
% 2.12/2.36 (~b(s(s(elem!1)), elem!1)),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[4764, 8912, 964, 3285, 8791, 8911, 8908])).
% 2.12/2.36 tff(8914,plain,
% 2.12/2.36 (~(elem!1 = s(s(elem!1)))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[4475, 8908, 4464])).
% 2.12/2.36 tff(8915,plain,
% 2.12/2.36 (~(s(s(elem!1)) = elem!1)),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[2555, 8914])).
% 2.12/2.36 tff(8916,plain,
% 2.12/2.36 (r(s(s(elem!1)), elem!1)),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[2673, 8915, 8913])).
% 2.12/2.36 tff(8917,plain,
% 2.12/2.36 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[4486, 8916, 3285])).
% 2.12/2.36 tff(8918,plain,
% 2.12/2.36 (~r(s(z), elem!1)),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[7152, 8917, 300, 3285, 8916])).
% 2.12/2.36 tff(8919,plain,
% 2.12/2.36 ($false),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[8918, 8910])).
% 2.12/2.36 tff(8920,plain,((~(s(s(s(s(z)))) = elem!1)) | (~r(z, elem!1)) | (~b(s(s(z)), elem!1)) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.36 tff(8921,plain,
% 2.12/2.36 (~(s(s(s(s(z)))) = elem!1)),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[8920, 14, 8892, 7108])).
% 2.12/2.36 tff(8922,plain,
% 2.12/2.36 (b(s(s(s(s(z)))), elem!1)),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[283, 8921, 12])).
% 2.12/2.36 tff(8923,plain,
% 2.12/2.36 (~(elem!1 = s(s(s(s(z)))))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[273, 8921])).
% 2.12/2.36 tff(8924,plain,
% 2.12/2.36 (s(s(s(z))) = s(s(elem!1))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[84, 909])).
% 2.12/2.36 tff(8925,plain,
% 2.12/2.36 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.12/2.36 inference(monotonicity,[status(thm)],[8924])).
% 2.12/2.36 tff(8926,plain,
% 2.12/2.36 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.12/2.36 inference(symmetry,[status(thm)],[8925])).
% 2.12/2.36 tff(8927,plain,
% 2.12/2.36 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.12/2.36 inference(monotonicity,[status(thm)],[8926])).
% 2.12/2.36 tff(8928,plain,
% 2.12/2.36 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.12/2.36 inference(symmetry,[status(thm)],[8927])).
% 2.12/2.36 tff(8929,plain,
% 2.12/2.36 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.12/2.36 inference(monotonicity,[status(thm)],[8924])).
% 2.12/2.36 tff(8930,plain,
% 2.12/2.36 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.12/2.36 inference(transitivity,[status(thm)],[8929, 8928])).
% 2.12/2.36 tff(8931,plain,
% 2.12/2.36 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(s(z)))))),
% 2.12/2.36 inference(monotonicity,[status(thm)],[8926])).
% 2.12/2.36 tff(8932,plain,
% 2.12/2.36 ((~b(elem!1, s(s(s(elem!1))))) <=> (~b(elem!1, s(s(s(s(z))))))),
% 2.12/2.36 inference(monotonicity,[status(thm)],[8931])).
% 2.12/2.36 tff(8933,plain,
% 2.12/2.36 (r(s(s(elem!1)), elem!1)),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[2671, 58, 1, 5022])).
% 2.12/2.36 tff(8934,plain,
% 2.12/2.36 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[5185, 8933, 7108, 837])).
% 2.12/2.36 tff(8935,plain,
% 2.12/2.36 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[813, 8934, 720])).
% 2.12/2.36 tff(8936,plain,
% 2.12/2.36 (b(s(elem!1), elem!1)),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[968, 93, 8892])).
% 2.12/2.36 tff(8937,plain,
% 2.12/2.36 (~(s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[862, 860])).
% 2.12/2.36 tff(8938,plain,
% 2.12/2.36 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(z)))),
% 2.12/2.36 inference(monotonicity,[status(thm)],[619])).
% 2.12/2.36 tff(8939,plain,
% 2.12/2.36 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(z)) = s(s(s(s(z)))))),
% 2.12/2.36 inference(transitivity,[status(thm)],[8938, 640])).
% 2.12/2.36 tff(8940,plain,
% 2.12/2.36 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 2.12/2.36 inference(symmetry,[status(thm)],[8939])).
% 2.12/2.36 tff(8941,plain,
% 2.12/2.36 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 2.12/2.36 inference(monotonicity,[status(thm)],[8940])).
% 2.12/2.36 tff(8942,plain,
% 2.12/2.36 (~(s(s(s(s(z)))) = s(elem!1))),
% 2.12/2.36 inference(modus_ponens,[status(thm)],[459, 8941])).
% 2.12/2.36 tff(8943,plain,
% 2.12/2.36 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(elem!1))),
% 2.12/2.36 inference(monotonicity,[status(thm)],[4874])).
% 2.12/2.36 tff(8944,plain,
% 2.12/2.36 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(elem!1))),
% 2.12/2.36 inference(symmetry,[status(thm)],[8943])).
% 2.12/2.36 tff(8945,plain,
% 2.12/2.36 ((~(s(s(s(s(z)))) = s(elem!1))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 2.12/2.36 inference(monotonicity,[status(thm)],[8944])).
% 2.12/2.36 tff(8946,assumption,(~(s(s(s(s(z)))) = s(elem!1))), introduced(assumption)).
% 2.12/2.36 tff(8947,plain,
% 2.12/2.36 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.12/2.36 inference(modus_ponens,[status(thm)],[8946, 8945])).
% 2.12/2.36 tff(8948,plain,
% 2.12/2.36 (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[3079, 75, 1168, 706, 922])).
% 2.12/2.36 tff(8949,plain,
% 2.12/2.36 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[3083, 58, 868, 8948])).
% 2.12/2.36 tff(8950,plain,
% 2.12/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.36 inference(rewrite,[status(thm)],[])).
% 2.12/2.36 tff(8951,plain,
% 2.12/2.36 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~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(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.36 inference(rewrite,[status(thm)],[])).
% 2.12/2.36 tff(8952,plain,
% 2.12/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 2.12/2.36 inference(monotonicity,[status(thm)],[8951])).
% 2.12/2.36 tff(8953,plain,
% 2.12/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.36 inference(transitivity,[status(thm)],[8952, 8950])).
% 2.12/2.36 tff(8954,plain,
% 2.12/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.36 inference(quant_inst,[status(thm)],[])).
% 2.12/2.36 tff(8955,plain,
% 2.12/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 2.12/2.36 inference(modus_ponens,[status(thm)],[8954, 8953])).
% 2.12/2.36 tff(8956,plain,
% 2.12/2.36 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[8955, 75, 1168, 921, 706, 922])).
% 2.12/2.36 tff(8957,plain,
% 2.12/2.36 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[793, 58, 790, 8956])).
% 2.12/2.36 tff(8958,plain,
% 2.12/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.36 inference(rewrite,[status(thm)],[])).
% 2.12/2.36 tff(8959,plain,
% 2.12/2.36 (((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.36 inference(rewrite,[status(thm)],[])).
% 2.12/2.36 tff(8960,plain,
% 2.12/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(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(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))))),
% 2.12/2.36 inference(monotonicity,[status(thm)],[8959])).
% 2.12/2.36 tff(8961,plain,
% 2.12/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(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(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 2.12/2.36 inference(transitivity,[status(thm)],[8960, 8958])).
% 2.12/2.36 tff(8962,plain,
% 2.12/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 2.12/2.36 inference(quant_inst,[status(thm)],[])).
% 2.12/2.36 tff(8963,plain,
% 2.12/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))),
% 2.12/2.36 inference(modus_ponens,[status(thm)],[8962, 8961])).
% 2.12/2.36 tff(8964,plain,
% 2.12/2.36 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[8963, 37, 8957, 8949])).
% 2.12/2.36 tff(8965,plain,
% 2.12/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), 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(X1, 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), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.12/2.36 inference(rewrite,[status(thm)],[])).
% 2.12/2.36 tff(8966,plain,
% 2.12/2.36 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.12/2.36 inference(rewrite,[status(thm)],[])).
% 2.12/2.36 tff(8967,plain,
% 2.12/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))))),
% 2.12/2.36 inference(monotonicity,[status(thm)],[8966])).
% 2.12/2.36 tff(8968,plain,
% 2.12/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.12/2.37 inference(transitivity,[status(thm)],[8967, 8965])).
% 2.12/2.37 tff(8969,plain,
% 2.12/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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))))),
% 2.12/2.37 inference(quant_inst,[status(thm)],[])).
% 2.12/2.37 tff(8970,plain,
% 2.12/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))),
% 2.12/2.37 inference(modus_ponens,[status(thm)],[8969, 8968])).
% 2.12/2.37 tff(8971,plain,
% 2.12/2.37 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[8970, 75, 921, 706, 922])).
% 2.12/2.37 tff(8972,plain,
% 2.12/2.37 ((s(s(s(elem!1))) = s(elem!1)) | r(s(s(s(elem!1))), s(elem!1))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[655, 58, 8971])).
% 2.12/2.37 tff(8973,plain,
% 2.12/2.37 ($false),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[8972, 8964, 8947])).
% 2.12/2.37 tff(8974,plain,((~b(elem!1, s(s(s(elem!1))))) | (s(s(s(s(z)))) = s(elem!1)) | (~(s(s(s(z))) = s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.37 tff(8975,plain,
% 2.12/2.37 (~b(elem!1, s(s(s(elem!1))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[8974, 8942, 8924, 8937, 737, 8936, 3061, 8935])).
% 2.12/2.37 tff(8976,plain,
% 2.12/2.37 (~b(elem!1, s(s(s(s(z)))))),
% 2.12/2.37 inference(modus_ponens,[status(thm)],[8975, 8932])).
% 2.12/2.37 tff(8977,plain,
% 2.12/2.37 (r(elem!1, s(s(s(s(z)))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[278, 8976, 860])).
% 2.12/2.37 tff(8978,plain,
% 2.12/2.37 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(z))),
% 2.12/2.37 inference(symmetry,[status(thm)],[904])).
% 2.12/2.37 tff(8979,plain,
% 2.12/2.37 ((~b(s(s(elem!1)), elem!1)) <=> (~b(s(s(elem!1)), s(z)))),
% 2.12/2.37 inference(monotonicity,[status(thm)],[8978])).
% 2.12/2.37 tff(8980,plain,
% 2.12/2.37 (~b(s(s(elem!1)), s(z))),
% 2.12/2.37 inference(modus_ponens,[status(thm)],[1, 8979])).
% 2.12/2.37 tff(8981,plain,
% 2.12/2.37 (r(s(s(elem!1)), s(z))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[561, 8980])).
% 2.12/2.37 tff(8982,plain,
% 2.12/2.37 (r(z, s(z))),
% 2.12/2.37 inference(modus_ponens,[status(thm)],[7108, 907])).
% 2.12/2.37 tff(8983,plain,
% 2.12/2.37 (~r(s(s(elem!1)), z)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[6190, 8982, 8981])).
% 2.12/2.37 tff(8984,plain,
% 2.12/2.37 (b(s(s(elem!1)), z)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[2696, 8983])).
% 2.12/2.37 tff(8985,plain,
% 2.12/2.37 (~r(z, s(s(elem!1)))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[7137, 37, 7108, 8933])).
% 2.12/2.37 tff(8986,plain,
% 2.12/2.37 (b(z, s(s(elem!1)))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[6314, 8985])).
% 2.12/2.37 tff(8987,plain,
% 2.12/2.37 (~(s(s(elem!1)) = s(s(z)))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[4866, 8924])).
% 2.12/2.37 tff(8988,plain,
% 2.12/2.37 (~(z = elem!1)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[293, 8987])).
% 2.12/2.37 tff(8989,plain,
% 2.12/2.37 (~(elem!1 = z)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[304, 8988])).
% 2.12/2.37 tff(8990,plain,
% 2.12/2.37 (b(elem!1, s(s(s(s(z))))) <=> b(s(z), s(s(s(s(z)))))),
% 2.12/2.37 inference(symmetry,[status(thm)],[917])).
% 2.12/2.37 tff(8991,plain,
% 2.12/2.37 (b(elem!1, s(s(s(elem!1)))) <=> b(s(z), s(s(s(s(z)))))),
% 2.12/2.37 inference(transitivity,[status(thm)],[8931, 8990])).
% 2.12/2.37 tff(8992,plain,
% 2.12/2.37 ((~b(elem!1, s(s(s(elem!1))))) <=> (~b(s(z), s(s(s(s(z))))))),
% 2.12/2.37 inference(monotonicity,[status(thm)],[8991])).
% 2.12/2.37 tff(8993,plain,
% 2.12/2.37 (~b(s(z), s(s(s(s(z)))))),
% 2.12/2.37 inference(modus_ponens,[status(thm)],[8975, 8992])).
% 2.12/2.37 tff(8994,plain,
% 2.12/2.37 (r(s(z), s(s(s(s(z)))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[489, 8993])).
% 2.12/2.37 tff(8995,plain,
% 2.12/2.37 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[5219, 8994, 12, 8892, 93, 8987])).
% 2.12/2.37 tff(8996,plain,
% 2.12/2.37 (b(s(s(z)), s(s(s(s(z)))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[465, 8995])).
% 2.12/2.37 tff(8997,plain,
% 2.12/2.37 (~b(elem!1, s(s(z)))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[2255, 8996, 8892, 287])).
% 2.12/2.37 tff(8998,plain,
% 2.12/2.37 (~b(s(z), s(s(z)))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[5418, 8997, 93])).
% 2.12/2.37 tff(8999,plain,
% 2.12/2.37 (r(s(z), s(s(z)))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[416, 8998])).
% 2.12/2.37 tff(9000,plain,
% 2.12/2.37 (r(elem!1, s(s(z)))),
% 2.12/2.37 inference(modus_ponens,[status(thm)],[1997, 4991])).
% 2.12/2.37 tff(9001,assumption,(~r(elem!1, s(s(z)))), introduced(assumption)).
% 2.12/2.37 tff(9002,plain,
% 2.12/2.37 ($false),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[9001, 9000])).
% 2.12/2.37 tff(9003,plain,((~r(s(z), s(s(z)))) | r(elem!1, s(s(z))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.37 tff(9004,plain,
% 2.12/2.37 (r(elem!1, s(s(z)))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[9003, 8999, 93])).
% 2.12/2.37 tff(9005,plain,
% 2.12/2.37 (r(s(z), s(elem!1)) <=> r(elem!1, s(elem!1))),
% 2.12/2.37 inference(monotonicity,[status(thm)],[93])).
% 2.12/2.37 tff(9006,plain,
% 2.12/2.37 (r(elem!1, s(elem!1)) <=> r(s(z), s(elem!1))),
% 2.12/2.37 inference(symmetry,[status(thm)],[9005])).
% 2.12/2.37 tff(9007,plain,
% 2.12/2.37 (r(s(z), s(s(z))) <=> r(s(z), s(elem!1))),
% 2.12/2.37 inference(transitivity,[status(thm)],[4991, 4993, 9006])).
% 2.12/2.37 tff(9008,plain,
% 2.12/2.37 (r(s(z), s(elem!1))),
% 2.12/2.37 inference(modus_ponens,[status(thm)],[8999, 9007])).
% 2.12/2.37 tff(9009,plain,
% 2.12/2.37 (~r(z, s(s(z)))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[2005, 8999, 8982])).
% 2.12/2.37 tff(9010,plain,
% 2.12/2.37 (b(z, s(s(z)))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[351, 9009])).
% 2.12/2.37 tff(9011,plain,
% 2.12/2.37 (r(s(z), s(s(z))) <=> r(elem!1, s(elem!1))),
% 2.12/2.37 inference(transitivity,[status(thm)],[4991, 4993])).
% 2.12/2.37 tff(9012,plain,
% 2.12/2.37 (r(elem!1, s(elem!1))),
% 2.12/2.37 inference(modus_ponens,[status(thm)],[8999, 9011])).
% 2.12/2.37 tff(9013,plain,
% 2.12/2.37 (~(s(elem!1) = s(s(elem!1)))),
% 2.12/2.37 inference(modus_ponens,[status(thm)],[8987, 5028])).
% 2.12/2.37 tff(9014,assumption,(s(s(elem!1)) = s(elem!1)), introduced(assumption)).
% 2.12/2.37 tff(9015,plain,
% 2.12/2.37 (s(elem!1) = s(s(elem!1))),
% 2.12/2.37 inference(symmetry,[status(thm)],[9014])).
% 2.12/2.37 tff(9016,plain,
% 2.12/2.37 ($false),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[1845, 9015])).
% 2.12/2.37 tff(9017,plain,((~(s(s(elem!1)) = s(elem!1))) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.37 tff(9018,plain,
% 2.12/2.37 (~(s(s(elem!1)) = s(elem!1))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[9017, 9013])).
% 2.12/2.37 tff(9019,plain,
% 2.12/2.37 (~r(s(s(z)), z)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[4401, 155, 1489])).
% 2.12/2.37 tff(9020,plain,
% 2.12/2.37 (b(s(s(z)), z)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[202, 9019])).
% 2.12/2.37 tff(9021,plain,
% 2.12/2.37 (r(s(z), z) <=> r(elem!1, z)),
% 2.12/2.37 inference(monotonicity,[status(thm)],[93])).
% 2.12/2.37 tff(9022,plain,
% 2.12/2.37 (r(elem!1, z) <=> r(s(z), z)),
% 2.12/2.37 inference(symmetry,[status(thm)],[9021])).
% 2.12/2.37 tff(9023,plain,
% 2.12/2.37 (r(s(z), z)),
% 2.12/2.37 inference(modus_ponens,[status(thm)],[155, 9022])).
% 2.12/2.37 tff(9024,plain,
% 2.12/2.37 (~r(s(elem!1), z)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[1761, 9023, 1753])).
% 2.12/2.37 tff(9025,plain,
% 2.12/2.37 (b(s(elem!1), z)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[766, 9024])).
% 2.12/2.37 tff(9026,plain,
% 2.12/2.37 (~b(s(s(elem!1)), s(elem!1))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[6654, 9025, 370, 9020, 1892])).
% 2.12/2.37 tff(9027,assumption,(~(s(s(elem!1)) = s(elem!1))), introduced(assumption)).
% 2.12/2.37 tff(9028,assumption,(~r(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 2.12/2.37 tff(9029,plain,
% 2.12/2.37 (((~![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)))),
% 2.12/2.37 inference(rewrite,[status(thm)],[])).
% 2.12/2.37 tff(9030,plain,
% 2.12/2.37 ((~![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)))),
% 2.12/2.37 inference(quant_inst,[status(thm)],[])).
% 2.12/2.37 tff(9031,plain,
% 2.12/2.37 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1))),
% 2.12/2.37 inference(modus_ponens,[status(thm)],[9030, 9029])).
% 2.12/2.37 tff(9032,plain,
% 2.12/2.37 ($false),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[9031, 58, 1863, 9028, 9027])).
% 2.12/2.37 tff(9033,plain,(r(s(s(elem!1)), s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | (s(s(elem!1)) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.37 tff(9034,plain,
% 2.12/2.37 (r(s(s(elem!1)), s(elem!1))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[9033, 9026, 9018])).
% 2.12/2.37 tff(9035,plain,
% 2.12/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.12/2.37 inference(rewrite,[status(thm)],[])).
% 2.12/2.37 tff(9036,plain,
% 2.12/2.37 (((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.12/2.37 inference(rewrite,[status(thm)],[])).
% 2.12/2.37 tff(9037,plain,
% 2.12/2.37 (((~![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, 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(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))))),
% 2.12/2.37 inference(monotonicity,[status(thm)],[9036])).
% 2.12/2.37 tff(9038,plain,
% 2.12/2.37 (((~![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, 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(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.12/2.37 inference(transitivity,[status(thm)],[9037, 9035])).
% 2.12/2.37 tff(9039,plain,
% 2.12/2.37 ((~![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, z)) | (~r(s(s(elem!1)), elem!1)))),
% 2.12/2.37 inference(quant_inst,[status(thm)],[])).
% 2.12/2.37 tff(9040,plain,
% 2.12/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))),
% 2.12/2.37 inference(modus_ponens,[status(thm)],[9039, 9038])).
% 2.12/2.37 tff(9041,plain,
% 2.12/2.37 ($false),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[9040, 37, 155, 8485, 2647, 9034])).
% 2.12/2.37 tff(9042,plain,((~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~r(s(z), s(elem!1))) | (~(s(z) = elem!1)) | (~r(elem!1, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.37 tff(9043,plain,
% 2.12/2.37 (~r(elem!1, z)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[9042, 9012, 8933, 9010, 8984, 9008, 93, 9004])).
% 2.12/2.37 tff(9044,plain,
% 2.12/2.37 (b(elem!1, z)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[387, 9043, 8989])).
% 2.12/2.37 tff(9045,plain,
% 2.12/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)))),
% 2.12/2.37 inference(rewrite,[status(thm)],[])).
% 2.12/2.37 tff(9046,plain,
% 2.12/2.37 (((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)))),
% 2.12/2.37 inference(rewrite,[status(thm)],[])).
% 2.12/2.37 tff(9047,plain,
% 2.12/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, z)) | (~b(z, s(s(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(X1, 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)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z))))),
% 2.12/2.37 inference(monotonicity,[status(thm)],[9046])).
% 2.12/2.37 tff(9048,plain,
% 2.12/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, z)) | (~b(z, s(s(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(X1, 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)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)))),
% 2.12/2.37 inference(transitivity,[status(thm)],[9047, 9045])).
% 2.12/2.37 tff(9049,plain,
% 2.12/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))))),
% 2.12/2.37 inference(quant_inst,[status(thm)],[])).
% 2.12/2.37 tff(9050,plain,
% 2.12/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), z)) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z))),
% 2.12/2.37 inference(modus_ponens,[status(thm)],[9049, 9048])).
% 2.12/2.37 tff(9051,plain,
% 2.12/2.37 (~b(elem!1, s(s(elem!1)))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[9050, 75, 9044, 8986, 8984])).
% 2.12/2.37 tff(9052,plain,
% 2.12/2.37 (r(elem!1, s(s(elem!1)))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[1617, 9051, 5031])).
% 2.12/2.37 tff(9053,plain,
% 2.12/2.37 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[5049, 9052, 93, 8977])).
% 2.12/2.37 tff(9054,plain,
% 2.12/2.37 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[2898, 9053])).
% 2.12/2.37 tff(9055,plain,
% 2.12/2.37 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.12/2.37 inference(modus_ponens,[status(thm)],[9054, 8930])).
% 2.12/2.37 tff(9056,plain,
% 2.12/2.37 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.12/2.37 inference(monotonicity,[status(thm)],[8925])).
% 2.12/2.37 tff(9057,plain,
% 2.12/2.37 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[1655, 8994, 8981])).
% 2.12/2.37 tff(9058,plain,
% 2.12/2.37 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[1660, 9057, 1011])).
% 2.12/2.37 tff(9059,plain,
% 2.12/2.37 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.12/2.37 inference(modus_ponens,[status(thm)],[9058, 9056])).
% 2.12/2.37 tff(9060,plain,
% 2.12/2.37 (b(s(elem!1), s(s(s(elem!1))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[5375, 8996, 8924])).
% 2.12/2.37 tff(9061,plain,
% 2.12/2.37 (~r(s(s(elem!1)), s(s(z)))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[1498, 9052, 9004])).
% 2.12/2.37 tff(9062,plain,
% 2.12/2.37 (b(s(s(elem!1)), s(elem!1))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[4966, 9061, 909])).
% 2.12/2.37 tff(9063,plain,
% 2.12/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.12/2.37 inference(rewrite,[status(thm)],[])).
% 2.12/2.37 tff(9064,plain,
% 2.12/2.37 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.12/2.37 inference(rewrite,[status(thm)],[])).
% 2.12/2.37 tff(9065,plain,
% 2.12/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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))))) | (~b(s(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(X1, 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(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 2.12/2.37 inference(monotonicity,[status(thm)],[9064])).
% 2.12/2.37 tff(9066,plain,
% 2.12/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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))))) | (~b(s(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(X1, 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(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.12/2.37 inference(transitivity,[status(thm)],[9065, 9063])).
% 2.12/2.37 tff(9067,plain,
% 2.12/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.12/2.37 inference(quant_inst,[status(thm)],[])).
% 2.12/2.37 tff(9068,plain,
% 2.12/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 2.12/2.37 inference(modus_ponens,[status(thm)],[9067, 9066])).
% 2.12/2.37 tff(9069,plain,
% 2.12/2.37 ($false),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[9068, 75, 9062, 9060, 9059, 9055])).
% 2.12/2.37 tff(9070,plain,((~(s(z) = elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (s(s(elem!1)) = s(s(s(s(z))))) | r(s(s(s(s(z)))), elem!1) | (elem!1 = s(s(s(s(z))))) | b(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.12/2.37 tff(9071,plain,
% 2.12/2.37 (~(s(z) = elem!1)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[9070, 1, 1011, 12, 8923, 8922])).
% 2.12/2.37 tff(9072,plain,
% 2.12/2.37 (~r(s(s(s(z))), elem!1)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[1362, 3745, 300])).
% 2.12/2.37 tff(9073,plain,
% 2.12/2.37 (~(s(s(s(s(z)))) = elem!1)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[8920, 14, 964, 300])).
% 2.12/2.37 tff(9074,plain,
% 2.12/2.37 (~(elem!1 = s(s(s(s(z)))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[273, 9073])).
% 2.12/2.37 tff(9075,plain,
% 2.12/2.37 (~r(elem!1, s(s(s(s(z)))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[8127, 113, 300])).
% 2.12/2.37 tff(9076,plain,
% 2.12/2.37 (b(elem!1, s(s(s(s(z)))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[278, 9075, 9074])).
% 2.12/2.37 tff(9077,plain,
% 2.12/2.37 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[4818, 75, 964, 286, 287])).
% 2.12/2.37 tff(9078,plain,
% 2.12/2.37 (r(s(s(z)), s(s(s(s(z)))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[465, 9077])).
% 2.12/2.37 tff(9079,plain,
% 2.12/2.37 (b(s(s(z)), s(s(elem!1)))),
% 2.12/2.37 inference(modus_ponens,[status(thm)],[964, 2222])).
% 2.12/2.37 tff(9080,plain,
% 2.12/2.37 (b(s(s(s(z))), elem!1)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[1115, 2267, 1710])).
% 2.12/2.37 tff(9081,plain,
% 2.12/2.37 (b(s(s(s(z))), s(s(elem!1)))),
% 2.12/2.37 inference(modus_ponens,[status(thm)],[9080, 2266])).
% 2.12/2.37 tff(9082,plain,
% 2.12/2.37 (~b(s(s(z)), s(s(s(z))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[2340, 75, 2269, 9081, 9079, 2221])).
% 2.12/2.37 tff(9083,plain,
% 2.12/2.37 (r(s(s(z)), s(s(s(z))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[8252, 9082])).
% 2.12/2.37 tff(9084,plain,
% 2.12/2.37 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[2348, 75, 2269, 9081, 2221])).
% 2.12/2.37 tff(9085,plain,
% 2.12/2.37 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[575, 9084])).
% 2.12/2.37 tff(9086,plain,
% 2.12/2.37 ($false),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[8352, 9085, 9083, 9078])).
% 2.12/2.37 tff(9087,plain,((~(elem!1 = s(s(elem!1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.12/2.37 tff(9088,plain,
% 2.12/2.37 (~(elem!1 = s(s(elem!1)))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[9087, 9076, 287, 964, 9072])).
% 2.12/2.37 tff(9089,plain,
% 2.12/2.37 (~(s(s(elem!1)) = elem!1)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[2555, 9088])).
% 2.12/2.37 tff(9090,plain,
% 2.12/2.37 (r(s(s(elem!1)), elem!1)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[2673, 9089, 1])).
% 2.12/2.37 tff(9091,plain,
% 2.12/2.37 (~r(s(z), s(s(elem!1)))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[3753, 9090, 3745])).
% 2.12/2.37 tff(9092,plain,
% 2.12/2.37 (b(s(z), s(s(elem!1)))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[1890, 9091])).
% 2.12/2.37 tff(9093,plain,
% 2.12/2.37 (~r(z, s(z))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[1358, 3745, 300])).
% 2.12/2.37 tff(9094,plain,
% 2.12/2.37 (b(z, s(z))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[187, 9093])).
% 2.12/2.37 tff(9095,plain,
% 2.12/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 2.12/2.37 inference(rewrite,[status(thm)],[])).
% 2.12/2.37 tff(9096,plain,
% 2.12/2.37 (((~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)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 2.12/2.37 inference(rewrite,[status(thm)],[])).
% 2.12/2.37 tff(9097,plain,
% 2.12/2.37 (((~![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)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1))))),
% 2.12/2.37 inference(monotonicity,[status(thm)],[9096])).
% 2.12/2.37 tff(9098,plain,
% 2.12/2.37 (((~![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)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 2.12/2.37 inference(transitivity,[status(thm)],[9097, 9095])).
% 2.12/2.37 tff(9099,plain,
% 2.12/2.37 ((~![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)))),
% 2.12/2.37 inference(quant_inst,[status(thm)],[])).
% 2.12/2.37 tff(9100,plain,
% 2.12/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1))),
% 2.12/2.37 inference(modus_ponens,[status(thm)],[9099, 9098])).
% 2.12/2.38 tff(9101,plain,
% 2.12/2.38 ($false),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[9100, 37, 494, 114, 2647])).
% 2.12/2.38 tff(9102,plain,((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.38 tff(9103,plain,
% 2.12/2.38 (~r(s(s(elem!1)), s(z))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[9102, 9090, 113])).
% 2.12/2.38 tff(9104,plain,
% 2.12/2.38 (b(s(s(elem!1)), s(z))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[561, 9103])).
% 2.12/2.38 tff(9105,plain,
% 2.12/2.38 (~b(z, s(s(elem!1)))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[7150, 75, 9104, 9094, 9092])).
% 2.12/2.38 tff(9106,plain,
% 2.12/2.38 (r(z, s(s(elem!1)))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[6314, 9105])).
% 2.12/2.38 tff(9107,plain,
% 2.12/2.38 ($false),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[7137, 37, 300, 9106, 9090])).
% 2.12/2.38 tff(9108,plain,((s(z) = elem!1) | (~r(z, elem!1)) | b(s(s(elem!1)), elem!1) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | b(elem!1, s(z)) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.12/2.38 tff(9109,plain,
% 2.12/2.38 (b(s(z), elem!1)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[9108, 9071, 1, 8922, 8892, 14, 7108])).
% 2.12/2.38 tff(9110,plain,
% 2.12/2.38 (~(elem!1 = s(z))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[111, 9071])).
% 2.12/2.38 tff(9111,plain,
% 2.12/2.38 (r(elem!1, s(z))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[89, 9110, 14])).
% 2.12/2.38 tff(9112,plain,
% 2.12/2.38 (~r(elem!1, s(s(s(s(z)))))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[8127, 9111, 7108])).
% 2.12/2.38 tff(9113,plain,
% 2.12/2.38 (b(elem!1, s(s(s(s(z)))))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[278, 9112, 8923])).
% 2.12/2.38 tff(9114,plain,
% 2.12/2.38 (~b(s(z), s(s(s(s(z)))))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[586, 9113, 8922, 9109])).
% 2.12/2.38 tff(9115,plain,
% 2.12/2.38 (r(s(z), s(s(s(s(z)))))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[489, 9114])).
% 2.12/2.38 tff(9116,plain,
% 2.12/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)))),
% 2.12/2.38 inference(rewrite,[status(thm)],[])).
% 2.12/2.38 tff(9117,plain,
% 2.12/2.38 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z)))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)))),
% 2.12/2.38 inference(rewrite,[status(thm)],[])).
% 2.12/2.38 tff(9118,plain,
% 2.12/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(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(X1, 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(z)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1))))),
% 2.12/2.38 inference(monotonicity,[status(thm)],[9117])).
% 2.12/2.38 tff(9119,plain,
% 2.12/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(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(X1, 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(z)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)))),
% 2.12/2.38 inference(transitivity,[status(thm)],[9118, 9116])).
% 2.12/2.38 tff(9120,plain,
% 2.12/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))),
% 2.12/2.38 inference(quant_inst,[status(thm)],[])).
% 2.12/2.38 tff(9121,plain,
% 2.12/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1))),
% 2.12/2.38 inference(modus_ponens,[status(thm)],[9120, 9119])).
% 2.12/2.38 tff(9122,plain,
% 2.12/2.38 (~b(s(s(z)), s(z))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[9121, 75, 9109, 8892, 9113, 8922])).
% 2.12/2.38 tff(9123,plain,
% 2.12/2.38 (r(s(s(z)), s(z))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[153, 9122])).
% 2.12/2.38 tff(9124,plain,
% 2.12/2.38 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[4818, 75, 8892, 9113, 8922])).
% 2.12/2.38 tff(9125,plain,
% 2.12/2.38 (r(s(s(z)), s(s(s(s(z)))))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[465, 9124])).
% 2.12/2.38 tff(9126,plain,
% 2.12/2.38 ($false),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[476, 9125, 9123, 9115])).
% 2.12/2.38 tff(9127,plain,(b(s(s(elem!1)), elem!1) | b(elem!1, s(z)) | (s(s(elem!1)) = s(s(s(s(z))))) | r(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.12/2.38 tff(9128,plain,
% 2.12/2.38 (b(s(s(elem!1)), elem!1)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[9127, 1011, 14, 12])).
% 2.12/2.38 tff(9129,plain,
% 2.12/2.38 (~r(elem!1, s(s(s(s(z)))))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[8127, 113, 7108])).
% 2.12/2.38 tff(9130,plain,
% 2.12/2.38 (b(elem!1, s(s(s(s(z)))))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[278, 9129, 8923])).
% 2.12/2.38 tff(9131,plain,
% 2.12/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.12/2.38 inference(rewrite,[status(thm)],[])).
% 2.12/2.38 tff(9132,plain,
% 2.12/2.38 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(z))))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.12/2.38 inference(rewrite,[status(thm)],[])).
% 2.12/2.38 tff(9133,plain,
% 2.12/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1))))),
% 2.12/2.38 inference(monotonicity,[status(thm)],[9132])).
% 2.12/2.38 tff(9134,plain,
% 2.12/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.12/2.38 inference(transitivity,[status(thm)],[9133, 9131])).
% 2.12/2.38 tff(9135,plain,
% 2.12/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.12/2.38 inference(quant_inst,[status(thm)],[])).
% 2.12/2.38 tff(9136,plain,
% 2.12/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1))),
% 2.12/2.38 inference(modus_ponens,[status(thm)],[9135, 9134])).
% 2.12/2.38 tff(9137,plain,
% 2.12/2.38 (~b(s(s(elem!1)), s(s(z)))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[9136, 75, 8892, 9130, 8922, 9128])).
% 2.12/2.38 tff(9138,plain,
% 2.12/2.38 (r(s(s(elem!1)), s(s(z)))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[1476, 9137, 8901])).
% 2.12/2.38 tff(9139,plain,
% 2.12/2.38 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[4818, 75, 8892, 9130, 8922])).
% 2.12/2.38 tff(9140,plain,
% 2.12/2.38 (r(s(s(z)), s(s(s(s(z)))))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[465, 9139])).
% 2.12/2.38 tff(9141,plain,
% 2.12/2.38 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[4155, 75, 9130, 8922, 9128])).
% 2.12/2.38 tff(9142,plain,
% 2.12/2.38 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[1660, 9141, 1011])).
% 2.12/2.38 tff(9143,plain,
% 2.12/2.38 (((~![X0: $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(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.12/2.38 inference(rewrite,[status(thm)],[])).
% 2.12/2.38 tff(9144,plain,
% 2.12/2.38 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.12/2.38 inference(rewrite,[status(thm)],[])).
% 2.12/2.38 tff(9145,plain,
% 2.12/2.38 (((~![X0: $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(elem!1)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(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(z)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(z))))))))),
% 2.12/2.38 inference(monotonicity,[status(thm)],[9144])).
% 2.12/2.38 tff(9146,plain,
% 2.12/2.38 (((~![X0: $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(elem!1)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(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(z)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.12/2.38 inference(transitivity,[status(thm)],[9145, 9143])).
% 2.12/2.38 tff(9147,plain,
% 2.12/2.38 ((~![X0: $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(elem!1)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.12/2.38 inference(quant_inst,[status(thm)],[])).
% 2.12/2.38 tff(9148,plain,
% 2.12/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(z))))))),
% 2.12/2.38 inference(modus_ponens,[status(thm)],[9147, 9146])).
% 2.12/2.38 tff(9149,plain,
% 2.12/2.38 ($false),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[9148, 37, 9142, 9140, 9138])).
% 2.12/2.38 tff(9150,plain,((s(z) = elem!1) | (s(s(elem!1)) = s(s(s(s(z))))) | r(s(s(s(s(z)))), elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.38 tff(9151,plain,
% 2.12/2.38 (s(z) = elem!1),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[9150, 1011, 12, 14])).
% 2.12/2.38 tff(9152,plain,
% 2.12/2.38 (elem!1 = s(z)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[97, 9151])).
% 2.12/2.38 tff(9153,plain,
% 2.12/2.38 (s(s(s(z))) = s(s(elem!1))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[84, 9152])).
% 2.12/2.38 tff(9154,plain,
% 2.12/2.38 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(z)), s(s(elem!1)))),
% 2.12/2.38 inference(monotonicity,[status(thm)],[9153])).
% 2.12/2.38 tff(9155,plain,
% 2.12/2.38 (b(s(s(z)), s(s(elem!1))) <=> b(s(s(z)), s(s(s(z))))),
% 2.12/2.38 inference(symmetry,[status(thm)],[9154])).
% 2.12/2.38 tff(9156,plain,
% 2.12/2.38 (s(s(z)) = s(elem!1)),
% 2.12/2.38 inference(monotonicity,[status(thm)],[9151])).
% 2.12/2.38 tff(9157,plain,
% 2.12/2.38 (s(elem!1) = s(s(z))),
% 2.12/2.38 inference(symmetry,[status(thm)],[9156])).
% 2.12/2.38 tff(9158,plain,
% 2.12/2.38 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(z)), s(s(elem!1)))),
% 2.12/2.38 inference(monotonicity,[status(thm)],[9157])).
% 2.12/2.38 tff(9159,plain,
% 2.12/2.38 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(z)), s(s(s(z))))),
% 2.12/2.38 inference(transitivity,[status(thm)],[9158, 9155])).
% 2.12/2.38 tff(9160,plain,
% 2.12/2.38 ((~b(s(elem!1), s(s(elem!1)))) <=> (~b(s(s(z)), s(s(s(z)))))),
% 2.12/2.38 inference(monotonicity,[status(thm)],[9159])).
% 2.12/2.38 tff(9161,plain,
% 2.12/2.38 (b(s(s(s(elem!1))), elem!1)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[935, 9151, 8922])).
% 2.12/2.38 tff(9162,plain,
% 2.12/2.38 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.12/2.38 inference(monotonicity,[status(thm)],[9153])).
% 2.12/2.38 tff(9163,plain,
% 2.12/2.38 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.12/2.38 inference(symmetry,[status(thm)],[9162])).
% 2.12/2.38 tff(9164,plain,
% 2.12/2.38 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(s(z)))))),
% 2.12/2.38 inference(monotonicity,[status(thm)],[9163])).
% 2.12/2.38 tff(9165,plain,
% 2.12/2.38 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.12/2.38 inference(symmetry,[status(thm)],[9164])).
% 2.12/2.38 tff(9166,plain,
% 2.12/2.38 (b(s(z), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 2.12/2.38 inference(monotonicity,[status(thm)],[9151])).
% 2.12/2.38 tff(9167,plain,
% 2.12/2.38 (b(s(z), s(s(s(s(z))))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.12/2.38 inference(transitivity,[status(thm)],[9166, 9165])).
% 2.12/2.38 tff(9168,plain,
% 2.12/2.38 (~(s(s(elem!1)) = s(s(z)))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[4866, 9153])).
% 2.12/2.38 tff(9169,plain,
% 2.12/2.38 ((elem!1 = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(s(z)))))),
% 2.12/2.38 inference(monotonicity,[status(thm)],[9163])).
% 2.12/2.38 tff(9170,plain,
% 2.12/2.38 ((elem!1 = s(s(s(s(z))))) <=> (elem!1 = s(s(s(elem!1))))),
% 2.12/2.38 inference(symmetry,[status(thm)],[9169])).
% 2.12/2.38 tff(9171,plain,
% 2.12/2.38 ((~(elem!1 = s(s(s(s(z)))))) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 2.12/2.38 inference(monotonicity,[status(thm)],[9170])).
% 2.12/2.38 tff(9172,plain,
% 2.12/2.38 (~(elem!1 = s(s(s(elem!1))))),
% 2.12/2.38 inference(modus_ponens,[status(thm)],[8923, 9171])).
% 2.12/2.38 tff(9173,plain,
% 2.12/2.38 (~b(elem!1, s(s(elem!1)))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[5171, 9013, 707, 3061, 5017, 93])).
% 2.12/2.38 tff(9174,plain,
% 2.12/2.38 (r(elem!1, s(s(elem!1)))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[1617, 9173, 5031])).
% 2.12/2.38 tff(9175,plain,
% 2.12/2.38 (r(elem!1, s(s(s(s(z))))) <=> r(elem!1, s(s(s(elem!1))))),
% 2.12/2.38 inference(monotonicity,[status(thm)],[8925])).
% 2.12/2.38 tff(9176,plain,
% 2.12/2.38 (r(elem!1, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(s(z)))))),
% 2.12/2.38 inference(symmetry,[status(thm)],[9175])).
% 2.12/2.38 tff(9177,plain,
% 2.12/2.38 (b(s(elem!1), s(s(s(elem!1))))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[5375, 895, 8924])).
% 2.12/2.38 tff(9178,plain,
% 2.12/2.38 (~b(elem!1, s(s(s(elem!1))))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[960, 9177, 300, 93, 5017])).
% 2.12/2.38 tff(9179,plain,
% 2.12/2.38 (r(elem!1, s(s(s(elem!1))))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[5967, 9178, 5802])).
% 2.12/2.38 tff(9180,plain,
% 2.12/2.38 (r(elem!1, s(s(s(s(z)))))),
% 2.12/2.38 inference(modus_ponens,[status(thm)],[9179, 9176])).
% 2.12/2.38 tff(9181,plain,
% 2.12/2.38 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[5049, 9180, 93, 9174])).
% 2.12/2.38 tff(9182,plain,
% 2.12/2.38 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[2898, 9181])).
% 2.12/2.38 tff(9183,plain,
% 2.12/2.38 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.12/2.38 inference(modus_ponens,[status(thm)],[9182, 8930])).
% 2.12/2.38 tff(9184,plain,
% 2.12/2.38 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.12/2.38 inference(monotonicity,[status(thm)],[8924])).
% 2.12/2.38 tff(9185,plain,
% 2.12/2.38 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.12/2.38 inference(transitivity,[status(thm)],[9184, 9056])).
% 2.12/2.38 tff(9186,plain,
% 2.12/2.38 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 2.12/2.38 inference(monotonicity,[status(thm)],[93])).
% 2.12/2.38 tff(9187,plain,
% 2.12/2.38 (r(elem!1, s(s(s(z)))) <=> r(s(z), s(s(s(z))))),
% 2.12/2.38 inference(symmetry,[status(thm)],[9186])).
% 2.12/2.38 tff(9188,plain,
% 2.12/2.38 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 2.12/2.38 inference(monotonicity,[status(thm)],[8924])).
% 2.12/2.38 tff(9189,plain,
% 2.12/2.38 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(s(z))))),
% 2.12/2.38 inference(symmetry,[status(thm)],[9188])).
% 2.12/2.38 tff(9190,plain,
% 2.12/2.38 (r(elem!1, s(s(elem!1))) <=> r(s(z), s(s(s(z))))),
% 2.12/2.38 inference(transitivity,[status(thm)],[9189, 9187])).
% 2.12/2.38 tff(9191,plain,
% 2.12/2.38 (r(s(z), s(s(s(z))))),
% 2.12/2.38 inference(modus_ponens,[status(thm)],[9174, 9190])).
% 2.12/2.38 tff(9192,plain,
% 2.12/2.38 (r(s(z), s(s(s(s(z)))))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[7540, 895, 300, 908, 8987, 1011])).
% 2.12/2.38 tff(9193,plain,
% 2.12/2.38 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[1316, 9192, 9191])).
% 2.12/2.38 tff(9194,plain,
% 2.12/2.38 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[575, 9193])).
% 2.12/2.38 tff(9195,plain,
% 2.12/2.38 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.12/2.38 inference(modus_ponens,[status(thm)],[9194, 9185])).
% 2.12/2.38 tff(9196,plain,
% 2.12/2.38 (~b(elem!1, s(s(z)))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[2255, 895, 964, 287])).
% 2.12/2.38 tff(9197,plain,
% 2.12/2.38 (~b(s(z), s(s(z)))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[5418, 9196, 93])).
% 2.12/2.38 tff(9198,plain,
% 2.12/2.38 (r(s(z), s(s(z)))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[416, 9197])).
% 2.12/2.38 tff(9199,plain,
% 2.12/2.38 (r(elem!1, s(s(z)))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[9003, 9198, 93])).
% 2.12/2.38 tff(9200,plain,
% 2.12/2.38 (~r(s(s(elem!1)), s(s(z)))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[1498, 9199, 9174])).
% 2.12/2.38 tff(9201,plain,
% 2.12/2.38 (b(s(s(elem!1)), s(elem!1))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[4966, 9200, 909])).
% 2.12/2.38 tff(9202,plain,
% 2.12/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.12/2.38 inference(rewrite,[status(thm)],[])).
% 2.12/2.38 tff(9203,plain,
% 2.12/2.38 (((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.12/2.38 inference(rewrite,[status(thm)],[])).
% 2.12/2.38 tff(9204,plain,
% 2.12/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 2.12/2.39 inference(monotonicity,[status(thm)],[9203])).
% 2.12/2.39 tff(9205,plain,
% 2.12/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.12/2.39 inference(transitivity,[status(thm)],[9204, 9202])).
% 2.12/2.39 tff(9206,plain,
% 2.12/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.12/2.39 inference(quant_inst,[status(thm)],[])).
% 2.12/2.39 tff(9207,plain,
% 2.12/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 2.12/2.39 inference(modus_ponens,[status(thm)],[9206, 9205])).
% 2.12/2.39 tff(9208,plain,
% 2.12/2.39 ($false),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[9207, 75, 5017, 9201, 707, 9177, 9195, 9183])).
% 2.12/2.39 tff(9209,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), elem!1)) | (~(s(z) = elem!1)) | (elem!1 = s(s(s(elem!1)))) | (~r(z, elem!1)) | (s(s(elem!1)) = s(s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.39 tff(9210,plain,
% 2.12/2.39 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[9209, 9128, 9151, 9172, 7108, 1011, 8892, 8922])).
% 2.12/2.39 tff(9211,plain,
% 2.12/2.39 (r(s(s(z)), s(s(s(s(z)))))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[465, 9210])).
% 2.12/2.39 tff(9212,plain,
% 2.12/2.39 (~r(s(z), s(s(s(s(z)))))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[5219, 9211, 12, 8892, 9151, 9168])).
% 2.12/2.39 tff(9213,plain,
% 2.12/2.39 (b(s(z), s(s(s(s(z)))))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[489, 9212])).
% 2.12/2.39 tff(9214,plain,
% 2.12/2.39 (b(elem!1, s(s(s(elem!1))))),
% 2.12/2.39 inference(modus_ponens,[status(thm)],[9213, 9167])).
% 2.12/2.39 tff(9215,plain,
% 2.12/2.39 (b(s(elem!1), elem!1)),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[968, 9151, 8892])).
% 2.12/2.39 tff(9216,plain,
% 2.12/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(X1, 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))))))),
% 2.12/2.39 inference(rewrite,[status(thm)],[])).
% 2.12/2.39 tff(9217,plain,
% 2.12/2.39 (((~b(s(s(s(elem!1))), elem!1)) | (~b(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))))))),
% 2.12/2.39 inference(rewrite,[status(thm)],[])).
% 2.12/2.39 tff(9218,plain,
% 2.12/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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)))))))),
% 2.12/2.39 inference(monotonicity,[status(thm)],[9217])).
% 2.12/2.39 tff(9219,plain,
% 2.12/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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))))))),
% 2.12/2.39 inference(transitivity,[status(thm)],[9218, 9216])).
% 2.12/2.39 tff(9220,plain,
% 2.12/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))))),
% 2.12/2.39 inference(quant_inst,[status(thm)],[])).
% 2.12/2.39 tff(9221,plain,
% 2.12/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))))),
% 2.12/2.39 inference(modus_ponens,[status(thm)],[9220, 9219])).
% 2.12/2.39 tff(9222,plain,
% 2.12/2.39 (~b(s(elem!1), s(s(elem!1)))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[9221, 75, 9215, 9128, 9214, 9161])).
% 2.12/2.39 tff(9223,plain,
% 2.12/2.39 (~b(s(s(z)), s(s(s(z))))),
% 2.12/2.39 inference(modus_ponens,[status(thm)],[9222, 9160])).
% 2.12/2.39 tff(9224,plain,
% 2.12/2.39 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(z)))), elem!1)),
% 2.12/2.39 inference(monotonicity,[status(thm)],[9151])).
% 2.12/2.39 tff(9225,plain,
% 2.12/2.39 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(z))),
% 2.12/2.39 inference(symmetry,[status(thm)],[9224])).
% 2.12/2.39 tff(9226,plain,
% 2.12/2.39 (b(s(s(s(s(z)))), s(z))),
% 2.12/2.39 inference(modus_ponens,[status(thm)],[8922, 9225])).
% 2.12/2.39 tff(9227,plain,
% 2.12/2.39 (b(s(s(s(z))), s(z)) <=> b(s(s(s(z))), elem!1)),
% 2.12/2.39 inference(monotonicity,[status(thm)],[9151])).
% 2.12/2.39 tff(9228,plain,
% 2.12/2.39 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(z))),
% 2.12/2.39 inference(symmetry,[status(thm)],[9227])).
% 2.12/2.39 tff(9229,plain,
% 2.12/2.39 (b(s(s(s(z))), elem!1)),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[3645, 9152, 9128])).
% 2.12/2.39 tff(9230,plain,
% 2.12/2.39 (b(s(s(s(z))), s(z))),
% 2.12/2.39 inference(modus_ponens,[status(thm)],[9229, 9228])).
% 2.12/2.39 tff(9231,plain,
% 2.12/2.39 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[991, 9213, 9230, 9226])).
% 2.12/2.39 tff(9232,plain,
% 2.12/2.39 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[575, 9231])).
% 2.12/2.39 tff(9233,plain,
% 2.12/2.39 (~r(s(s(z)), s(s(s(z))))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[8352, 9232, 9211])).
% 2.12/2.39 tff(9234,plain,
% 2.12/2.39 (b(s(s(z)), s(s(s(z))))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[8252, 9233])).
% 2.12/2.39 tff(9235,plain,
% 2.12/2.39 ($false),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[9234, 9223])).
% 2.12/2.39 tff(9236,plain,((s(s(elem!1)) = s(s(s(s(z))))) | r(s(s(s(s(z)))), elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.39 tff(9237,plain,
% 2.12/2.39 (b(elem!1, s(z))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[9236, 8899, 12])).
% 2.12/2.39 tff(9238,plain,
% 2.12/2.39 (~(s(z) = elem!1)),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[1393, 9237])).
% 2.12/2.39 tff(9239,plain,
% 2.12/2.39 (~(z = elem!1)),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[6116, 9237, 12])).
% 2.12/2.39 tff(9240,plain,
% 2.12/2.39 (~(elem!1 = z)),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[304, 9239])).
% 2.12/2.39 tff(9241,plain,
% 2.12/2.39 (~(s(s(elem!1)) = s(s(z)))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[237, 9239])).
% 2.12/2.39 tff(9242,plain,
% 2.12/2.39 (b(z, elem!1)),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[8091, 3285, 300, 266, 2478, 353])).
% 2.12/2.39 tff(9243,plain,
% 2.12/2.39 (b(s(z), s(s(s(s(z))))) <=> b(s(z), elem!1)),
% 2.12/2.39 inference(monotonicity,[status(thm)],[3285])).
% 2.12/2.39 tff(9244,plain,
% 2.12/2.39 (b(s(z), elem!1) <=> b(s(z), s(s(s(s(z)))))),
% 2.12/2.39 inference(symmetry,[status(thm)],[9243])).
% 2.12/2.39 tff(9245,plain,
% 2.12/2.39 (b(s(z), s(s(s(s(z)))))),
% 2.12/2.39 inference(modus_ponens,[status(thm)],[107, 9244])).
% 2.12/2.39 tff(9246,plain,
% 2.12/2.39 (~b(s(z), s(s(s(s(z)))))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[6164, 107, 964, 1391, 1518, 3285])).
% 2.12/2.39 tff(9247,plain,
% 2.12/2.39 ($false),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[9246, 9245])).
% 2.12/2.39 tff(9248,plain,((~b(s(z), elem!1)) | (~(s(s(s(s(z)))) = elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.39 tff(9249,plain,
% 2.12/2.39 (~b(s(z), elem!1)),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[9248, 3285, 964, 1391, 9242])).
% 2.12/2.39 tff(9250,plain,
% 2.12/2.39 (r(s(z), elem!1)),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[601, 9249, 2478])).
% 2.12/2.39 tff(9251,plain,
% 2.12/2.39 (~r(z, s(z))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[1358, 9250, 300])).
% 2.12/2.39 tff(9252,plain,
% 2.12/2.39 (b(z, s(z))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[187, 9251])).
% 2.12/2.39 tff(9253,plain,
% 2.12/2.39 (~r(s(z), z)),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[7555, 9250, 300])).
% 2.12/2.39 tff(9254,plain,
% 2.12/2.39 (b(s(z), z)),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[169, 9253])).
% 2.12/2.39 tff(9255,plain,
% 2.12/2.39 ($false),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[2596, 9254, 9252, 1391, 9242])).
% 2.12/2.39 tff(9256,plain,((~(s(s(s(s(z)))) = elem!1)) | (~b(elem!1, s(z))) | (~r(z, elem!1)) | (~b(s(s(z)), elem!1)) | (s(s(elem!1)) = s(s(z))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 2.12/2.39 tff(9257,plain,
% 2.12/2.39 (~(s(s(s(s(z)))) = elem!1)),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[9256, 9237, 7108, 8892, 9241, 9240])).
% 2.12/2.39 tff(9258,plain,
% 2.12/2.39 (b(s(s(s(s(z)))), elem!1)),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[283, 9257, 12])).
% 2.12/2.39 tff(9259,plain,
% 2.12/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 2.12/2.39 inference(rewrite,[status(thm)],[])).
% 2.12/2.39 tff(9260,plain,
% 2.12/2.39 (((~b(s(z), elem!1)) | (~b(s(s(s(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(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 2.12/2.39 inference(rewrite,[status(thm)],[])).
% 2.12/2.39 tff(9261,plain,
% 2.12/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))))),
% 2.12/2.39 inference(monotonicity,[status(thm)],[9260])).
% 2.12/2.39 tff(9262,plain,
% 2.12/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 2.12/2.39 inference(transitivity,[status(thm)],[9261, 9259])).
% 2.12/2.39 tff(9263,plain,
% 2.12/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))))))),
% 2.12/2.39 inference(quant_inst,[status(thm)],[])).
% 2.12/2.39 tff(9264,plain,
% 2.12/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))),
% 2.12/2.39 inference(modus_ponens,[status(thm)],[9263, 9262])).
% 2.12/2.39 tff(9265,plain,
% 2.12/2.39 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[9264, 75, 107, 1391, 964, 287])).
% 2.12/2.39 tff(9266,plain,
% 2.12/2.39 (r(s(s(z)), s(s(s(s(z)))))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[465, 9265])).
% 2.12/2.39 tff(9267,plain,
% 2.12/2.39 ($false),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[476, 9266, 7473, 6530])).
% 2.12/2.39 tff(9268,plain,((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.39 tff(9269,plain,
% 2.12/2.39 (~b(s(z), elem!1)),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[9268, 9237, 8892, 9258])).
% 2.12/2.39 tff(9270,plain,
% 2.12/2.39 (r(s(z), elem!1)),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[601, 9269, 9238])).
% 2.12/2.39 tff(9271,plain,
% 2.12/2.39 (~r(s(s(s(z))), elem!1)),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[1362, 9270, 7108])).
% 2.12/2.39 tff(9272,plain,
% 2.12/2.39 (~r(z, s(z))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[1358, 9270, 7108])).
% 2.12/2.39 tff(9273,plain,
% 2.12/2.39 (b(z, s(z))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[187, 9272])).
% 2.12/2.39 tff(9274,plain,
% 2.12/2.39 (~r(s(z), z)),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[7555, 9270, 7108])).
% 2.12/2.39 tff(9275,plain,
% 2.12/2.39 (b(s(z), z)),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[169, 9274])).
% 2.12/2.39 tff(9276,plain,
% 2.12/2.39 (~b(s(s(z)), s(z))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[7565, 9275, 8892, 9237, 9273])).
% 2.12/2.39 tff(9277,plain,
% 2.12/2.39 (r(s(s(z)), s(z))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[153, 9276])).
% 2.12/2.39 tff(9278,plain,
% 2.12/2.39 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[8898, 964])).
% 2.12/2.39 tff(9279,plain,
% 2.12/2.39 ($false),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[7583, 75, 1958, 372, 371, 1391])).
% 2.12/2.39 tff(9280,plain,((~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.39 tff(9281,plain,
% 2.12/2.39 (~b(s(z), z)),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[9280, 1958, 372, 1391])).
% 2.12/2.39 tff(9282,plain,
% 2.12/2.39 (r(s(z), z)),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[169, 9281])).
% 2.12/2.39 tff(9283,plain,
% 2.12/2.39 (~r(s(z), elem!1)),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[7555, 9282, 300])).
% 2.12/2.39 tff(9284,plain,
% 2.12/2.39 (b(s(z), elem!1)),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[601, 9283, 108])).
% 2.12/2.39 tff(9285,plain,
% 2.12/2.39 ($false),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[2101, 75, 1958, 372, 9284, 1391])).
% 2.12/2.39 tff(9286,plain,((~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (s(z) = elem!1) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.39 tff(9287,plain,
% 2.12/2.39 (~b(elem!1, z)),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[9286, 7141, 1391, 2478, 300])).
% 2.12/2.39 tff(9288,plain,
% 2.12/2.39 (r(elem!1, z)),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[387, 9287, 353])).
% 2.12/2.39 tff(9289,plain,
% 2.12/2.39 (~r(s(s(elem!1)), z)),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[4774, 2647, 155])).
% 2.12/2.39 tff(9290,plain,
% 2.12/2.39 (b(s(s(elem!1)), z)),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[2696, 9289])).
% 2.12/2.39 tff(9291,plain,
% 2.12/2.39 (~b(s(s(elem!1)), s(z))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[4754, 9290, 372, 371])).
% 2.12/2.39 tff(9292,plain,
% 2.12/2.39 (r(s(s(elem!1)), s(z))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[561, 9291])).
% 2.12/2.39 tff(9293,plain,
% 2.12/2.39 ($false),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[5680, 37, 9292, 588, 2647])).
% 2.12/2.39 tff(9294,plain,((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.39 tff(9295,plain,
% 2.12/2.39 (~r(s(s(elem!1)), elem!1)),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[9294, 588, 7141, 8409, 9288])).
% 2.12/2.39 tff(9296,plain,
% 2.12/2.39 (s(s(elem!1)) = elem!1),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[2673, 9295, 1])).
% 2.12/2.39 tff(9297,plain,
% 2.12/2.39 (elem!1 = s(s(elem!1))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[2555, 9296])).
% 2.12/2.39 tff(9298,plain,
% 2.12/2.39 (~b(elem!1, s(s(s(s(z)))))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[9087, 9297, 287, 964, 2495])).
% 2.12/2.39 tff(9299,plain,
% 2.12/2.39 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[7600, 9297, 9298])).
% 2.12/2.39 tff(9300,plain,
% 2.12/2.39 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[1660, 9299, 9278])).
% 2.12/2.39 tff(9301,plain,
% 2.12/2.39 ((s(s(s(z))) = elem!1) <=> (s(s(s(z))) = s(s(elem!1)))),
% 2.12/2.39 inference(monotonicity,[status(thm)],[9297])).
% 2.12/2.39 tff(9302,plain,
% 2.12/2.39 ((s(s(s(z))) = elem!1) <=> (s(s(elem!1)) = s(s(s(z))))),
% 2.12/2.39 inference(transitivity,[status(thm)],[9301, 1909])).
% 2.12/2.39 tff(9303,plain,
% 2.12/2.39 ((~(s(s(s(z))) = elem!1)) <=> (~(s(s(elem!1)) = s(s(s(z)))))),
% 2.12/2.39 inference(monotonicity,[status(thm)],[9302])).
% 2.12/2.39 tff(9304,plain,
% 2.12/2.39 (~(s(s(s(z))) = elem!1)),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[1612, 9297])).
% 2.12/2.39 tff(9305,plain,
% 2.12/2.39 (~(s(s(elem!1)) = s(s(s(z))))),
% 2.12/2.39 inference(modus_ponens,[status(thm)],[9304, 9303])).
% 2.12/2.39 tff(9306,plain,
% 2.12/2.39 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(elem!1)))),
% 2.12/2.39 inference(monotonicity,[status(thm)],[9297])).
% 2.12/2.39 tff(9307,plain,
% 2.12/2.39 (b(s(s(s(z))), elem!1)),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[1115, 9304, 2495])).
% 2.12/2.39 tff(9308,plain,
% 2.12/2.39 (b(s(s(s(z))), s(s(elem!1)))),
% 2.12/2.39 inference(modus_ponens,[status(thm)],[9307, 9306])).
% 2.12/2.39 tff(9309,plain,
% 2.12/2.39 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.12/2.39 inference(monotonicity,[status(thm)],[9297])).
% 2.12/2.39 tff(9310,plain,
% 2.12/2.39 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.12/2.39 inference(modus_ponens,[status(thm)],[287, 9309])).
% 2.12/2.39 tff(9311,plain,
% 2.12/2.39 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(elem!1)))),
% 2.12/2.39 inference(monotonicity,[status(thm)],[9297])).
% 2.12/2.39 tff(9312,plain,
% 2.12/2.39 (b(s(s(z)), s(s(elem!1)))),
% 2.12/2.39 inference(modus_ponens,[status(thm)],[964, 9311])).
% 2.12/2.39 tff(9313,plain,
% 2.12/2.39 (~b(s(s(z)), s(z))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[7565, 8409, 964, 1391, 7141])).
% 2.12/2.39 tff(9314,plain,
% 2.12/2.39 (r(s(s(z)), s(z))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[153, 9313])).
% 2.12/2.39 tff(9315,plain,
% 2.12/2.39 (~b(s(s(s(z))), s(z))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[8081, 9307, 1391, 8409, 7141])).
% 2.12/2.39 tff(9316,plain,
% 2.12/2.39 (r(s(s(s(z))), s(z))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[1081, 9315])).
% 2.12/2.39 tff(9317,plain,
% 2.12/2.39 (~r(s(s(z)), s(s(s(z))))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[6502, 1067, 115])).
% 2.12/2.39 tff(9318,plain,
% 2.12/2.39 (b(s(s(z)), s(s(s(z))))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[8252, 9317])).
% 2.12/2.39 tff(9319,plain,
% 2.12/2.39 (b(s(s(z)), s(s(elem!1)))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[6336, 58, 2244, 8001])).
% 2.12/2.39 tff(9320,plain,
% 2.12/2.39 (~r(s(s(s(z))), s(s(z)))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[8089, 37, 115, 1067])).
% 2.12/2.39 tff(9321,plain,
% 2.12/2.39 (b(s(s(s(z))), s(s(z)))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[2173, 58, 9320, 8230])).
% 2.12/2.39 tff(9322,plain,
% 2.12/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.12/2.39 inference(rewrite,[status(thm)],[])).
% 2.12/2.39 tff(9323,plain,
% 2.12/2.39 (((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.12/2.39 inference(rewrite,[status(thm)],[])).
% 2.12/2.39 tff(9324,plain,
% 2.12/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1))))))),
% 2.12/2.39 inference(monotonicity,[status(thm)],[9323])).
% 2.12/2.39 tff(9325,plain,
% 2.12/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.12/2.39 inference(transitivity,[status(thm)],[9324, 9322])).
% 2.12/2.39 tff(9326,plain,
% 2.12/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.12/2.39 inference(quant_inst,[status(thm)],[])).
% 2.12/2.39 tff(9327,plain,
% 2.12/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1))))),
% 2.12/2.39 inference(modus_ponens,[status(thm)],[9326, 9325])).
% 2.12/2.39 tff(9328,plain,
% 2.12/2.39 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[9327, 37, 494, 1067])).
% 2.12/2.39 tff(9329,plain,
% 2.12/2.39 (b(s(s(s(z))), s(s(elem!1)))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[62, 9328, 16])).
% 2.12/2.39 tff(9330,plain,
% 2.12/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.12/2.39 inference(rewrite,[status(thm)],[])).
% 2.12/2.39 tff(9331,plain,
% 2.12/2.39 (((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.12/2.39 inference(rewrite,[status(thm)],[])).
% 2.12/2.39 tff(9332,plain,
% 2.12/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 2.12/2.39 inference(monotonicity,[status(thm)],[9331])).
% 2.12/2.39 tff(9333,plain,
% 2.12/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.22/2.40 inference(transitivity,[status(thm)],[9332, 9330])).
% 2.22/2.40 tff(9334,plain,
% 2.22/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.22/2.40 inference(quant_inst,[status(thm)],[])).
% 2.22/2.40 tff(9335,plain,
% 2.22/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 2.22/2.40 inference(modus_ponens,[status(thm)],[9334, 9333])).
% 2.22/2.40 tff(9336,plain,
% 2.22/2.40 ($false),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[9335, 75, 9329, 9321, 1283, 9319])).
% 2.22/2.40 tff(9337,plain,((~r(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (s(s(z)) = s(s(elem!1))) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.40 tff(9338,plain,
% 2.22/2.40 (~r(s(s(elem!1)), s(z))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[9337, 1283, 8001, 16, 1067, 115])).
% 2.22/2.40 tff(9339,plain,
% 2.22/2.40 (b(s(s(elem!1)), s(z))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[561, 9338])).
% 2.22/2.40 tff(9340,plain,
% 2.22/2.40 (~b(s(s(elem!1)), z)),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[4754, 9339, 372, 371])).
% 2.22/2.40 tff(9341,plain,
% 2.22/2.40 (r(s(s(elem!1)), z)),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[2696, 9340])).
% 2.22/2.40 tff(9342,plain,
% 2.22/2.40 (~r(s(s(elem!1)), elem!1)),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[4774, 9341, 155])).
% 2.22/2.40 tff(9343,plain,
% 2.22/2.40 (s(s(elem!1)) = elem!1),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[2673, 9342, 1])).
% 2.22/2.40 tff(9344,plain,
% 2.22/2.40 (elem!1 = s(s(elem!1))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[2555, 9343])).
% 2.22/2.40 tff(9345,plain,
% 2.22/2.40 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(elem!1)))),
% 2.22/2.40 inference(monotonicity,[status(thm)],[9344])).
% 2.22/2.40 tff(9346,plain,
% 2.22/2.40 (b(s(s(z)), s(s(elem!1)))),
% 2.22/2.40 inference(modus_ponens,[status(thm)],[964, 9345])).
% 2.22/2.40 tff(9347,plain,
% 2.22/2.40 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(elem!1)))),
% 2.22/2.40 inference(monotonicity,[status(thm)],[9344])).
% 2.22/2.40 tff(9348,plain,
% 2.22/2.40 (b(s(s(s(z))), s(s(elem!1)))),
% 2.22/2.40 inference(modus_ponens,[status(thm)],[1119, 9347])).
% 2.22/2.40 tff(9349,plain,
% 2.22/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.22/2.40 inference(rewrite,[status(thm)],[])).
% 2.22/2.40 tff(9350,plain,
% 2.22/2.40 (((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.22/2.40 inference(rewrite,[status(thm)],[])).
% 2.22/2.40 tff(9351,plain,
% 2.22/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 2.22/2.40 inference(monotonicity,[status(thm)],[9350])).
% 2.22/2.40 tff(9352,plain,
% 2.22/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.22/2.40 inference(transitivity,[status(thm)],[9351, 9349])).
% 2.22/2.40 tff(9353,plain,
% 2.22/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.22/2.40 inference(quant_inst,[status(thm)],[])).
% 2.22/2.40 tff(9354,plain,
% 2.22/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 2.22/2.40 inference(modus_ponens,[status(thm)],[9353, 9352])).
% 2.22/2.40 tff(9355,plain,
% 2.22/2.40 ($false),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[9354, 75, 9348, 1283, 9346, 9318])).
% 2.22/2.40 tff(9356,plain,((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | b(s(s(elem!1)), elem!1) | (~r(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), z)) | (s(s(z)) = s(s(elem!1))) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.40 tff(9357,plain,
% 2.22/2.40 (~b(s(s(elem!1)), s(s(z)))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[9356, 9316, 964, 1, 9288, 7141, 8409, 7548, 5493, 9307, 9314])).
% 2.22/2.40 tff(9358,plain,
% 2.22/2.40 (r(s(s(elem!1)), s(s(z)))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[1476, 9357, 266])).
% 2.22/2.40 tff(9359,plain,
% 2.22/2.40 ($false),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[9148, 37, 1647, 467, 1488])).
% 2.22/2.40 tff(9360,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.40 tff(9361,plain,
% 2.22/2.40 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[9360, 9300, 9358])).
% 2.22/2.40 tff(9362,plain,
% 2.22/2.40 (b(s(s(z)), s(s(s(s(z)))))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[465, 9361])).
% 2.22/2.40 tff(9363,plain,
% 2.22/2.40 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[7622, 9362, 9312, 9310, 9308])).
% 2.22/2.40 tff(9364,plain,
% 2.22/2.40 (r(s(s(elem!1)), s(s(s(z))))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[1936, 9363, 9305])).
% 2.22/2.40 tff(9365,plain,
% 2.22/2.40 (~b(z, elem!1)),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[2596, 8409, 1391, 7141])).
% 2.22/2.40 tff(9366,plain,
% 2.22/2.40 (r(s(z), s(s(s(s(z)))))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[7757, 9362, 9365, 266, 9278])).
% 2.22/2.40 tff(9367,plain,
% 2.22/2.40 (r(s(z), elem!1) <=> r(s(z), s(s(elem!1)))),
% 2.22/2.40 inference(monotonicity,[status(thm)],[9297])).
% 2.22/2.40 tff(9368,plain,
% 2.22/2.40 (r(s(z), s(s(elem!1)))),
% 2.22/2.40 inference(modus_ponens,[status(thm)],[588, 9367])).
% 2.22/2.40 tff(9369,plain,
% 2.22/2.40 (((~![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(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.22/2.40 inference(rewrite,[status(thm)],[])).
% 2.22/2.40 tff(9370,plain,
% 2.22/2.40 (((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.22/2.40 inference(rewrite,[status(thm)],[])).
% 2.22/2.40 tff(9371,plain,
% 2.22/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 2.22/2.40 inference(monotonicity,[status(thm)],[9370])).
% 2.22/2.40 tff(9372,plain,
% 2.22/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.22/2.40 inference(transitivity,[status(thm)],[9371, 9369])).
% 2.22/2.40 tff(9373,plain,
% 2.22/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))))),
% 2.22/2.40 inference(quant_inst,[status(thm)],[])).
% 2.22/2.40 tff(9374,plain,
% 2.22/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 2.22/2.40 inference(modus_ponens,[status(thm)],[9373, 9372])).
% 2.22/2.40 tff(9375,plain,
% 2.22/2.40 ($false),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[9374, 37, 9368, 9366, 9364, 9300])).
% 2.22/2.40 tff(9376,plain,((~r(s(z), elem!1)) | (s(s(elem!1)) = s(s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | b(s(s(elem!1)), elem!1) | (~b(elem!1, s(z))) | (elem!1 = z) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.40 tff(9377,plain,
% 2.22/2.40 (b(s(s(elem!1)), elem!1)),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[9376, 9270, 9258, 8892, 9241, 9237, 9240, 7108])).
% 2.22/2.40 tff(9378,plain,
% 2.22/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))))),
% 2.22/2.40 inference(rewrite,[status(thm)],[])).
% 2.22/2.40 tff(9379,plain,
% 2.22/2.40 (((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))))),
% 2.22/2.40 inference(rewrite,[status(thm)],[])).
% 2.22/2.40 tff(9380,plain,
% 2.22/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z)))))),
% 2.22/2.40 inference(monotonicity,[status(thm)],[9379])).
% 2.22/2.40 tff(9381,plain,
% 2.22/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))))),
% 2.22/2.40 inference(transitivity,[status(thm)],[9380, 9378])).
% 2.22/2.40 tff(9382,plain,
% 2.22/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))),
% 2.22/2.40 inference(quant_inst,[status(thm)],[])).
% 2.22/2.40 tff(9383,plain,
% 2.22/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z)))),
% 2.22/2.40 inference(modus_ponens,[status(thm)],[9382, 9381])).
% 2.22/2.40 tff(9384,plain,
% 2.22/2.40 ($false),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[9383, 75, 1457, 372, 371, 1391, 707])).
% 2.22/2.40 tff(9385,plain,((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.40 tff(9386,plain,
% 2.22/2.40 (~b(s(s(elem!1)), s(z))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[9385, 9273, 9275, 9237, 9377])).
% 2.22/2.40 tff(9387,plain,
% 2.22/2.40 (r(s(s(elem!1)), s(z))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[561, 9386])).
% 2.22/2.40 tff(9388,plain,
% 2.22/2.40 (~(s(s(z)) = s(elem!1))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[3261, 9238])).
% 2.22/2.40 tff(9389,plain,
% 2.22/2.40 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[4541, 9388])).
% 2.22/2.40 tff(9390,plain,
% 2.22/2.40 (~(s(s(z)) = s(s(elem!1)))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[6319, 9241])).
% 2.22/2.40 tff(9391,plain,
% 2.22/2.40 ($false),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[500, 37, 494, 115, 1488])).
% 2.22/2.40 tff(9392,plain,((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.40 tff(9393,plain,
% 2.22/2.40 (~r(s(s(elem!1)), s(s(z)))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[9392, 9387, 9277])).
% 2.22/2.40 tff(9394,plain,
% 2.22/2.40 (b(s(s(elem!1)), s(s(z)))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[1476, 9393, 9241])).
% 2.22/2.40 tff(9395,plain,
% 2.22/2.40 (~r(s(s(s(z))), s(z))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[9337, 9394, 9390, 9389, 9387, 9277])).
% 2.22/2.40 tff(9396,plain,
% 2.22/2.40 (b(s(s(s(z))), s(z))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[1081, 9395])).
% 2.22/2.40 tff(9397,plain,
% 2.22/2.40 (~b(s(s(s(z))), elem!1)),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[8081, 9396, 9237, 9275, 9273])).
% 2.22/2.40 tff(9398,plain,
% 2.22/2.40 (s(s(s(z))) = elem!1),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[1115, 9397, 9271])).
% 2.22/2.40 tff(9399,plain,
% 2.22/2.40 (s(s(s(s(z)))) = s(elem!1)),
% 2.22/2.40 inference(monotonicity,[status(thm)],[9398])).
% 2.22/2.40 tff(9400,plain,
% 2.22/2.40 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 2.22/2.40 inference(monotonicity,[status(thm)],[9399])).
% 2.22/2.40 tff(9401,plain,
% 2.22/2.40 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 2.22/2.40 inference(symmetry,[status(thm)],[9400])).
% 2.22/2.40 tff(9402,plain,
% 2.22/2.40 (s(s(s(elem!1))) = s(s(s(s(s(s(z))))))),
% 2.22/2.40 inference(monotonicity,[status(thm)],[9401])).
% 2.22/2.40 tff(9403,plain,
% 2.22/2.40 (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))),
% 2.22/2.40 inference(symmetry,[status(thm)],[9402])).
% 2.22/2.40 tff(9404,plain,
% 2.22/2.40 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[1247, 9270, 7108])).
% 2.22/2.40 tff(9405,plain,
% 2.22/2.40 (elem!1 = s(s(s(z)))),
% 2.22/2.40 inference(modus_ponens,[status(thm)],[9398, 3425])).
% 2.22/2.40 tff(9406,plain,
% 2.22/2.40 (s(s(s(z))) = elem!1),
% 2.22/2.40 inference(symmetry,[status(thm)],[1029])).
% 2.22/2.40 tff(9407,plain,
% 2.22/2.40 (s(s(s(z))) = s(s(s(s(s(s(s(z)))))))),
% 2.22/2.40 inference(transitivity,[status(thm)],[9406, 3291])).
% 2.22/2.40 tff(9408,plain,
% 2.22/2.40 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 2.22/2.40 inference(monotonicity,[status(thm)],[9407])).
% 2.22/2.40 tff(9409,plain,
% 2.22/2.40 (s(s(z)) = s(s(s(s(s(s(z))))))),
% 2.22/2.40 inference(transitivity,[status(thm)],[254, 9408, 713])).
% 2.22/2.40 tff(9410,plain,
% 2.22/2.40 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(s(z)))))))),
% 2.22/2.40 inference(monotonicity,[status(thm)],[9409])).
% 2.22/2.40 tff(9411,plain,
% 2.22/2.40 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(z)))),
% 2.22/2.40 inference(symmetry,[status(thm)],[9410])).
% 2.22/2.40 tff(9412,plain,
% 2.22/2.40 (s(s(elem!1)) = s(z)),
% 2.22/2.40 inference(transitivity,[status(thm)],[2385, 731, 9411, 133])).
% 2.22/2.40 tff(9413,plain,
% 2.22/2.40 ($false),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[556, 9412])).
% 2.22/2.40 tff(9414,plain,((~(s(s(s(s(s(s(s(z))))))) = elem!1)) | (~(elem!1 = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.40 tff(9415,plain,
% 2.22/2.40 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[9414, 9405])).
% 2.22/2.40 tff(9416,plain,
% 2.22/2.40 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[813, 9415, 9404])).
% 2.22/2.40 tff(9417,plain,
% 2.22/2.40 (~r(s(s(z)), s(s(elem!1)))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[2243, 37, 9387, 9277])).
% 2.22/2.40 tff(9418,plain,
% 2.22/2.40 (b(s(s(z)), s(s(elem!1)))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[6336, 58, 9417, 9390])).
% 2.22/2.40 tff(9419,plain,
% 2.22/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.22/2.40 inference(rewrite,[status(thm)],[])).
% 2.22/2.40 tff(9420,plain,
% 2.22/2.40 (((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.22/2.40 inference(rewrite,[status(thm)],[])).
% 2.22/2.40 tff(9421,plain,
% 2.22/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 2.22/2.40 inference(monotonicity,[status(thm)],[9420])).
% 2.22/2.40 tff(9422,plain,
% 2.22/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.22/2.41 inference(transitivity,[status(thm)],[9421, 9419])).
% 2.22/2.41 tff(9423,plain,
% 2.22/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.22/2.41 inference(quant_inst,[status(thm)],[])).
% 2.22/2.41 tff(9424,plain,
% 2.22/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.22/2.41 inference(modus_ponens,[status(thm)],[9423, 9422])).
% 2.22/2.41 tff(9425,plain,
% 2.22/2.41 ($false),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[9424, 75, 372, 371, 1391, 1168, 8629])).
% 2.22/2.41 tff(9426,plain,((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.41 tff(9427,plain,
% 2.22/2.41 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[9426, 9273, 9275, 9237, 9416])).
% 2.22/2.41 tff(9428,plain,
% 2.22/2.41 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[1230, 58, 1227, 9427])).
% 2.22/2.41 tff(9429,assumption,(r(s(s(s(s(s(s(s(z))))))), s(z))), introduced(assumption)).
% 2.22/2.41 tff(9430,plain,
% 2.22/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.22/2.41 inference(rewrite,[status(thm)],[])).
% 2.22/2.41 tff(9431,plain,
% 2.22/2.41 (((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.22/2.41 inference(rewrite,[status(thm)],[])).
% 2.22/2.41 tff(9432,plain,
% 2.22/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(elem!1)), s(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(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 2.22/2.41 inference(monotonicity,[status(thm)],[9431])).
% 2.22/2.41 tff(9433,plain,
% 2.22/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(elem!1)), s(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(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.22/2.41 inference(transitivity,[status(thm)],[9432, 9430])).
% 2.22/2.41 tff(9434,plain,
% 2.22/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.41 inference(quant_inst,[status(thm)],[])).
% 2.22/2.41 tff(9435,plain,
% 2.22/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.22/2.41 inference(modus_ponens,[status(thm)],[9434, 9433])).
% 2.22/2.41 tff(9436,plain,
% 2.22/2.41 (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[9435, 37, 494, 9429])).
% 2.22/2.41 tff(9437,plain,
% 2.22/2.41 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[840, 58, 3067, 9436])).
% 2.22/2.41 tff(9438,plain,
% 2.22/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.22/2.41 inference(rewrite,[status(thm)],[])).
% 2.22/2.41 tff(9439,plain,
% 2.22/2.41 (((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.22/2.41 inference(rewrite,[status(thm)],[])).
% 2.22/2.41 tff(9440,plain,
% 2.22/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 2.22/2.41 inference(monotonicity,[status(thm)],[9439])).
% 2.22/2.41 tff(9441,plain,
% 2.22/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.22/2.41 inference(transitivity,[status(thm)],[9440, 9438])).
% 2.22/2.41 tff(9442,plain,
% 2.22/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.22/2.41 inference(quant_inst,[status(thm)],[])).
% 2.22/2.41 tff(9443,plain,
% 2.22/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.22/2.41 inference(modus_ponens,[status(thm)],[9442, 9441])).
% 2.22/2.41 tff(9444,plain,
% 2.22/2.41 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[9443, 37, 115, 9429])).
% 2.22/2.41 tff(9445,plain,
% 2.22/2.41 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(z))) | b(s(s(s(s(s(s(s(z))))))), s(s(z))) | r(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(z))) | b(s(s(s(s(s(s(s(z))))))), s(s(z))) | r(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 2.22/2.41 inference(rewrite,[status(thm)],[])).
% 2.22/2.41 tff(9446,plain,
% 2.22/2.41 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(z))) | b(s(s(s(s(s(s(s(z))))))), s(s(z))) | r(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 2.22/2.41 inference(quant_inst,[status(thm)],[])).
% 2.22/2.41 tff(9447,plain,
% 2.22/2.41 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(z))) | b(s(s(s(s(s(s(s(z))))))), s(s(z))) | r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.22/2.41 inference(modus_ponens,[status(thm)],[9446, 9445])).
% 2.22/2.41 tff(9448,plain,
% 2.22/2.41 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[9447, 58, 1045, 9444])).
% 2.22/2.41 tff(9449,plain,
% 2.22/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.22/2.41 inference(rewrite,[status(thm)],[])).
% 2.22/2.41 tff(9450,plain,
% 2.22/2.41 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.22/2.41 inference(rewrite,[status(thm)],[])).
% 2.22/2.41 tff(9451,plain,
% 2.22/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 2.22/2.41 inference(monotonicity,[status(thm)],[9450])).
% 2.22/2.41 tff(9452,plain,
% 2.22/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.22/2.41 inference(transitivity,[status(thm)],[9451, 9449])).
% 2.22/2.41 tff(9453,plain,
% 2.22/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.41 inference(quant_inst,[status(thm)],[])).
% 2.22/2.41 tff(9454,plain,
% 2.22/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.22/2.41 inference(modus_ponens,[status(thm)],[9453, 9452])).
% 2.22/2.41 tff(9455,plain,
% 2.22/2.41 ((~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[9454, 75, 1168, 1283, 7613, 707])).
% 2.22/2.41 tff(9456,plain,
% 2.22/2.41 ($false),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[9455, 9448, 9437])).
% 2.22/2.41 tff(9457,plain,((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.41 tff(9458,plain,
% 2.22/2.41 (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[9457, 9428, 9394, 9418, 9377, 9416, 9277, 9387])).
% 2.22/2.41 tff(9459,plain,
% 2.22/2.41 (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))),
% 2.22/2.41 inference(symmetry,[status(thm)],[9458])).
% 2.22/2.41 tff(9460,plain,
% 2.22/2.41 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(s(elem!1)))),
% 2.22/2.41 inference(monotonicity,[status(thm)],[9459])).
% 2.22/2.41 tff(9461,plain,
% 2.22/2.41 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 2.22/2.41 inference(symmetry,[status(thm)],[9460])).
% 2.22/2.41 tff(9462,plain,
% 2.22/2.41 (s(elem!1) = s(s(s(elem!1)))),
% 2.22/2.41 inference(transitivity,[status(thm)],[229, 9461, 713, 9403])).
% 2.22/2.41 tff(9463,plain,
% 2.22/2.41 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 2.22/2.41 inference(monotonicity,[status(thm)],[9462])).
% 2.22/2.41 tff(9464,plain,
% 2.22/2.41 (elem!1 = s(s(elem!1))),
% 2.22/2.41 inference(transitivity,[status(thm)],[725, 9463, 11])).
% 2.22/2.41 tff(9465,plain,
% 2.22/2.41 (b(s(s(elem!1)), elem!1) <=> b(elem!1, elem!1)),
% 2.22/2.41 inference(monotonicity,[status(thm)],[2323])).
% 2.22/2.41 tff(9466,plain,
% 2.22/2.41 (b(elem!1, elem!1) <=> b(s(s(elem!1)), elem!1)),
% 2.22/2.41 inference(symmetry,[status(thm)],[9465])).
% 2.22/2.41 tff(9467,plain,
% 2.22/2.41 ((~b(elem!1, elem!1)) <=> (~b(s(s(elem!1)), elem!1))),
% 2.22/2.41 inference(monotonicity,[status(thm)],[9466])).
% 2.22/2.41 tff(9468,plain,
% 2.22/2.41 (~b(s(s(elem!1)), elem!1)),
% 2.22/2.41 inference(modus_ponens,[status(thm)],[1389, 9467])).
% 2.22/2.41 tff(9469,plain,
% 2.22/2.41 ($false),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[707, 9468])).
% 2.22/2.41 tff(9470,plain,((~(elem!1 = s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.41 tff(9471,plain,
% 2.22/2.41 (~(elem!1 = s(s(elem!1)))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[9470, 9377])).
% 2.22/2.41 tff(9472,plain,
% 2.22/2.41 ($false),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[9471, 9464])).
% 2.22/2.41 tff(9473,plain,(r(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.22/2.41 tff(9474,plain,
% 2.22/2.41 (r(s(s(s(s(z)))), elem!1)),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[7107, 13])).
% 2.22/2.41 tff(9475,assumption,(~r(s(z), elem!1)), introduced(assumption)).
% 2.22/2.41 tff(9476,plain,
% 2.22/2.41 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.22/2.41 inference(symmetry,[status(thm)],[5584])).
% 2.22/2.41 tff(9477,plain,
% 2.22/2.41 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[4866, 3839])).
% 2.22/2.41 tff(9478,plain,
% 2.22/2.41 ((~r(s(s(s(elem!1))), s(s(elem!1)))) <=> (~r(s(s(s(z))), s(s(elem!1))))),
% 2.22/2.41 inference(monotonicity,[status(thm)],[5536])).
% 2.22/2.41 tff(9479,plain,
% 2.22/2.41 (r(s(s(s(s(z)))), z) <=> r(s(s(s(s(z)))), elem!1)),
% 2.22/2.41 inference(monotonicity,[status(thm)],[288])).
% 2.22/2.41 tff(9480,plain,
% 2.22/2.41 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), z)),
% 2.22/2.41 inference(symmetry,[status(thm)],[9479])).
% 2.22/2.41 tff(9481,plain,
% 2.22/2.41 (r(s(s(s(s(z)))), z)),
% 2.22/2.41 inference(modus_ponens,[status(thm)],[698, 9480])).
% 2.22/2.41 tff(9482,assumption,(~r(s(s(s(s(z)))), z)), introduced(assumption)).
% 2.22/2.41 tff(9483,plain,
% 2.22/2.41 ($false),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[9482, 9481])).
% 2.22/2.41 tff(9484,plain,((~(z = elem!1)) | r(s(s(s(s(z)))), z) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.41 tff(9485,plain,
% 2.22/2.41 (r(s(s(s(s(z)))), z)),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[9484, 288, 9474])).
% 2.22/2.41 tff(9486,plain,
% 2.22/2.41 (~b(z, s(z))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[8118, 288, 14])).
% 2.22/2.41 tff(9487,plain,
% 2.22/2.41 (r(z, s(z))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[187, 9486])).
% 2.22/2.41 tff(9488,plain,
% 2.22/2.41 (~r(s(s(s(s(z)))), s(z))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[1417, 9487, 9485])).
% 2.22/2.41 tff(9489,plain,
% 2.22/2.41 (~r(s(s(s(s(z)))), s(elem!1))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[4253, 9488, 288])).
% 2.22/2.41 tff(9490,plain,
% 2.22/2.41 (b(s(s(s(s(z)))), s(elem!1))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[4263, 58, 4260, 9489])).
% 2.22/2.41 tff(9491,plain,
% 2.22/2.41 (~(elem!1 = s(z))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[84, 9477])).
% 2.22/2.41 tff(9492,plain,
% 2.22/2.41 (r(elem!1, s(z))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[89, 9491, 14])).
% 2.22/2.41 tff(9493,plain,
% 2.22/2.41 (~b(s(s(s(z))), s(z))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[3544, 1061, 698, 288, 114, 5589])).
% 2.22/2.41 tff(9494,plain,
% 2.22/2.41 ($false),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[1081, 1076, 9493])).
% 2.22/2.41 tff(9495,plain,((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.41 tff(9496,plain,
% 2.22/2.41 (~r(s(s(s(z))), elem!1)),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[9495, 9492, 9474, 288])).
% 2.22/2.41 tff(9497,plain,
% 2.22/2.41 (b(s(s(s(z))), elem!1)),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[1115, 9496, 4145])).
% 2.22/2.41 tff(9498,plain,
% 2.22/2.41 (b(s(s(s(elem!1))), elem!1)),
% 2.22/2.41 inference(modus_ponens,[status(thm)],[9497, 5490])).
% 2.22/2.41 tff(9499,plain,
% 2.22/2.41 (r(s(elem!1), elem!1) <=> r(s(z), elem!1)),
% 2.22/2.41 inference(symmetry,[status(thm)],[4002])).
% 2.22/2.41 tff(9500,plain,
% 2.22/2.41 (r(s(elem!1), elem!1) <=> r(s(z), z)),
% 2.22/2.41 inference(transitivity,[status(thm)],[9499, 5533])).
% 2.22/2.41 tff(9501,plain,
% 2.22/2.41 (~(s(z) = elem!1)),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[2724, 9487, 13])).
% 2.22/2.41 tff(9502,plain,
% 2.22/2.41 (~b(elem!1, s(z))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[5500, 5498, 288])).
% 2.22/2.41 tff(9503,plain,
% 2.22/2.41 (r(elem!1, s(z))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[89, 9502, 112])).
% 2.22/2.41 tff(9504,plain,
% 2.22/2.41 (~r(s(z), s(s(s(s(z)))))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[3203, 9503, 3195])).
% 2.22/2.41 tff(9505,plain,
% 2.22/2.41 (b(s(z), s(s(s(s(z)))))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[489, 9504])).
% 2.22/2.41 tff(9506,plain,
% 2.22/2.41 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[3920, 106, 3839, 5479, 114, 578])).
% 2.22/2.41 tff(9507,plain,
% 2.22/2.41 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[3926, 9506, 3839])).
% 2.22/2.41 tff(9508,plain,
% 2.22/2.41 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[1660, 9507, 5479])).
% 2.22/2.41 tff(9509,plain,
% 2.22/2.41 ($false),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[3884, 37, 9508, 698, 3841])).
% 2.22/2.41 tff(9510,plain,((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~(z = elem!1)) | (~r(elem!1, s(z))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.41 tff(9511,plain,
% 2.22/2.41 (~r(s(s(z)), elem!1)),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[9510, 9505, 288, 698, 9503])).
% 2.22/2.41 tff(9512,plain,
% 2.22/2.41 (b(s(s(z)), elem!1)),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[104, 9511, 5480])).
% 2.22/2.41 tff(9513,plain,
% 2.22/2.41 (r(z, s(z))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[187, 5498])).
% 2.22/2.41 tff(9514,plain,
% 2.22/2.41 (~r(s(s(s(z))), elem!1)),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[3255, 9503, 3195])).
% 2.22/2.41 tff(9515,plain,
% 2.22/2.41 (b(s(s(s(z))), elem!1)),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[1115, 9514, 4145])).
% 2.22/2.41 tff(9516,plain,
% 2.22/2.41 (b(s(s(s(elem!1))), elem!1)),
% 2.22/2.41 inference(modus_ponens,[status(thm)],[9515, 3836])).
% 2.22/2.41 tff(9517,plain,
% 2.22/2.41 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(z)), s(z))),
% 2.22/2.41 inference(symmetry,[status(thm)],[3570])).
% 2.22/2.41 tff(9518,plain,
% 2.22/2.41 (b(s(s(elem!1)), s(z)) <=> b(s(s(z)), s(z))),
% 2.22/2.41 inference(transitivity,[status(thm)],[5706, 9517])).
% 2.22/2.41 tff(9519,plain,
% 2.22/2.41 (b(s(z), elem!1) <=> b(s(z), z)),
% 2.22/2.41 inference(symmetry,[status(thm)],[6056])).
% 2.22/2.41 tff(9520,plain,
% 2.22/2.41 (b(s(z), z)),
% 2.22/2.41 inference(modus_ponens,[status(thm)],[107, 9519])).
% 2.22/2.41 tff(9521,plain,
% 2.22/2.41 (~r(elem!1, s(s(elem!1)))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[4762, 37, 494, 114])).
% 2.22/2.41 tff(9522,plain,
% 2.22/2.41 (b(elem!1, s(s(elem!1)))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[1617, 3432, 9521])).
% 2.22/2.41 tff(9523,plain,
% 2.22/2.41 (b(elem!1, s(s(z)))),
% 2.22/2.41 inference(modus_ponens,[status(thm)],[9522, 4269])).
% 2.22/2.41 tff(9524,plain,
% 2.22/2.41 (r(s(s(elem!1)), elem!1) <=> r(s(s(z)), elem!1)),
% 2.22/2.41 inference(monotonicity,[status(thm)],[291])).
% 2.22/2.41 tff(9525,plain,
% 2.22/2.41 ((~r(s(s(elem!1)), elem!1)) <=> (~r(s(s(z)), elem!1))),
% 2.22/2.41 inference(monotonicity,[status(thm)],[9524])).
% 2.22/2.41 tff(9526,plain,
% 2.22/2.41 (~r(s(s(elem!1)), elem!1)),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[9100, 37, 494, 114])).
% 2.22/2.41 tff(9527,plain,
% 2.22/2.41 (~r(s(s(z)), elem!1)),
% 2.22/2.41 inference(modus_ponens,[status(thm)],[9526, 9525])).
% 2.22/2.41 tff(9528,plain,
% 2.22/2.41 (b(s(s(z)), elem!1)),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[104, 9527, 15])).
% 2.22/2.41 tff(9529,plain,
% 2.22/2.41 (r(s(s(elem!1)), s(z)) <=> r(s(s(z)), s(elem!1))),
% 2.22/2.41 inference(monotonicity,[status(thm)],[291, 289])).
% 2.22/2.41 tff(9530,plain,
% 2.22/2.41 (r(s(s(elem!1)), s(z)) <=> r(s(s(z)), s(z))),
% 2.22/2.41 inference(transitivity,[status(thm)],[9529, 5868])).
% 2.22/2.41 tff(9531,plain,
% 2.22/2.41 (r(s(s(z)), s(z))),
% 2.22/2.41 inference(modus_ponens,[status(thm)],[494, 9530])).
% 2.22/2.42 tff(9532,plain,
% 2.22/2.42 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 2.22/2.42 inference(monotonicity,[status(thm)],[3571])).
% 2.22/2.42 tff(9533,plain,
% 2.22/2.42 ((~b(s(s(s(z))), s(s(z)))) <=> (~b(s(s(s(z))), s(s(elem!1))))),
% 2.22/2.42 inference(monotonicity,[status(thm)],[9532])).
% 2.22/2.42 tff(9534,plain,
% 2.22/2.42 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 2.22/2.42 inference(monotonicity,[status(thm)],[3843])).
% 2.22/2.42 tff(9535,plain,
% 2.22/2.42 ((s(s(s(z))) = z) <=> (elem!1 = s(s(s(z))))),
% 2.22/2.42 inference(transitivity,[status(thm)],[9534, 3425])).
% 2.22/2.42 tff(9536,plain,
% 2.22/2.42 ((~(s(s(s(z))) = z)) <=> (~(elem!1 = s(s(s(z)))))),
% 2.22/2.42 inference(monotonicity,[status(thm)],[9535])).
% 2.22/2.42 tff(9537,plain,
% 2.22/2.42 (~(elem!1 = s(s(s(z))))),
% 2.22/2.42 inference(modus_ponens,[status(thm)],[221, 9536])).
% 2.22/2.42 tff(9538,plain,
% 2.22/2.42 (((~![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))))))),
% 2.22/2.42 inference(rewrite,[status(thm)],[])).
% 2.22/2.42 tff(9539,plain,
% 2.22/2.42 (((~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))))))),
% 2.22/2.42 inference(rewrite,[status(thm)],[])).
% 2.22/2.42 tff(9540,plain,
% 2.22/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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)))))))),
% 2.22/2.42 inference(monotonicity,[status(thm)],[9539])).
% 2.22/2.42 tff(9541,plain,
% 2.22/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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))))))),
% 2.22/2.42 inference(transitivity,[status(thm)],[9540, 9538])).
% 2.22/2.42 tff(9542,plain,
% 2.22/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))))),
% 2.22/2.42 inference(quant_inst,[status(thm)],[])).
% 2.22/2.42 tff(9543,plain,
% 2.22/2.42 ((~![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)))))),
% 2.22/2.42 inference(modus_ponens,[status(thm)],[9542, 9541])).
% 2.22/2.42 tff(9544,plain,
% 2.22/2.42 (~r(elem!1, s(s(s(z))))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[9543, 37, 114, 1067])).
% 2.22/2.42 tff(9545,plain,
% 2.22/2.42 (b(elem!1, s(s(s(z))))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[1279, 9544, 9537])).
% 2.22/2.42 tff(9546,plain,
% 2.22/2.42 ((~(s(s(s(z))) = z)) <=> (~(s(s(s(z))) = elem!1))),
% 2.22/2.42 inference(monotonicity,[status(thm)],[9534])).
% 2.22/2.42 tff(9547,plain,
% 2.22/2.42 (~(s(s(s(z))) = elem!1)),
% 2.22/2.42 inference(modus_ponens,[status(thm)],[221, 9546])).
% 2.22/2.42 tff(9548,plain,
% 2.22/2.42 (~r(s(s(s(z))), elem!1)),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[1073, 37, 114, 1067])).
% 2.22/2.42 tff(9549,plain,
% 2.22/2.42 (b(s(s(s(z))), elem!1)),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[1115, 9548, 9547])).
% 2.22/2.42 tff(9550,plain,
% 2.22/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.22/2.42 inference(rewrite,[status(thm)],[])).
% 2.22/2.42 tff(9551,plain,
% 2.22/2.42 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.22/2.42 inference(rewrite,[status(thm)],[])).
% 2.22/2.42 tff(9552,plain,
% 2.22/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))))),
% 2.22/2.42 inference(monotonicity,[status(thm)],[9551])).
% 2.22/2.42 tff(9553,plain,
% 2.22/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.22/2.42 inference(transitivity,[status(thm)],[9552, 9550])).
% 2.22/2.42 tff(9554,plain,
% 2.22/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))))),
% 2.22/2.42 inference(quant_inst,[status(thm)],[])).
% 2.22/2.42 tff(9555,plain,
% 2.22/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 2.22/2.42 inference(modus_ponens,[status(thm)],[9554, 9553])).
% 2.22/2.42 tff(9556,plain,
% 2.22/2.42 (~b(s(s(s(z))), s(s(z)))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[9555, 75, 964, 9549, 9545])).
% 2.22/2.42 tff(9557,plain,
% 2.22/2.42 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.22/2.42 inference(modus_ponens,[status(thm)],[9556, 9533])).
% 2.22/2.42 tff(9558,plain,
% 2.22/2.42 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[4866, 225])).
% 2.22/2.42 tff(9559,plain,
% 2.22/2.42 (r(s(s(s(z))), s(s(z))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 2.22/2.42 inference(monotonicity,[status(thm)],[3571])).
% 2.22/2.42 tff(9560,plain,
% 2.22/2.42 ((~r(s(s(s(z))), s(s(z)))) <=> (~r(s(s(s(z))), s(s(elem!1))))),
% 2.22/2.42 inference(monotonicity,[status(thm)],[9559])).
% 2.22/2.42 tff(9561,plain,
% 2.22/2.42 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.22/2.42 inference(modus_ponens,[status(thm)],[9320, 9560])).
% 2.22/2.42 tff(9562,plain,
% 2.22/2.42 (b(s(s(s(z))), s(s(elem!1)))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[62, 9561, 9558])).
% 2.22/2.42 tff(9563,plain,
% 2.22/2.42 ($false),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[9562, 9557])).
% 2.22/2.42 tff(9564,plain,((~r(s(s(s(z))), s(z))) | (~(s(s(elem!1)) = s(s(z)))) | (~b(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.42 tff(9565,plain,
% 2.22/2.42 (~r(s(s(s(z))), s(z))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[9564, 9531, 9528, 291, 114])).
% 2.22/2.42 tff(9566,plain,
% 2.22/2.42 (b(s(s(s(z))), s(z))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[1081, 9565])).
% 2.22/2.42 tff(9567,plain,
% 2.22/2.42 (b(s(z), elem!1)),
% 2.22/2.42 inference(modus_ponens,[status(thm)],[371, 6056])).
% 2.22/2.42 tff(9568,plain,
% 2.22/2.42 (~r(s(s(s(z))), elem!1)),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[3606, 9567, 114, 288, 4145, 9521])).
% 2.22/2.42 tff(9569,plain,
% 2.22/2.42 (b(s(s(s(z))), elem!1)),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[1115, 9568, 4145])).
% 2.22/2.42 tff(9570,plain,
% 2.22/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 2.22/2.42 inference(rewrite,[status(thm)],[])).
% 2.22/2.42 tff(9571,plain,
% 2.22/2.42 (((~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 2.22/2.42 inference(rewrite,[status(thm)],[])).
% 2.22/2.42 tff(9572,plain,
% 2.22/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))), elem!1)) | (~b(elem!1, 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(X1, 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(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(z)))))),
% 2.22/2.42 inference(monotonicity,[status(thm)],[9571])).
% 2.22/2.42 tff(9573,plain,
% 2.22/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))), elem!1)) | (~b(elem!1, 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(X1, 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(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 2.22/2.42 inference(transitivity,[status(thm)],[9572, 9570])).
% 2.22/2.42 tff(9574,plain,
% 2.22/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 2.22/2.42 inference(quant_inst,[status(thm)],[])).
% 2.22/2.42 tff(9575,plain,
% 2.22/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(z)))),
% 2.22/2.42 inference(modus_ponens,[status(thm)],[9574, 9573])).
% 2.22/2.42 tff(9576,plain,
% 2.22/2.42 ($false),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[9575, 75, 107, 964, 1119, 984, 2247])).
% 2.22/2.42 tff(9577,plain,((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.42 tff(9578,plain,
% 2.22/2.42 (~b(elem!1, s(s(z)))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[9577, 9569, 9567, 9528, 9566])).
% 2.22/2.42 tff(9579,plain,
% 2.22/2.42 ($false),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[9578, 9523])).
% 2.22/2.42 tff(9580,plain,((~(z = elem!1)) | (~r(elem!1, s(z))) | (s(s(z)) = elem!1) | (~r(s(s(elem!1)), s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.42 tff(9581,plain,
% 2.22/2.42 (~r(s(s(elem!1)), s(z))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[9580, 9520, 288, 5480, 114])).
% 2.22/2.42 tff(9582,plain,
% 2.22/2.42 (b(s(s(elem!1)), s(z))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[561, 9581])).
% 2.22/2.42 tff(9583,plain,
% 2.22/2.42 (b(s(s(z)), s(z))),
% 2.22/2.42 inference(modus_ponens,[status(thm)],[9582, 9518])).
% 2.22/2.42 tff(9584,plain,
% 2.22/2.42 (~b(elem!1, s(s(elem!1)))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[7397, 9583, 964, 4146, 107])).
% 2.22/2.42 tff(9585,plain,
% 2.22/2.42 (r(elem!1, s(s(elem!1)))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[1617, 9584, 3432])).
% 2.22/2.42 tff(9586,plain,
% 2.22/2.42 (b(s(elem!1), z) <=> b(s(elem!1), elem!1)),
% 2.22/2.42 inference(monotonicity,[status(thm)],[288])).
% 2.22/2.42 tff(9587,plain,
% 2.22/2.42 (b(s(elem!1), elem!1) <=> b(s(elem!1), z)),
% 2.22/2.42 inference(symmetry,[status(thm)],[9586])).
% 2.22/2.42 tff(9588,plain,
% 2.22/2.42 (b(s(z), elem!1) <=> b(s(elem!1), z)),
% 2.22/2.42 inference(transitivity,[status(thm)],[3568, 9587])).
% 2.22/2.42 tff(9589,plain,
% 2.22/2.42 (b(s(elem!1), z)),
% 2.22/2.42 inference(modus_ponens,[status(thm)],[107, 9588])).
% 2.22/2.42 tff(9590,plain,
% 2.22/2.42 (b(s(s(elem!1)), s(elem!1))),
% 2.22/2.42 inference(modus_ponens,[status(thm)],[9582, 5706])).
% 2.22/2.42 tff(9591,plain,
% 2.22/2.42 (~b(z, s(s(z)))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[6654, 9590, 5546, 5541, 9589])).
% 2.22/2.42 tff(9592,plain,
% 2.22/2.42 (r(z, s(s(z)))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[351, 9591])).
% 2.22/2.42 tff(9593,plain,
% 2.22/2.42 (~r(s(z), s(s(z)))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[2005, 9592, 506])).
% 2.22/2.42 tff(9594,plain,
% 2.22/2.42 (b(s(z), s(s(z)))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[416, 9593])).
% 2.22/2.42 tff(9595,plain,
% 2.22/2.42 (b(s(elem!1), s(s(elem!1)))),
% 2.22/2.42 inference(modus_ponens,[status(thm)],[9594, 5864])).
% 2.22/2.42 tff(9596,plain,
% 2.22/2.42 (~b(elem!1, s(s(s(elem!1))))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[930, 920, 922, 921])).
% 2.22/2.42 tff(9597,plain,
% 2.22/2.42 (r(elem!1, s(s(s(elem!1))))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[5967, 9596, 5796])).
% 2.22/2.42 tff(9598,plain,
% 2.22/2.42 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.22/2.42 inference(modus_ponens,[status(thm)],[27, 5537])).
% 2.22/2.42 tff(9599,plain,
% 2.22/2.42 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[5046, 37, 1490, 5311])).
% 2.22/2.42 tff(9600,plain,
% 2.22/2.42 ($false),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[9599, 9598])).
% 2.22/2.42 tff(9601,plain,((~r(s(s(s(z))), s(s(elem!1)))) | (~(z = elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.42 tff(9602,plain,
% 2.22/2.42 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[9601, 9597, 1490, 288])).
% 2.22/2.42 tff(9603,plain,
% 2.22/2.42 (b(s(s(s(z))), s(s(elem!1)))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[62, 9602, 16])).
% 2.22/2.42 tff(9604,plain,
% 2.22/2.42 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.22/2.42 inference(modus_ponens,[status(thm)],[9603, 9476])).
% 2.22/2.42 tff(9605,plain,
% 2.22/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(elem!1))) | (~b(s(elem!1), 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(X1, 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(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.22/2.42 inference(rewrite,[status(thm)],[])).
% 2.22/2.42 tff(9606,plain,
% 2.22/2.42 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(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(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.22/2.42 inference(rewrite,[status(thm)],[])).
% 2.22/2.42 tff(9607,plain,
% 2.22/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 2.22/2.42 inference(monotonicity,[status(thm)],[9606])).
% 2.22/2.42 tff(9608,plain,
% 2.22/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.22/2.42 inference(transitivity,[status(thm)],[9607, 9605])).
% 2.22/2.42 tff(9609,plain,
% 2.22/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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))))))),
% 2.22/2.42 inference(quant_inst,[status(thm)],[])).
% 2.22/2.42 tff(9610,plain,
% 2.22/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 2.22/2.42 inference(modus_ponens,[status(thm)],[9609, 9608])).
% 2.22/2.42 tff(9611,plain,
% 2.22/2.42 ($false),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[9610, 75, 3069, 3581, 920, 9604])).
% 2.22/2.42 tff(9612,plain,((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~(z = elem!1)) | (s(s(s(z))) = s(s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.42 tff(9613,plain,
% 2.22/2.42 (~b(s(elem!1), s(s(s(elem!1))))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[9612, 9590, 9595, 288, 16, 9585, 922, 3569])).
% 2.22/2.42 tff(9614,plain,
% 2.22/2.42 (~b(s(z), s(s(s(z))))),
% 2.22/2.42 inference(modus_ponens,[status(thm)],[9613, 5582])).
% 2.22/2.42 tff(9615,plain,
% 2.22/2.42 (r(s(z), s(s(s(z))))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[1263, 9614])).
% 2.22/2.42 tff(9616,plain,
% 2.22/2.42 (~r(elem!1, s(s(s(z))))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[1274, 9615, 114])).
% 2.22/2.42 tff(9617,plain,
% 2.22/2.42 (b(elem!1, s(s(s(z))))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[1279, 9616, 5589])).
% 2.22/2.42 tff(9618,plain,
% 2.22/2.42 (b(elem!1, s(s(s(elem!1))))),
% 2.22/2.42 inference(modus_ponens,[status(thm)],[9617, 5586])).
% 2.22/2.42 tff(9619,plain,
% 2.22/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.22/2.42 inference(rewrite,[status(thm)],[])).
% 2.22/2.42 tff(9620,plain,
% 2.22/2.42 (((~b(s(s(s(elem!1))), elem!1)) | (~b(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(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.22/2.42 inference(rewrite,[status(thm)],[])).
% 2.22/2.42 tff(9621,plain,
% 2.22/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))))),
% 2.22/2.43 inference(monotonicity,[status(thm)],[9620])).
% 2.22/2.43 tff(9622,plain,
% 2.22/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.22/2.43 inference(transitivity,[status(thm)],[9621, 9619])).
% 2.22/2.43 tff(9623,plain,
% 2.22/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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))))),
% 2.22/2.43 inference(quant_inst,[status(thm)],[])).
% 2.22/2.43 tff(9624,plain,
% 2.22/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))),
% 2.22/2.43 inference(modus_ponens,[status(thm)],[9623, 9622])).
% 2.22/2.43 tff(9625,plain,
% 2.22/2.43 ($false),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[9624, 75, 3569, 9590, 4146, 9618, 922])).
% 2.22/2.43 tff(9626,plain,((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~(z = elem!1)) | (~r(elem!1, s(z))) | (s(s(s(z))) = s(s(elem!1))) | (~r(z, s(z))) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.43 tff(9627,plain,
% 2.22/2.43 (~b(s(z), elem!1)),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[9626, 9516, 288, 9503, 6204, 9513, 9512])).
% 2.22/2.43 tff(9628,plain,
% 2.22/2.43 (r(s(z), elem!1)),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[601, 9627, 108])).
% 2.22/2.43 tff(9629,plain,
% 2.22/2.43 (r(s(elem!1), elem!1)),
% 2.22/2.43 inference(modus_ponens,[status(thm)],[9628, 4002])).
% 2.22/2.43 tff(9630,plain,
% 2.22/2.43 (b(s(s(elem!1)), elem!1)),
% 2.22/2.43 inference(modus_ponens,[status(thm)],[9512, 3648])).
% 2.22/2.43 tff(9631,plain,
% 2.22/2.43 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(z))),
% 2.22/2.43 inference(monotonicity,[status(thm)],[3422])).
% 2.22/2.43 tff(9632,plain,
% 2.22/2.43 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(z) = s(s(s(s(z)))))),
% 2.22/2.43 inference(transitivity,[status(thm)],[9631, 247])).
% 2.22/2.43 tff(9633,plain,
% 2.22/2.43 ((s(z) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 2.22/2.43 inference(symmetry,[status(thm)],[9632])).
% 2.22/2.43 tff(9634,plain,
% 2.22/2.43 ((~(s(z) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 2.22/2.43 inference(monotonicity,[status(thm)],[9633])).
% 2.22/2.43 tff(9635,plain,
% 2.22/2.43 (~(s(s(s(s(z)))) = s(elem!1))),
% 2.22/2.43 inference(modus_ponens,[status(thm)],[484, 9634])).
% 2.22/2.43 tff(9636,plain,
% 2.22/2.43 (((~![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(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 2.22/2.43 inference(rewrite,[status(thm)],[])).
% 2.22/2.43 tff(9637,plain,
% 2.22/2.43 (((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1)))) <=> ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 2.22/2.43 inference(rewrite,[status(thm)],[])).
% 2.22/2.43 tff(9638,plain,
% 2.22/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1)))))),
% 2.22/2.43 inference(monotonicity,[status(thm)],[9637])).
% 2.22/2.43 tff(9639,plain,
% 2.22/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 2.22/2.43 inference(transitivity,[status(thm)],[9638, 9636])).
% 2.22/2.43 tff(9640,plain,
% 2.22/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 2.22/2.43 inference(quant_inst,[status(thm)],[])).
% 2.22/2.43 tff(9641,plain,
% 2.22/2.43 ((~![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(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 2.22/2.43 inference(modus_ponens,[status(thm)],[9640, 9639])).
% 2.22/2.43 tff(9642,plain,
% 2.22/2.43 (~r(s(s(s(s(z)))), s(elem!1))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[9641, 37, 698, 9629])).
% 2.22/2.43 tff(9643,plain,
% 2.22/2.43 ((s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[4263, 58, 9642])).
% 2.22/2.43 tff(9644,plain,
% 2.22/2.43 (b(s(s(s(s(z)))), s(elem!1))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[9643, 9635])).
% 2.22/2.43 tff(9645,plain,
% 2.22/2.43 (b(s(elem!1), s(s(s(s(z)))))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[3857, 9505, 288])).
% 2.22/2.43 tff(9646,plain,
% 2.22/2.43 (r(s(z), z)),
% 2.22/2.43 inference(modus_ponens,[status(thm)],[9628, 5533])).
% 2.22/2.43 tff(9647,plain,
% 2.22/2.43 (b(s(s(s(z))), z)),
% 2.22/2.43 inference(modus_ponens,[status(thm)],[9515, 5488])).
% 2.22/2.43 tff(9648,plain,
% 2.22/2.43 (b(s(s(elem!1)), z)),
% 2.22/2.43 inference(modus_ponens,[status(thm)],[9512, 5540])).
% 2.22/2.43 tff(9649,plain,
% 2.22/2.43 (((~![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(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, 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(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.22/2.43 inference(rewrite,[status(thm)],[])).
% 2.22/2.43 tff(9650,plain,
% 2.22/2.43 (((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(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(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.22/2.43 inference(rewrite,[status(thm)],[])).
% 2.22/2.43 tff(9651,plain,
% 2.22/2.43 (((~![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(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(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(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 2.22/2.43 inference(monotonicity,[status(thm)],[9650])).
% 2.22/2.43 tff(9652,plain,
% 2.22/2.43 (((~![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(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(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(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.22/2.43 inference(transitivity,[status(thm)],[9651, 9649])).
% 2.22/2.43 tff(9653,plain,
% 2.22/2.43 ((~![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(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.22/2.43 inference(quant_inst,[status(thm)],[])).
% 2.22/2.43 tff(9654,plain,
% 2.22/2.43 ((~![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(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 2.22/2.43 inference(modus_ponens,[status(thm)],[9653, 9652])).
% 2.22/2.43 tff(9655,plain,
% 2.22/2.43 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[9654, 37, 698, 738])).
% 2.22/2.43 tff(9656,plain,
% 2.22/2.43 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[1179, 58, 1176, 9655])).
% 2.22/2.43 tff(9657,plain,
% 2.22/2.43 (((~![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(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(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(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.43 inference(rewrite,[status(thm)],[])).
% 2.22/2.43 tff(9658,plain,
% 2.22/2.43 (((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.43 inference(rewrite,[status(thm)],[])).
% 2.22/2.43 tff(9659,plain,
% 2.22/2.43 (((~![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(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(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(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 2.22/2.43 inference(monotonicity,[status(thm)],[9658])).
% 2.22/2.43 tff(9660,plain,
% 2.22/2.43 (((~![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(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(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(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.43 inference(transitivity,[status(thm)],[9659, 9657])).
% 2.22/2.43 tff(9661,plain,
% 2.22/2.43 ((~![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(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.43 inference(quant_inst,[status(thm)],[])).
% 2.22/2.43 tff(9662,plain,
% 2.22/2.43 ((~![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(z)))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 2.22/2.43 inference(modus_ponens,[status(thm)],[9661, 9660])).
% 2.22/2.43 tff(9663,plain,
% 2.22/2.43 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[9662, 37, 698, 738])).
% 2.22/2.43 tff(9664,plain,
% 2.22/2.43 ((s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(s(z)))))),
% 2.22/2.43 inference(commutativity,[status(thm)],[])).
% 2.22/2.43 tff(9665,plain,
% 2.22/2.43 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(s(s(z))))))))),
% 2.22/2.43 inference(symmetry,[status(thm)],[9664])).
% 2.22/2.43 tff(9666,plain,
% 2.22/2.43 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))))),
% 2.22/2.43 inference(monotonicity,[status(thm)],[9665])).
% 2.22/2.43 tff(9667,plain,
% 2.22/2.43 (~(s(s(s(s(z)))) = s(s(s(s(s(s(s(z))))))))),
% 2.22/2.43 inference(modus_ponens,[status(thm)],[1176, 9666])).
% 2.22/2.43 tff(9668,plain,
% 2.22/2.43 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 2.22/2.43 inference(rewrite,[status(thm)],[])).
% 2.22/2.43 tff(9669,plain,
% 2.22/2.43 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 2.22/2.43 inference(quant_inst,[status(thm)],[])).
% 2.22/2.43 tff(9670,plain,
% 2.22/2.43 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.22/2.43 inference(modus_ponens,[status(thm)],[9669, 9668])).
% 2.22/2.43 tff(9671,plain,
% 2.22/2.43 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[9670, 58, 9667, 9663])).
% 2.22/2.43 tff(9672,plain,
% 2.22/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.43 inference(rewrite,[status(thm)],[])).
% 2.22/2.43 tff(9673,plain,
% 2.22/2.43 (((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))) <=> ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.43 inference(rewrite,[status(thm)],[])).
% 2.22/2.43 tff(9674,plain,
% 2.22/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 2.22/2.43 inference(monotonicity,[status(thm)],[9673])).
% 2.22/2.43 tff(9675,plain,
% 2.22/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.43 inference(transitivity,[status(thm)],[9674, 9672])).
% 2.22/2.43 tff(9676,plain,
% 2.22/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.22/2.43 inference(quant_inst,[status(thm)],[])).
% 2.22/2.43 tff(9677,plain,
% 2.22/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 2.22/2.43 inference(modus_ponens,[status(thm)],[9676, 9675])).
% 2.22/2.43 tff(9678,plain,
% 2.22/2.43 ($false),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[9677, 75, 3862, 9671, 9656, 5994])).
% 2.22/2.43 tff(9679,plain,((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.43 tff(9680,plain,
% 2.22/2.43 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[9679, 1918, 3954, 3989, 3862, 752, 698])).
% 2.22/2.43 tff(9681,plain,
% 2.22/2.43 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[813, 9680, 3966])).
% 2.22/2.43 tff(9682,plain,
% 2.22/2.43 (r(s(z), s(s(elem!1)))),
% 2.22/2.43 inference(modus_ponens,[status(thm)],[1918, 5543])).
% 2.22/2.43 tff(9683,plain,
% 2.22/2.43 (~r(elem!1, s(s(elem!1)))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[3615, 9682, 114])).
% 2.22/2.43 tff(9684,plain,
% 2.22/2.43 (b(elem!1, s(s(elem!1)))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[1617, 9683, 3432])).
% 2.22/2.43 tff(9685,plain,
% 2.22/2.43 (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[8735, 75, 9684, 9681, 707, 922])).
% 2.22/2.43 tff(9686,plain,
% 2.22/2.43 (r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[3083, 58, 3974, 9685])).
% 2.22/2.43 tff(9687,plain,
% 2.22/2.43 (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[8743, 75, 9684, 9681, 707])).
% 2.22/2.43 tff(9688,plain,
% 2.22/2.43 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[840, 58, 3959, 9687])).
% 2.22/2.43 tff(9689,plain,
% 2.22/2.43 (~r(z, s(s(elem!1)))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[5301, 9682, 1561])).
% 2.22/2.43 tff(9690,plain,
% 2.22/2.43 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[5576, 9689, 1892, 1083])).
% 2.22/2.43 tff(9691,plain,
% 2.22/2.43 (r(s(s(s(z))), s(s(elem!1)))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[62, 9690, 16])).
% 2.22/2.43 tff(9692,plain,
% 2.22/2.43 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.22/2.43 inference(modus_ponens,[status(thm)],[9691, 5537])).
% 2.22/2.43 tff(9693,plain,
% 2.22/2.43 ($false),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[8752, 37, 9692, 9688, 9686])).
% 2.22/2.43 tff(9694,plain,((~r(s(elem!1), s(s(elem!1)))) | (~(z = elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (s(s(s(z))) = s(s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~r(elem!1, s(z))) | (~r(s(z), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.43 tff(9695,plain,
% 2.22/2.43 (~r(s(elem!1), s(s(elem!1)))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[9694, 9630, 288, 9516, 6204, 9648, 9647, 9503, 9646, 9645, 9629, 698])).
% 2.22/2.43 tff(9696,plain,
% 2.22/2.43 (b(s(elem!1), s(s(elem!1)))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[1851, 9695, 3438])).
% 2.22/2.43 tff(9697,plain,
% 2.22/2.43 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[4280, 9696, 9645, 9644])).
% 2.22/2.43 tff(9698,plain,
% 2.22/2.43 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[1660, 9697, 5479])).
% 2.22/2.43 tff(9699,plain,
% 2.22/2.43 (~r(elem!1, s(s(elem!1)))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[3811, 9698, 3195])).
% 2.22/2.43 tff(9700,plain,
% 2.22/2.43 (b(elem!1, s(s(elem!1)))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[1617, 9699, 3432])).
% 2.22/2.43 tff(9701,plain,
% 2.22/2.43 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[5147, 75, 9700, 9630, 9516])).
% 2.22/2.43 tff(9702,plain,
% 2.22/2.43 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.22/2.43 inference(modus_ponens,[status(thm)],[9701, 5585])).
% 2.22/2.43 tff(9703,plain,
% 2.22/2.43 (r(s(s(s(z))), s(s(elem!1)))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[62, 9702, 6204])).
% 2.22/2.43 tff(9704,plain,
% 2.22/2.43 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.22/2.43 inference(modus_ponens,[status(thm)],[9703, 5537])).
% 2.22/2.43 tff(9705,plain,
% 2.22/2.43 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[8754, 9704, 3974, 3959, 9700, 9630, 9516])).
% 2.22/2.43 tff(9706,plain,
% 2.22/2.43 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[813, 9705, 3966])).
% 2.22/2.43 tff(9707,plain,
% 2.22/2.43 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[2998, 37, 9706, 9629])).
% 2.22/2.43 tff(9708,plain,
% 2.22/2.43 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[3010, 58, 3954, 9707])).
% 2.22/2.43 tff(9709,plain,
% 2.22/2.43 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[9654, 37, 698, 9706])).
% 2.22/2.43 tff(9710,plain,
% 2.22/2.43 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[1179, 58, 3989, 9709])).
% 2.22/2.43 tff(9711,plain,
% 2.22/2.43 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[9662, 37, 698, 9706])).
% 2.22/2.43 tff(9712,plain,
% 2.22/2.43 (~(s(s(s(s(z)))) = s(s(s(s(s(s(s(z))))))))),
% 2.22/2.43 inference(modus_ponens,[status(thm)],[3989, 9666])).
% 2.22/2.43 tff(9713,plain,
% 2.22/2.43 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[9670, 58, 9712, 9711])).
% 2.22/2.43 tff(9714,plain,
% 2.22/2.43 ($false),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[9677, 75, 9645, 9713, 9710, 9708])).
% 2.22/2.43 tff(9715,plain,(b(z, s(z)) | (~r(s(s(s(s(z)))), elem!1)) | (~(z = elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.22/2.43 tff(9716,plain,
% 2.22/2.43 (~r(elem!1, s(s(s(s(z)))))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[9715, 9501, 9474, 288, 9486])).
% 2.22/2.43 tff(9717,plain,
% 2.22/2.43 (b(elem!1, s(s(s(s(z)))))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[278, 3522, 9716])).
% 2.22/2.43 tff(9718,plain,
% 2.22/2.43 (~r(s(s(s(z))), elem!1)),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[9495, 114, 698, 288])).
% 2.22/2.43 tff(9719,plain,
% 2.22/2.43 (b(s(s(s(z))), elem!1)),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[1115, 9718, 4145])).
% 2.22/2.43 tff(9720,plain,
% 2.22/2.43 (b(s(s(s(elem!1))), elem!1)),
% 2.22/2.43 inference(modus_ponens,[status(thm)],[9719, 5490])).
% 2.22/2.43 tff(9721,plain,
% 2.22/2.43 (~b(s(s(z)), elem!1)),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[9626, 107, 288, 114, 9477, 9720, 506])).
% 2.22/2.43 tff(9722,plain,
% 2.22/2.43 (~b(s(s(elem!1)), elem!1)),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[3652, 9721, 288])).
% 2.22/2.43 tff(9723,plain,
% 2.22/2.43 (r(s(s(elem!1)), elem!1)),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[2673, 9722, 5484])).
% 2.22/2.43 tff(9724,plain,
% 2.22/2.43 (r(s(s(z)), elem!1)),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[104, 9721, 5480])).
% 2.22/2.43 tff(9725,plain,
% 2.22/2.43 (~r(s(s(z)), s(z))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[123, 9724, 114])).
% 2.22/2.43 tff(9726,plain,
% 2.22/2.43 (b(s(s(z)), s(z))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[153, 9725])).
% 2.22/2.43 tff(9727,plain,
% 2.22/2.43 (b(s(s(elem!1)), s(elem!1))),
% 2.22/2.43 inference(modus_ponens,[status(thm)],[9726, 3570])).
% 2.22/2.43 tff(9728,plain,
% 2.22/2.43 ((~b(elem!1, s(s(elem!1)))) <=> (~b(z, s(s(z))))),
% 2.22/2.43 inference(monotonicity,[status(thm)],[5549])).
% 2.22/2.43 tff(9729,plain,
% 2.22/2.43 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[3876, 58, 5701, 3873])).
% 2.22/2.43 tff(9730,plain,
% 2.22/2.43 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[1660, 3885, 5479])).
% 2.22/2.43 tff(9731,plain,
% 2.22/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.22/2.44 inference(rewrite,[status(thm)],[])).
% 2.22/2.44 tff(9732,plain,
% 2.22/2.44 (((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.22/2.44 inference(rewrite,[status(thm)],[])).
% 2.22/2.44 tff(9733,plain,
% 2.22/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))))),
% 2.22/2.44 inference(monotonicity,[status(thm)],[9732])).
% 2.22/2.44 tff(9734,plain,
% 2.22/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.22/2.44 inference(transitivity,[status(thm)],[9733, 9731])).
% 2.22/2.44 tff(9735,plain,
% 2.22/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(elem!1)))))),
% 2.22/2.44 inference(quant_inst,[status(thm)],[])).
% 2.22/2.44 tff(9736,plain,
% 2.22/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 2.22/2.44 inference(modus_ponens,[status(thm)],[9735, 9734])).
% 2.22/2.44 tff(9737,plain,
% 2.22/2.44 (~b(elem!1, s(s(elem!1)))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[9736, 75, 286, 9730, 9729])).
% 2.22/2.44 tff(9738,plain,
% 2.22/2.44 (~b(z, s(s(z)))),
% 2.22/2.44 inference(modus_ponens,[status(thm)],[9737, 9728])).
% 2.22/2.44 tff(9739,plain,
% 2.22/2.44 (b(s(s(z)), s(s(s(s(z)))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[3926, 9730, 3839])).
% 2.22/2.44 tff(9740,plain,
% 2.22/2.44 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.22/2.44 inference(monotonicity,[status(thm)],[290])).
% 2.22/2.44 tff(9741,plain,
% 2.22/2.44 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 2.22/2.44 inference(symmetry,[status(thm)],[9740])).
% 2.22/2.44 tff(9742,plain,
% 2.22/2.44 (b(s(s(s(s(z)))), s(s(z)))),
% 2.22/2.44 inference(modus_ponens,[status(thm)],[9729, 9741])).
% 2.22/2.44 tff(9743,plain,
% 2.22/2.44 (~b(s(elem!1), s(s(s(s(z)))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[3894, 2647, 698, 5479, 3069])).
% 2.22/2.44 tff(9744,plain,
% 2.22/2.44 (~b(s(z), s(s(s(s(z)))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[3857, 9743, 288])).
% 2.22/2.44 tff(9745,plain,
% 2.22/2.44 (r(s(z), s(s(s(s(z)))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[489, 9744])).
% 2.22/2.44 tff(9746,plain,
% 2.22/2.44 (r(s(elem!1), s(s(s(s(z)))))),
% 2.22/2.44 inference(modus_ponens,[status(thm)],[9745, 5478])).
% 2.22/2.44 tff(9747,plain,
% 2.22/2.44 ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) <=> (~b(s(s(s(z))), s(s(s(s(z))))))),
% 2.22/2.44 inference(monotonicity,[status(thm)],[3461])).
% 2.22/2.44 tff(9748,plain,
% 2.22/2.44 (b(elem!1, s(s(s(elem!1))))),
% 2.22/2.44 inference(modus_ponens,[status(thm)],[1307, 3477])).
% 2.22/2.44 tff(9749,assumption,(r(s(s(s(s(z)))), s(s(s(elem!1))))), introduced(assumption)).
% 2.22/2.44 tff(9750,plain,
% 2.22/2.44 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(z), s(s(s(z))))),
% 2.22/2.44 inference(monotonicity,[status(thm)],[3422, 3418])).
% 2.22/2.44 tff(9751,plain,
% 2.22/2.44 (r(s(z), s(s(s(z)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 2.22/2.44 inference(symmetry,[status(thm)],[9750])).
% 2.22/2.44 tff(9752,plain,
% 2.22/2.44 (r(s(elem!1), s(s(s(elem!1))))),
% 2.22/2.44 inference(modus_ponens,[status(thm)],[1265, 9751])).
% 2.22/2.44 tff(9753,plain,
% 2.22/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.22/2.44 inference(rewrite,[status(thm)],[])).
% 2.22/2.44 tff(9754,plain,
% 2.22/2.44 (((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.22/2.44 inference(rewrite,[status(thm)],[])).
% 2.22/2.44 tff(9755,plain,
% 2.22/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 2.22/2.44 inference(monotonicity,[status(thm)],[9754])).
% 2.22/2.44 tff(9756,plain,
% 2.22/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.22/2.44 inference(transitivity,[status(thm)],[9755, 9753])).
% 2.22/2.44 tff(9757,plain,
% 2.22/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.22/2.44 inference(quant_inst,[status(thm)],[])).
% 2.22/2.44 tff(9758,plain,
% 2.22/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(z))))))),
% 2.22/2.44 inference(modus_ponens,[status(thm)],[9757, 9756])).
% 2.22/2.44 tff(9759,plain,
% 2.22/2.44 ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[9758, 37, 1167])).
% 2.22/2.44 tff(9760,plain,
% 2.22/2.44 ($false),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[9759, 9752, 9749])).
% 2.22/2.44 tff(9761,plain,((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.44 tff(9762,plain,
% 2.22/2.44 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[9761, 1265, 1167, 288])).
% 2.22/2.44 tff(9763,plain,
% 2.22/2.44 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.22/2.44 inference(modus_ponens,[status(thm)],[9762, 3449])).
% 2.22/2.44 tff(9764,plain,
% 2.22/2.44 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[2898, 9763])).
% 2.22/2.44 tff(9765,plain,
% 2.22/2.44 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.22/2.44 inference(modus_ponens,[status(thm)],[9764, 3447])).
% 2.22/2.44 tff(9766,assumption,(b(s(s(s(s(z)))), s(s(s(elem!1))))), introduced(assumption)).
% 2.22/2.44 tff(9767,plain,
% 2.22/2.44 ($false),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[3541, 75, 286, 9766, 706, 5975])).
% 2.22/2.44 tff(9768,plain,((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.44 tff(9769,plain,
% 2.22/2.44 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[9768, 9765, 286, 9748])).
% 2.22/2.44 tff(9770,plain,
% 2.22/2.44 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.22/2.44 inference(modus_ponens,[status(thm)],[9769, 9747])).
% 2.22/2.44 tff(9771,plain,
% 2.22/2.44 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[575, 9770])).
% 2.22/2.44 tff(9772,plain,
% 2.22/2.44 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.22/2.44 inference(modus_ponens,[status(thm)],[9771, 3976])).
% 2.22/2.44 tff(9773,plain,
% 2.22/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.22/2.44 inference(rewrite,[status(thm)],[])).
% 2.22/2.44 tff(9774,plain,
% 2.22/2.44 (((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.22/2.44 inference(rewrite,[status(thm)],[])).
% 2.22/2.44 tff(9775,plain,
% 2.22/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~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(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 2.22/2.44 inference(monotonicity,[status(thm)],[9774])).
% 2.22/2.44 tff(9776,plain,
% 2.22/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~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(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.22/2.44 inference(transitivity,[status(thm)],[9775, 9773])).
% 2.22/2.44 tff(9777,plain,
% 2.22/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 2.22/2.44 inference(quant_inst,[status(thm)],[])).
% 2.22/2.44 tff(9778,plain,
% 2.22/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(z))))))),
% 2.22/2.44 inference(modus_ponens,[status(thm)],[9777, 9776])).
% 2.22/2.44 tff(9779,plain,
% 2.22/2.44 ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[9778, 37, 1167])).
% 2.22/2.44 tff(9780,plain,
% 2.22/2.44 ($false),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[9779, 9752, 9772])).
% 2.22/2.44 tff(9781,plain,((~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~(z = elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (elem!1 = s(s(s(z)))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.44 tff(9782,plain,
% 2.22/2.44 (~r(s(z), s(s(s(z))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[9781, 9746, 114, 5589, 286, 288])).
% 2.22/2.44 tff(9783,plain,
% 2.22/2.44 (b(s(z), s(s(s(z))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[1263, 9782])).
% 2.22/2.44 tff(9784,plain,
% 2.22/2.44 ((~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(z))), elem!1))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[3515, 484])).
% 2.22/2.44 tff(9785,plain,
% 2.22/2.44 (~r(s(s(s(z))), elem!1)),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[9784, 9783, 698, 114])).
% 2.22/2.44 tff(9786,plain,
% 2.22/2.44 (b(s(s(s(z))), elem!1)),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[1115, 9785, 4145])).
% 2.22/2.44 tff(9787,plain,
% 2.22/2.44 (b(s(s(s(elem!1))), elem!1)),
% 2.22/2.44 inference(modus_ponens,[status(thm)],[9786, 5490])).
% 2.22/2.44 tff(9788,plain,
% 2.22/2.44 (b(s(elem!1), s(s(s(elem!1))))),
% 2.22/2.44 inference(modus_ponens,[status(thm)],[9783, 3831])).
% 2.22/2.44 tff(9789,plain,
% 2.22/2.44 (~b(elem!1, s(s(s(elem!1))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[930, 9788, 921, 9787])).
% 2.22/2.44 tff(9790,plain,
% 2.22/2.44 (r(elem!1, s(s(s(elem!1))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[5967, 9789, 5796])).
% 2.22/2.44 tff(9791,plain,
% 2.22/2.44 (r(elem!1, s(s(elem!1)))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[1617, 9737, 3432])).
% 2.22/2.44 tff(9792,plain,
% 2.22/2.44 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[9601, 9791, 288, 9790])).
% 2.22/2.44 tff(9793,plain,
% 2.22/2.44 (b(s(s(s(z))), s(s(elem!1)))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[62, 9792, 9477])).
% 2.22/2.44 tff(9794,plain,
% 2.22/2.44 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 2.22/2.44 inference(monotonicity,[status(thm)],[290])).
% 2.22/2.44 tff(9795,plain,
% 2.22/2.44 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(z)))),
% 2.22/2.44 inference(symmetry,[status(thm)],[9794])).
% 2.22/2.44 tff(9796,plain,
% 2.22/2.44 (b(s(s(s(z))), s(s(z)))),
% 2.22/2.44 inference(modus_ponens,[status(thm)],[3628, 9795])).
% 2.22/2.44 tff(9797,assumption,(~b(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 2.22/2.44 tff(9798,plain,
% 2.22/2.44 ($false),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[9797, 9796])).
% 2.22/2.44 tff(9799,plain,((~b(s(s(s(z))), s(s(elem!1)))) | b(s(s(s(z))), s(s(z))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.44 tff(9800,plain,
% 2.22/2.44 (b(s(s(s(z))), s(s(z)))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[9799, 9793, 288])).
% 2.22/2.44 tff(9801,plain,
% 2.22/2.44 (~b(s(z), s(s(z)))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[1210, 9800, 9783, 9742, 9739])).
% 2.22/2.44 tff(9802,plain,
% 2.22/2.44 (r(s(z), s(s(z)))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[416, 9801])).
% 2.22/2.44 tff(9803,plain,
% 2.22/2.44 (~r(z, s(s(z)))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[2005, 9802, 506])).
% 2.22/2.44 tff(9804,plain,
% 2.22/2.44 (b(z, s(s(z)))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[351, 9803])).
% 2.22/2.44 tff(9805,plain,
% 2.22/2.44 ($false),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[9804, 9738])).
% 2.22/2.44 tff(9806,plain,((~r(s(s(elem!1)), elem!1)) | (~(z = elem!1)) | (~r(z, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~b(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.44 tff(9807,plain,
% 2.22/2.44 ($false),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[9806, 9727, 3569, 506, 286, 698, 288, 114, 9723])).
% 2.22/2.44 tff(9808,plain,((~b(s(z), elem!1)) | (~r(z, s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~(z = elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.44 tff(9809,plain,
% 2.22/2.44 (~b(s(z), elem!1)),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[9808, 9487, 9717, 9474, 288, 9492])).
% 2.22/2.44 tff(9810,plain,
% 2.22/2.44 (r(s(z), elem!1)),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[601, 9809, 9501])).
% 2.22/2.44 tff(9811,plain,
% 2.22/2.44 (r(s(elem!1), elem!1)),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[4005, 9810, 288])).
% 2.22/2.44 tff(9812,plain,
% 2.22/2.44 (r(s(z), z)),
% 2.22/2.44 inference(modus_ponens,[status(thm)],[9811, 9500])).
% 2.22/2.44 tff(9813,plain,
% 2.22/2.44 (~r(s(z), s(s(s(s(z)))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[2586, 9812, 9485])).
% 2.22/2.44 tff(9814,plain,
% 2.22/2.44 (b(s(z), s(s(s(s(z)))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[489, 9813])).
% 2.22/2.44 tff(9815,plain,
% 2.22/2.44 (b(s(elem!1), s(s(s(s(z)))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[3857, 9814, 288])).
% 2.22/2.44 tff(9816,plain,
% 2.22/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(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(X1, 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(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.22/2.44 inference(rewrite,[status(thm)],[])).
% 2.22/2.44 tff(9817,plain,
% 2.22/2.44 (((~b(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.22/2.44 inference(rewrite,[status(thm)],[])).
% 2.22/2.44 tff(9818,plain,
% 2.22/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 2.22/2.44 inference(monotonicity,[status(thm)],[9817])).
% 2.22/2.44 tff(9819,plain,
% 2.22/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.22/2.44 inference(transitivity,[status(thm)],[9818, 9816])).
% 2.22/2.44 tff(9820,plain,
% 2.22/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.22/2.44 inference(quant_inst,[status(thm)],[])).
% 2.22/2.44 tff(9821,plain,
% 2.22/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(s(z))))))),
% 2.22/2.44 inference(modus_ponens,[status(thm)],[9820, 9819])).
% 2.22/2.44 tff(9822,plain,
% 2.22/2.44 ($false),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[9821, 75, 286, 5975, 3862, 922, 4272])).
% 2.22/2.44 tff(9823,plain,((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.44 tff(9824,plain,
% 2.22/2.44 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[9823, 9717, 9815, 9498, 9490])).
% 2.22/2.45 tff(9825,plain,
% 2.22/2.45 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.22/2.45 inference(modus_ponens,[status(thm)],[9824, 3834])).
% 2.22/2.45 tff(9826,plain,
% 2.22/2.45 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[575, 9825])).
% 2.22/2.45 tff(9827,plain,
% 2.22/2.45 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.22/2.45 inference(modus_ponens,[status(thm)],[9826, 3976])).
% 2.22/2.45 tff(9828,plain,
% 2.22/2.45 (b(s(s(s(z))), z)),
% 2.22/2.45 inference(modus_ponens,[status(thm)],[9497, 5488])).
% 2.22/2.45 tff(9829,plain,
% 2.22/2.45 (~r(s(s(z)), elem!1)),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[9510, 9814, 9474, 288, 9492])).
% 2.22/2.45 tff(9830,plain,
% 2.22/2.45 (b(s(s(z)), elem!1)),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[104, 9829, 5480])).
% 2.22/2.45 tff(9831,plain,
% 2.22/2.45 (b(s(s(elem!1)), z)),
% 2.22/2.45 inference(modus_ponens,[status(thm)],[9830, 5540])).
% 2.22/2.45 tff(9832,plain,
% 2.22/2.45 (b(s(s(elem!1)), elem!1)),
% 2.22/2.45 inference(modus_ponens,[status(thm)],[9830, 3648])).
% 2.22/2.45 tff(9833,plain,
% 2.22/2.45 (~r(s(elem!1), s(s(elem!1)))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[9694, 9832, 9474, 288, 9477, 9498, 9831, 9492, 9828, 9812, 9811, 9815])).
% 2.22/2.45 tff(9834,plain,
% 2.22/2.45 (b(s(elem!1), s(s(elem!1)))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[1851, 9833, 3438])).
% 2.22/2.45 tff(9835,plain,
% 2.22/2.45 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[4280, 9834, 9815, 9490])).
% 2.22/2.45 tff(9836,plain,
% 2.22/2.45 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[1660, 9835, 5479])).
% 2.22/2.45 tff(9837,plain,
% 2.22/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(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(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.22/2.45 inference(rewrite,[status(thm)],[])).
% 2.22/2.45 tff(9838,plain,
% 2.22/2.45 (((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.22/2.45 inference(rewrite,[status(thm)],[])).
% 2.22/2.45 tff(9839,plain,
% 2.22/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(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(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))))),
% 2.22/2.45 inference(monotonicity,[status(thm)],[9838])).
% 2.22/2.45 tff(9840,plain,
% 2.22/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(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(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.22/2.45 inference(transitivity,[status(thm)],[9839, 9837])).
% 2.22/2.45 tff(9841,plain,
% 2.22/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.22/2.45 inference(quant_inst,[status(thm)],[])).
% 2.22/2.45 tff(9842,plain,
% 2.22/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 2.22/2.45 inference(modus_ponens,[status(thm)],[9841, 9840])).
% 2.22/2.45 tff(9843,plain,
% 2.22/2.45 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[9842, 37, 9836, 9827])).
% 2.22/2.45 tff(9844,plain,
% 2.22/2.45 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.22/2.45 inference(modus_ponens,[status(thm)],[9843, 9478])).
% 2.22/2.45 tff(9845,plain,
% 2.22/2.45 (b(s(s(s(z))), s(s(elem!1)))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[62, 9844, 9477])).
% 2.22/2.45 tff(9846,plain,
% 2.22/2.45 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.22/2.45 inference(modus_ponens,[status(thm)],[9845, 9476])).
% 2.22/2.45 tff(9847,plain,
% 2.22/2.45 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.22/2.45 inference(symmetry,[status(thm)],[4223])).
% 2.22/2.45 tff(9848,plain,
% 2.22/2.45 (~r(s(s(elem!1)), s(s(s(z))))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[4241, 9826, 9836])).
% 2.22/2.45 tff(9849,plain,
% 2.22/2.45 (b(s(s(elem!1)), s(s(s(z))))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[1936, 9848, 4222])).
% 2.22/2.45 tff(9850,plain,
% 2.22/2.45 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.22/2.45 inference(modus_ponens,[status(thm)],[9849, 9847])).
% 2.22/2.45 tff(9851,plain,
% 2.22/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.22/2.45 inference(rewrite,[status(thm)],[])).
% 2.22/2.45 tff(9852,plain,
% 2.22/2.45 (((~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(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(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(s(s(elem!1))), s(s(elem!1)))))),
% 2.22/2.45 inference(rewrite,[status(thm)],[])).
% 2.22/2.45 tff(9853,plain,
% 2.22/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(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(X1, 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(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 2.22/2.45 inference(monotonicity,[status(thm)],[9852])).
% 2.22/2.45 tff(9854,plain,
% 2.22/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(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(X1, 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(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.22/2.45 inference(transitivity,[status(thm)],[9853, 9851])).
% 2.22/2.45 tff(9855,plain,
% 2.22/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 2.22/2.45 inference(quant_inst,[status(thm)],[])).
% 2.22/2.45 tff(9856,plain,
% 2.22/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 2.22/2.45 inference(modus_ponens,[status(thm)],[9855, 9854])).
% 2.22/2.45 tff(9857,plain,
% 2.22/2.45 (~b(s(elem!1), s(s(s(elem!1))))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[9856, 75, 9834, 9850, 9846])).
% 2.22/2.45 tff(9858,plain,
% 2.22/2.45 (~b(s(z), s(s(s(z))))),
% 2.22/2.45 inference(modus_ponens,[status(thm)],[9857, 5582])).
% 2.22/2.45 tff(9859,plain,
% 2.22/2.45 (r(s(z), s(s(s(z))))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[1263, 9858])).
% 2.22/2.45 tff(9860,plain,
% 2.22/2.45 (~r(elem!1, s(s(s(z))))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[1274, 9859, 9492])).
% 2.22/2.45 tff(9861,plain,
% 2.22/2.45 (b(elem!1, s(s(s(z))))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[1279, 9860, 5589])).
% 2.22/2.45 tff(9862,plain,
% 2.22/2.45 (b(elem!1, s(s(s(elem!1))))),
% 2.22/2.45 inference(modus_ponens,[status(thm)],[9861, 5586])).
% 2.22/2.45 tff(9863,plain,
% 2.22/2.45 ($false),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[5609, 75, 9832, 9862, 9498, 9846])).
% 2.22/2.45 tff(9864,plain,((~(z = elem!1)) | b(elem!1, s(z)) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.22/2.45 tff(9865,plain,
% 2.22/2.45 (~(z = elem!1)),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[9864, 14, 13])).
% 2.22/2.45 tff(9866,plain,
% 2.22/2.45 (b(z, elem!1)),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[298, 9865, 13])).
% 2.22/2.45 tff(9867,plain,
% 2.22/2.45 (~(elem!1 = z)),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[304, 9865])).
% 2.22/2.45 tff(9868,assumption,(~r(s(s(z)), elem!1)), introduced(assumption)).
% 2.22/2.45 tff(9869,plain,
% 2.22/2.45 (s(s(z)) = elem!1),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[104, 9868, 99])).
% 2.22/2.45 tff(9870,plain,
% 2.22/2.45 (~b(s(s(z)), s(z))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[316, 9869, 14])).
% 2.22/2.45 tff(9871,plain,
% 2.22/2.45 (r(s(s(z)), s(z))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[153, 9870])).
% 2.22/2.45 tff(9872,plain,
% 2.22/2.45 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(z))),
% 2.22/2.45 inference(monotonicity,[status(thm)],[17])).
% 2.22/2.45 tff(9873,plain,
% 2.22/2.45 (r(s(s(z)), s(z)) <=> r(s(s(z)), elem!1)),
% 2.22/2.45 inference(symmetry,[status(thm)],[9872])).
% 2.22/2.45 tff(9874,plain,
% 2.22/2.45 (r(s(s(z)), elem!1)),
% 2.22/2.45 inference(modus_ponens,[status(thm)],[115, 9873])).
% 2.22/2.45 tff(9875,plain,
% 2.22/2.45 ($false),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[9868, 9874])).
% 2.22/2.45 tff(9876,plain,((~(elem!1 = s(z))) | r(s(s(z)), elem!1) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.45 tff(9877,plain,
% 2.22/2.45 (~(elem!1 = s(z))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[9876, 9871, 9868])).
% 2.22/2.45 tff(9878,plain,
% 2.22/2.45 (r(elem!1, s(z))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[89, 9877, 14])).
% 2.22/2.45 tff(9879,plain,
% 2.22/2.45 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[1013, 9869])).
% 2.22/2.45 tff(9880,plain,
% 2.22/2.45 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.22/2.45 inference(symmetry,[status(thm)],[9879])).
% 2.22/2.45 tff(9881,plain,
% 2.22/2.45 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 2.22/2.45 inference(monotonicity,[status(thm)],[9880])).
% 2.22/2.45 tff(9882,plain,
% 2.22/2.45 (r(s(s(elem!1)), elem!1)),
% 2.22/2.45 inference(modus_ponens,[status(thm)],[698, 9881])).
% 2.22/2.45 tff(9883,plain,
% 2.22/2.45 (~r(elem!1, z)),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[4786, 9882, 9878])).
% 2.22/2.45 tff(9884,plain,
% 2.22/2.45 (b(s(z), s(s(z))) <=> b(s(z), elem!1)),
% 2.22/2.45 inference(monotonicity,[status(thm)],[9869])).
% 2.22/2.45 tff(9885,plain,
% 2.22/2.45 (b(s(z), elem!1) <=> b(s(z), s(s(z)))),
% 2.22/2.45 inference(symmetry,[status(thm)],[9884])).
% 2.22/2.45 tff(9886,plain,
% 2.22/2.45 (~(s(z) = elem!1)),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[97, 9877])).
% 2.22/2.45 tff(9887,plain,
% 2.22/2.45 (b(s(z), elem!1)),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[601, 9886, 9475])).
% 2.22/2.45 tff(9888,plain,
% 2.22/2.45 (b(s(z), s(s(z)))),
% 2.22/2.45 inference(modus_ponens,[status(thm)],[9887, 9885])).
% 2.22/2.45 tff(9889,plain,
% 2.22/2.45 (b(z, s(s(z))) <=> b(z, elem!1)),
% 2.22/2.45 inference(monotonicity,[status(thm)],[9869])).
% 2.22/2.45 tff(9890,plain,
% 2.22/2.45 (b(z, elem!1) <=> b(z, s(s(z)))),
% 2.22/2.45 inference(symmetry,[status(thm)],[9889])).
% 2.22/2.45 tff(9891,plain,
% 2.22/2.45 (b(z, s(s(z)))),
% 2.22/2.45 inference(modus_ponens,[status(thm)],[1518, 9890])).
% 2.22/2.45 tff(9892,plain,
% 2.22/2.45 (~b(s(s(z)), z)),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[410, 9891, 372, 9888])).
% 2.22/2.45 tff(9893,plain,
% 2.22/2.45 (b(s(s(z)), z) <=> b(elem!1, z)),
% 2.22/2.45 inference(monotonicity,[status(thm)],[310])).
% 2.22/2.45 tff(9894,plain,
% 2.22/2.45 (b(elem!1, z) <=> b(s(s(z)), z)),
% 2.22/2.45 inference(symmetry,[status(thm)],[9893])).
% 2.22/2.45 tff(9895,plain,
% 2.22/2.45 (b(s(s(z)), z)),
% 2.22/2.45 inference(modus_ponens,[status(thm)],[1958, 9894])).
% 2.22/2.45 tff(9896,plain,
% 2.22/2.45 ($false),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[197, 9895])).
% 2.22/2.45 tff(9897,plain,((~b(elem!1, z)) | b(s(s(z)), z) | (~(s(s(z)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.45 tff(9898,plain,
% 2.22/2.45 (~b(elem!1, z)),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[9897, 9892, 9869])).
% 2.22/2.45 tff(9899,plain,
% 2.22/2.45 ($false),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[387, 9898, 9883, 353])).
% 2.22/2.45 tff(9900,plain,(r(s(s(z)), elem!1) | (elem!1 = z) | (~b(z, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | r(s(z), elem!1) | b(elem!1, s(z)) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.22/2.45 tff(9901,plain,
% 2.22/2.45 (r(s(s(z)), elem!1)),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[9900, 372, 353, 698, 1518, 9475, 14, 99])).
% 2.22/2.45 tff(9902,plain,
% 2.22/2.45 (~r(elem!1, s(z))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[123, 115, 106])).
% 2.22/2.45 tff(9903,plain,
% 2.22/2.45 (elem!1 = s(z)),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[89, 9902, 14])).
% 2.22/2.45 tff(9904,plain,
% 2.22/2.45 (s(elem!1) = s(s(z))),
% 2.22/2.45 inference(monotonicity,[status(thm)],[9903])).
% 2.22/2.45 tff(9905,plain,
% 2.22/2.45 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 2.22/2.45 inference(monotonicity,[status(thm)],[9904])).
% 2.22/2.45 tff(9906,plain,
% 2.22/2.45 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 2.22/2.45 inference(symmetry,[status(thm)],[9905])).
% 2.22/2.45 tff(9907,plain,
% 2.22/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)))),
% 2.22/2.45 inference(rewrite,[status(thm)],[])).
% 2.22/2.45 tff(9908,plain,
% 2.22/2.45 (((~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)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)))),
% 2.22/2.45 inference(rewrite,[status(thm)],[])).
% 2.22/2.45 tff(9909,plain,
% 2.22/2.45 (((~![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(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)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1))))),
% 2.22/2.45 inference(monotonicity,[status(thm)],[9908])).
% 2.22/2.45 tff(9910,plain,
% 2.22/2.45 (((~![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(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)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)))),
% 2.22/2.45 inference(transitivity,[status(thm)],[9909, 9907])).
% 2.22/2.45 tff(9911,plain,
% 2.22/2.45 ((~![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(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)))))))),
% 2.22/2.45 inference(quant_inst,[status(thm)],[])).
% 2.22/2.45 tff(9912,plain,
% 2.22/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1))),
% 2.22/2.45 inference(modus_ponens,[status(thm)],[9911, 9910])).
% 2.22/2.45 tff(9913,plain,
% 2.22/2.45 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[9912, 37, 106, 698])).
% 2.22/2.45 tff(9914,plain,
% 2.22/2.45 (b(s(s(z)), s(s(s(s(z)))))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[465, 9913])).
% 2.22/2.45 tff(9915,plain,
% 2.22/2.45 (b(s(elem!1), s(s(s(s(z)))))),
% 2.22/2.45 inference(modus_ponens,[status(thm)],[9914, 9906])).
% 2.22/2.45 tff(9916,plain,
% 2.22/2.45 ((elem!1 = s(s(elem!1))) <=> (s(z) = s(s(elem!1)))),
% 2.22/2.45 inference(monotonicity,[status(thm)],[9903])).
% 2.22/2.45 tff(9917,plain,
% 2.22/2.45 ((elem!1 = s(s(elem!1))) <=> (s(s(elem!1)) = s(z))),
% 2.22/2.45 inference(transitivity,[status(thm)],[9916, 1882])).
% 2.22/2.45 tff(9918,plain,
% 2.22/2.45 ((s(s(elem!1)) = s(z)) <=> (elem!1 = s(s(elem!1)))),
% 2.22/2.45 inference(symmetry,[status(thm)],[9917])).
% 2.22/2.45 tff(9919,plain,
% 2.22/2.45 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 2.22/2.45 inference(transitivity,[status(thm)],[9918, 4928])).
% 2.22/2.45 tff(9920,plain,
% 2.22/2.45 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = elem!1))),
% 2.22/2.45 inference(monotonicity,[status(thm)],[9919])).
% 2.22/2.45 tff(9921,plain,
% 2.22/2.45 (~(s(s(elem!1)) = elem!1)),
% 2.22/2.45 inference(modus_ponens,[status(thm)],[556, 9920])).
% 2.22/2.45 tff(9922,plain,
% 2.22/2.45 (r(s(s(elem!1)), elem!1)),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[2673, 9921, 1])).
% 2.22/2.45 tff(9923,plain,
% 2.22/2.45 (s(s(s(z))) = s(s(elem!1))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[84, 9903])).
% 2.22/2.45 tff(9924,plain,
% 2.22/2.45 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 2.22/2.45 inference(monotonicity,[status(thm)],[9923])).
% 2.22/2.45 tff(9925,plain,
% 2.22/2.45 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 2.22/2.45 inference(transitivity,[status(thm)],[9924, 3863])).
% 2.22/2.45 tff(9926,plain,
% 2.22/2.45 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(s(z))))))),
% 2.22/2.45 inference(monotonicity,[status(thm)],[9925])).
% 2.22/2.45 tff(9927,plain,
% 2.22/2.45 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 2.22/2.45 inference(modus_ponens,[status(thm)],[264, 9926])).
% 2.22/2.45 tff(9928,plain,
% 2.22/2.45 (~b(s(s(elem!1)), s(elem!1))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[3894, 9927, 698, 9922, 9915])).
% 2.22/2.45 tff(9929,plain,
% 2.22/2.45 (r(s(s(elem!1)), s(s(z)))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[4966, 9928, 9903])).
% 2.22/2.45 tff(9930,plain,
% 2.22/2.45 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(z))),
% 2.22/2.45 inference(monotonicity,[status(thm)],[9903])).
% 2.22/2.45 tff(9931,plain,
% 2.22/2.45 ((~b(s(s(elem!1)), elem!1)) <=> (~b(s(s(elem!1)), s(z)))),
% 2.22/2.45 inference(monotonicity,[status(thm)],[9930])).
% 2.22/2.45 tff(9932,plain,
% 2.22/2.45 (~b(s(s(elem!1)), s(z))),
% 2.22/2.45 inference(modus_ponens,[status(thm)],[1, 9931])).
% 2.22/2.45 tff(9933,plain,
% 2.22/2.45 (r(s(s(elem!1)), s(z))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[561, 9932])).
% 2.22/2.45 tff(9934,plain,
% 2.22/2.45 ($false),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[500, 37, 9933, 115, 9929])).
% 2.22/2.45 tff(9935,plain,((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), elem!1)) | b(s(s(elem!1)), elem!1) | b(elem!1, s(z)) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.45 tff(9936,plain,
% 2.22/2.45 (~r(s(s(z)), s(z))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[9935, 9901, 1, 14, 698])).
% 2.22/2.45 tff(9937,plain,
% 2.22/2.45 (b(s(s(z)), s(z))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[153, 9936])).
% 2.22/2.45 tff(9938,plain,
% 2.22/2.45 (~(elem!1 = s(z))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[358, 9937, 99])).
% 2.22/2.45 tff(9939,plain,
% 2.22/2.45 (~(s(z) = elem!1)),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[97, 9938])).
% 2.22/2.45 tff(9940,plain,
% 2.22/2.45 (b(s(z), elem!1)),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[601, 9939, 9475])).
% 2.22/2.45 tff(9941,plain,
% 2.22/2.45 (r(elem!1, s(z))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[89, 9938, 14])).
% 2.22/2.45 tff(9942,plain,
% 2.22/2.45 (~r(elem!1, z)),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[211, 9941, 9901])).
% 2.22/2.45 tff(9943,plain,
% 2.22/2.45 (b(elem!1, z)),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[387, 9942, 353])).
% 2.22/2.45 tff(9944,plain,
% 2.22/2.45 ($false),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[4527, 75, 1518, 9943, 372, 9940])).
% 2.22/2.45 tff(9945,plain,((~b(z, s(z))) | (~b(z, elem!1)) | (elem!1 = z) | r(s(z), elem!1) | b(elem!1, s(z)) | b(s(s(z)), elem!1) | b(s(s(elem!1)), elem!1) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.45 tff(9946,plain,
% 2.22/2.45 (~b(z, s(z))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[9945, 1, 9867, 9475, 14, 99, 9866, 9474])).
% 2.22/2.45 tff(9947,plain,
% 2.22/2.45 (r(z, s(z))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[187, 9946])).
% 2.22/2.45 tff(9948,plain,
% 2.22/2.45 (~(s(z) = elem!1)),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[2724, 9947, 13])).
% 2.22/2.45 tff(9949,plain,
% 2.22/2.45 (b(s(z), elem!1)),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[601, 9948, 9475])).
% 2.22/2.45 tff(9950,plain,
% 2.22/2.45 (~b(s(s(elem!1)), s(z))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[8581, 1602, 14])).
% 2.22/2.45 tff(9951,plain,
% 2.22/2.45 (r(s(s(elem!1)), s(z))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[561, 9950])).
% 2.22/2.45 tff(9952,plain,
% 2.22/2.45 (~r(s(s(elem!1)), z)),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[6190, 9951, 506])).
% 2.22/2.45 tff(9953,plain,
% 2.22/2.45 (b(s(s(elem!1)), z)),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[2696, 9952])).
% 2.22/2.45 tff(9954,plain,
% 2.22/2.45 (b(z, elem!1) <=> b(z, s(s(elem!1)))),
% 2.22/2.45 inference(monotonicity,[status(thm)],[1602])).
% 2.22/2.45 tff(9955,plain,
% 2.22/2.45 (b(z, s(s(elem!1)))),
% 2.22/2.45 inference(modus_ponens,[status(thm)],[9866, 9954])).
% 2.22/2.45 tff(9956,plain,
% 2.22/2.45 (~(elem!1 = s(z))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[111, 2725])).
% 2.22/2.45 tff(9957,plain,
% 2.22/2.45 (r(elem!1, s(z))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[89, 9956, 14])).
% 2.22/2.45 tff(9958,plain,
% 2.22/2.45 (r(elem!1, s(s(elem!1))) <=> r(elem!1, elem!1)),
% 2.22/2.45 inference(monotonicity,[status(thm)],[2323])).
% 2.22/2.45 tff(9959,plain,
% 2.22/2.45 (r(elem!1, elem!1) <=> r(elem!1, s(s(elem!1)))),
% 2.22/2.45 inference(symmetry,[status(thm)],[9958])).
% 2.22/2.45 tff(9960,plain,
% 2.22/2.45 ((~r(elem!1, elem!1)) <=> (~r(elem!1, s(s(elem!1))))),
% 2.22/2.45 inference(monotonicity,[status(thm)],[9959])).
% 2.22/2.45 tff(9961,plain,
% 2.22/2.45 (~r(elem!1, s(s(elem!1)))),
% 2.22/2.45 inference(modus_ponens,[status(thm)],[6307, 9960])).
% 2.22/2.45 tff(9962,plain,
% 2.22/2.45 (~r(s(s(s(z))), elem!1)),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[4675, 9961, 506, 9957, 107, 2267, 13])).
% 2.22/2.45 tff(9963,plain,
% 2.22/2.45 (b(s(s(s(z))), elem!1)),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[1115, 9962, 2267])).
% 2.22/2.45 tff(9964,plain,
% 2.22/2.45 (b(s(s(s(z))), s(s(elem!1)))),
% 2.22/2.45 inference(modus_ponens,[status(thm)],[9963, 2266])).
% 2.22/2.45 tff(9965,plain,
% 2.22/2.45 (~b(s(s(s(z))), z)),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[7537, 75, 9964, 9955, 9953])).
% 2.22/2.45 tff(9966,plain,
% 2.22/2.45 (r(s(s(s(z))), z)),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[1334, 58, 221, 9965])).
% 2.22/2.45 tff(9967,plain,
% 2.22/2.45 (b(s(z), s(s(elem!1)))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[2329, 1602, 107])).
% 2.22/2.45 tff(9968,plain,
% 2.22/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.22/2.45 inference(rewrite,[status(thm)],[])).
% 2.22/2.45 tff(9969,plain,
% 2.22/2.45 (((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.22/2.45 inference(rewrite,[status(thm)],[])).
% 2.22/2.45 tff(9970,plain,
% 2.22/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 2.22/2.45 inference(monotonicity,[status(thm)],[9969])).
% 2.22/2.45 tff(9971,plain,
% 2.22/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.22/2.46 inference(transitivity,[status(thm)],[9970, 9968])).
% 2.22/2.46 tff(9972,plain,
% 2.22/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))))),
% 2.22/2.46 inference(quant_inst,[status(thm)],[])).
% 2.22/2.46 tff(9973,plain,
% 2.22/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 2.22/2.46 inference(modus_ponens,[status(thm)],[9972, 9971])).
% 2.22/2.46 tff(9974,plain,
% 2.22/2.46 (~b(s(s(s(z))), s(z))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[9973, 75, 9967, 9964, 9955, 9953])).
% 2.22/2.46 tff(9975,plain,
% 2.22/2.46 (r(s(s(s(z))), s(z))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[1081, 9974])).
% 2.22/2.46 tff(9976,plain,
% 2.22/2.46 ($false),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[6259, 37, 506, 9975, 9966])).
% 2.22/2.46 tff(9977,plain,((~(elem!1 = s(s(elem!1)))) | (~r(z, s(z))) | (~b(s(z), elem!1)) | r(z, elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.46 tff(9978,plain,
% 2.22/2.46 (~(elem!1 = s(s(elem!1)))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[9977, 9947, 9949, 13, 14])).
% 2.22/2.46 tff(9979,plain,
% 2.22/2.46 (~(s(s(elem!1)) = elem!1)),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[2555, 9978])).
% 2.22/2.46 tff(9980,plain,
% 2.22/2.46 (r(s(s(elem!1)), elem!1)),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[2673, 9979, 1])).
% 2.22/2.46 tff(9981,plain,
% 2.22/2.46 (~(s(s(elem!1)) = s(s(z)))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[237, 9865])).
% 2.22/2.46 tff(9982,plain,
% 2.22/2.46 (~b(s(s(z)), s(z))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[316, 310, 14])).
% 2.22/2.46 tff(9983,plain,
% 2.22/2.46 (r(s(s(z)), s(z))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[153, 9982])).
% 2.22/2.46 tff(9984,plain,
% 2.22/2.46 (~r(z, s(s(z)))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[6456, 9983, 506])).
% 2.22/2.46 tff(9985,plain,
% 2.22/2.46 (b(z, s(s(z)))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[351, 9984])).
% 2.22/2.46 tff(9986,plain,
% 2.22/2.46 (~r(elem!1, z)),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[177, 9957, 506])).
% 2.22/2.46 tff(9987,plain,
% 2.22/2.46 (b(elem!1, z)),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[387, 9986, 9867])).
% 2.22/2.46 tff(9988,plain,
% 2.22/2.46 (b(s(s(z)), z)),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[9897, 310, 9987])).
% 2.22/2.46 tff(9989,plain,
% 2.22/2.46 (~b(s(z), z)),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[2625, 9986, 13, 9865, 107])).
% 2.22/2.46 tff(9990,plain,
% 2.22/2.46 (r(s(z), z)),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[169, 9989])).
% 2.22/2.46 tff(9991,assumption,(~(s(z) = s(elem!1))), introduced(assumption)).
% 2.22/2.46 tff(9992,plain,
% 2.22/2.46 (~b(s(z), s(elem!1))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[3219, 921, 107, 1958, 1518])).
% 2.22/2.46 tff(9993,plain,
% 2.22/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 2.22/2.46 inference(rewrite,[status(thm)],[])).
% 2.22/2.46 tff(9994,plain,
% 2.22/2.46 (((~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 2.22/2.46 inference(rewrite,[status(thm)],[])).
% 2.22/2.46 tff(9995,plain,
% 2.22/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))))),
% 2.22/2.46 inference(monotonicity,[status(thm)],[9994])).
% 2.22/2.46 tff(9996,plain,
% 2.22/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 2.22/2.46 inference(transitivity,[status(thm)],[9995, 9993])).
% 2.22/2.46 tff(9997,plain,
% 2.22/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1), z)) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))),
% 2.22/2.46 inference(quant_inst,[status(thm)],[])).
% 2.22/2.46 tff(9998,plain,
% 2.22/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))),
% 2.22/2.46 inference(modus_ponens,[status(thm)],[9997, 9996])).
% 2.22/2.46 tff(9999,plain,
% 2.22/2.46 ($false),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[9998, 75, 1958, 370, 401, 921, 798])).
% 2.22/2.46 tff(10000,plain,((~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.46 tff(10001,plain,
% 2.22/2.46 (~b(s(elem!1), z)),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[10000, 921, 1958, 401, 370])).
% 2.22/2.46 tff(10002,plain,
% 2.22/2.46 (r(s(elem!1), z)),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[766, 10001])).
% 2.22/2.46 tff(10003,plain,
% 2.22/2.46 (~r(s(z), s(elem!1))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[1761, 10002, 1561])).
% 2.22/2.46 tff(10004,plain,
% 2.22/2.46 ($false),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[8483, 58, 10003, 9992, 9991])).
% 2.22/2.46 tff(10005,plain,((~b(s(elem!1), elem!1)) | (s(z) = s(elem!1)) | (~r(s(z), z)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.46 tff(10006,plain,
% 2.22/2.46 (~b(s(elem!1), elem!1)),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[10005, 8444, 9990, 107, 9987, 9866, 9988, 9985])).
% 2.22/2.46 tff(10007,plain,
% 2.22/2.46 (~b(s(s(s(z))), elem!1)),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[1122, 10006, 1047])).
% 2.22/2.46 tff(10008,plain,
% 2.22/2.46 (r(s(s(s(z))), elem!1)),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[1115, 10007, 8308])).
% 2.22/2.46 tff(10009,plain,
% 2.22/2.46 (r(elem!1, s(s(elem!1)))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[4675, 10008, 506, 9957, 107, 8308, 13])).
% 2.22/2.46 tff(10010,plain,
% 2.22/2.46 (~r(s(z), s(s(elem!1)))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[3615, 10009, 9957])).
% 2.22/2.46 tff(10011,plain,
% 2.22/2.46 ((s(s(elem!1)) = s(s(z))) <=> (s(s(elem!1)) = elem!1)),
% 2.22/2.46 inference(monotonicity,[status(thm)],[310])).
% 2.22/2.46 tff(10012,plain,
% 2.22/2.46 ((s(s(elem!1)) = s(s(z))) <=> (elem!1 = s(s(elem!1)))),
% 2.22/2.46 inference(transitivity,[status(thm)],[10011, 3428])).
% 2.22/2.46 tff(10013,plain,
% 2.22/2.46 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(elem!1 = s(s(elem!1))))),
% 2.22/2.46 inference(monotonicity,[status(thm)],[10012])).
% 2.22/2.46 tff(10014,plain,
% 2.22/2.46 (~(elem!1 = s(s(elem!1)))),
% 2.22/2.46 inference(modus_ponens,[status(thm)],[9981, 10013])).
% 2.22/2.46 tff(10015,plain,
% 2.22/2.46 (r(s(s(elem!1)), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 2.22/2.46 inference(monotonicity,[status(thm)],[1020])).
% 2.22/2.46 tff(10016,plain,
% 2.22/2.46 (r(s(s(s(s(z)))), s(z))),
% 2.22/2.46 inference(modus_ponens,[status(thm)],[494, 10015])).
% 2.22/2.46 tff(10017,plain,
% 2.22/2.46 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(s(s(z)))))),
% 2.22/2.46 inference(monotonicity,[status(thm)],[1020])).
% 2.22/2.46 tff(10018,plain,
% 2.22/2.46 (r(elem!1, s(s(elem!1)))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[1617, 6956, 1630])).
% 2.22/2.46 tff(10019,plain,
% 2.22/2.46 (r(elem!1, s(s(s(s(z)))))),
% 2.22/2.46 inference(modus_ponens,[status(thm)],[10018, 10017])).
% 2.22/2.46 tff(10020,plain,
% 2.22/2.46 ($false),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[3249, 37, 114, 10019, 10016])).
% 2.22/2.46 tff(10021,plain,((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~(s(s(elem!1)) = s(s(s(s(z)))))) | (elem!1 = s(s(elem!1))) | (~b(z, elem!1)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.46 tff(10022,plain,
% 2.22/2.46 (~r(s(s(elem!1)), s(z))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[10021, 1047, 9957, 10014, 9866, 506])).
% 2.22/2.46 tff(10023,plain,
% 2.22/2.46 (b(s(s(elem!1)), s(z))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[561, 10022])).
% 2.22/2.46 tff(10024,plain,
% 2.22/2.46 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.22/2.46 inference(symmetry,[status(thm)],[1047])).
% 2.22/2.46 tff(10025,plain,
% 2.22/2.46 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 2.22/2.46 inference(monotonicity,[status(thm)],[10024])).
% 2.22/2.46 tff(10026,plain,
% 2.22/2.46 (r(s(s(elem!1)), elem!1)),
% 2.22/2.46 inference(modus_ponens,[status(thm)],[9474, 10025])).
% 2.22/2.46 tff(10027,plain,
% 2.22/2.46 (~(s(s(z)) = s(elem!1))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[3261, 2725])).
% 2.22/2.46 tff(10028,plain,
% 2.22/2.46 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[4541, 10027])).
% 2.22/2.46 tff(10029,plain,
% 2.22/2.46 (~r(s(s(s(z))), s(z))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[1075, 10008, 9957])).
% 2.22/2.46 tff(10030,plain,
% 2.22/2.46 (b(s(s(s(z))), s(z))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[1081, 10029])).
% 2.22/2.46 tff(10031,plain,
% 2.22/2.46 (~b(s(z), s(s(elem!1)))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[4506, 10030, 10028, 10026, 10023, 10008])).
% 2.22/2.46 tff(10032,plain,
% 2.22/2.46 ($false),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[1890, 10031, 10010])).
% 2.22/2.46 tff(10033,plain,((~(s(s(z)) = elem!1)) | (~r(z, s(z))) | (~b(s(z), elem!1)) | r(z, elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.46 tff(10034,plain,
% 2.22/2.46 (~(s(s(z)) = elem!1)),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[10033, 9947, 9949, 13, 14])).
% 2.22/2.46 tff(10035,plain,
% 2.22/2.46 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[1425, 10034])).
% 2.22/2.46 tff(10036,plain,
% 2.22/2.46 (r(s(s(z)), elem!1)),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[104, 10034, 99])).
% 2.22/2.46 tff(10037,plain,
% 2.22/2.46 (((~![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(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)))),
% 2.22/2.46 inference(rewrite,[status(thm)],[])).
% 2.22/2.46 tff(10038,plain,
% 2.22/2.46 (((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)))),
% 2.22/2.46 inference(rewrite,[status(thm)],[])).
% 2.22/2.46 tff(10039,plain,
% 2.22/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1))))),
% 2.22/2.46 inference(monotonicity,[status(thm)],[10038])).
% 2.22/2.46 tff(10040,plain,
% 2.22/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)))),
% 2.22/2.46 inference(transitivity,[status(thm)],[10039, 10037])).
% 2.22/2.46 tff(10041,plain,
% 2.22/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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)))))),
% 2.22/2.46 inference(quant_inst,[status(thm)],[])).
% 2.22/2.46 tff(10042,plain,
% 2.22/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1))),
% 2.22/2.46 inference(modus_ponens,[status(thm)],[10041, 10040])).
% 2.22/2.46 tff(10043,plain,
% 2.22/2.46 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[10042, 37, 10036, 9474])).
% 2.22/2.46 tff(10044,assumption,(s(s(s(s(z)))) = s(s(z))), introduced(assumption)).
% 2.22/2.46 tff(10045,plain,
% 2.22/2.46 (s(s(z)) = s(s(s(s(z))))),
% 2.22/2.46 inference(symmetry,[status(thm)],[10044])).
% 2.22/2.46 tff(10046,plain,
% 2.22/2.46 ($false),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[459, 10045])).
% 2.22/2.46 tff(10047,plain,(~(s(s(s(s(z)))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.46 tff(10048,plain,
% 2.22/2.46 (b(s(s(s(s(z)))), s(s(z)))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[2167, 58, 10047, 10043])).
% 2.22/2.46 tff(10049,plain,
% 2.22/2.46 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[9912, 37, 10036, 9474])).
% 2.22/2.46 tff(10050,plain,
% 2.22/2.46 (b(s(s(z)), s(s(s(s(z)))))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[465, 10049])).
% 2.22/2.46 tff(10051,plain,
% 2.22/2.46 (b(s(s(elem!1)), s(s(z)))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[1476, 1473, 266])).
% 2.22/2.46 tff(10052,plain,
% 2.22/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.22/2.46 inference(rewrite,[status(thm)],[])).
% 2.22/2.46 tff(10053,plain,
% 2.22/2.46 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(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(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(z))))) <=> ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.22/2.46 inference(rewrite,[status(thm)],[])).
% 2.22/2.46 tff(10054,plain,
% 2.22/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 2.22/2.46 inference(monotonicity,[status(thm)],[10053])).
% 2.22/2.46 tff(10055,plain,
% 2.22/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.22/2.46 inference(transitivity,[status(thm)],[10054, 10052])).
% 2.22/2.46 tff(10056,plain,
% 2.22/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.22/2.46 inference(quant_inst,[status(thm)],[])).
% 2.22/2.46 tff(10057,plain,
% 2.22/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 2.22/2.46 inference(modus_ponens,[status(thm)],[10056, 10055])).
% 2.22/2.46 tff(10058,plain,
% 2.22/2.46 ($false),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[10057, 75, 3886, 895, 10051, 1154])).
% 2.22/2.46 tff(10059,plain,(r(s(s(elem!1)), s(s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (s(s(elem!1)) = s(s(s(s(z))))) | (s(s(elem!1)) = s(s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.46 tff(10060,plain,
% 2.22/2.46 (r(s(s(elem!1)), s(s(z)))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[10059, 10050, 10048, 10035, 9981, 9474, 9980])).
% 2.22/2.46 tff(10061,plain,
% 2.22/2.46 ($false),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[2661, 37, 10036, 10060, 9980])).
% 2.22/2.46 tff(10062,plain,(b(s(s(elem!1)), elem!1) | r(z, elem!1) | b(elem!1, s(z)) | b(s(s(z)), elem!1) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.22/2.46 tff(10063,plain,
% 2.22/2.46 (b(s(s(elem!1)), elem!1)),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[10062, 9475, 14, 99, 13])).
% 2.22/2.46 tff(10064,plain,
% 2.22/2.46 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(elem!1))),
% 2.22/2.46 inference(monotonicity,[status(thm)],[8926])).
% 2.22/2.46 tff(10065,plain,
% 2.22/2.46 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(elem!1))),
% 2.22/2.46 inference(symmetry,[status(thm)],[10064])).
% 2.22/2.46 tff(10066,plain,
% 2.22/2.46 ((~(s(s(s(s(z)))) = s(elem!1))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 2.22/2.46 inference(monotonicity,[status(thm)],[10065])).
% 2.22/2.46 tff(10067,plain,
% 2.22/2.46 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.22/2.46 inference(modus_ponens,[status(thm)],[8942, 10066])).
% 2.22/2.46 tff(10068,plain,
% 2.22/2.46 (r(s(s(s(elem!1))), elem!1)),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[702, 93, 9474])).
% 2.22/2.46 tff(10069,plain,
% 2.22/2.46 (~r(z, s(z))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[2724, 93, 13])).
% 2.22/2.46 tff(10070,plain,
% 2.22/2.46 (b(z, s(z))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[187, 10069])).
% 2.22/2.46 tff(10071,plain,
% 2.22/2.46 (r(s(s(z)), elem!1)),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[9900, 10070, 9867, 9474, 9866, 9475, 14, 99])).
% 2.22/2.46 tff(10072,plain,
% 2.22/2.46 (r(s(elem!1), elem!1)),
% 2.22/2.46 inference(modus_ponens,[status(thm)],[10071, 626])).
% 2.22/2.46 tff(10073,plain,
% 2.22/2.46 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[651, 37, 10072, 10068])).
% 2.22/2.46 tff(10074,plain,
% 2.22/2.46 ((s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[655, 58, 10073])).
% 2.22/2.46 tff(10075,plain,
% 2.22/2.46 (b(s(s(s(elem!1))), s(elem!1))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[10074, 10067])).
% 2.22/2.46 tff(10076,plain,
% 2.22/2.46 (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[4198, 738, 752, 790, 3064, 4190])).
% 2.22/2.46 tff(10077,plain,
% 2.22/2.46 ($false),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[3083, 58, 868, 10076, 5826])).
% 2.22/2.46 tff(10078,plain,((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (s(s(s(s(s(s(s(z))))))) = s(elem!1)) | (~b(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.46 tff(10079,plain,
% 2.22/2.46 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[10078, 863, 10068, 10072, 737, 3007, 10075])).
% 2.22/2.46 tff(10080,plain,
% 2.22/2.46 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[813, 10079, 720])).
% 2.22/2.46 tff(10081,plain,
% 2.22/2.46 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 2.22/2.47 inference(symmetry,[status(thm)],[4999])).
% 2.22/2.47 tff(10082,plain,
% 2.22/2.47 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 2.22/2.47 inference(monotonicity,[status(thm)],[8925])).
% 2.22/2.47 tff(10083,plain,
% 2.22/2.47 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 2.22/2.47 inference(symmetry,[status(thm)],[10082])).
% 2.22/2.47 tff(10084,plain,
% 2.22/2.47 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 2.22/2.47 inference(transitivity,[status(thm)],[10083, 10081])).
% 2.22/2.47 tff(10085,plain,
% 2.22/2.47 ((~r(s(elem!1), s(s(s(elem!1))))) <=> (~r(s(s(z)), s(s(s(s(z))))))),
% 2.22/2.47 inference(monotonicity,[status(thm)],[10084])).
% 2.22/2.47 tff(10086,plain,
% 2.22/2.47 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[633, 37, 10072, 10068])).
% 2.22/2.47 tff(10087,plain,
% 2.22/2.47 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.22/2.47 inference(modus_ponens,[status(thm)],[10086, 10085])).
% 2.22/2.47 tff(10088,plain,
% 2.22/2.47 (b(s(s(z)), s(s(s(s(z)))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[465, 10087])).
% 2.22/2.47 tff(10089,plain,
% 2.22/2.47 (b(s(elem!1), s(s(s(elem!1))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[5375, 10088, 8924])).
% 2.22/2.47 tff(10090,plain,
% 2.22/2.47 (~(s(elem!1) = s(s(elem!1)))),
% 2.22/2.47 inference(modus_ponens,[status(thm)],[9981, 5028])).
% 2.22/2.47 tff(10091,plain,
% 2.22/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.22/2.47 inference(rewrite,[status(thm)],[])).
% 2.22/2.47 tff(10092,plain,
% 2.22/2.47 (((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.22/2.47 inference(rewrite,[status(thm)],[])).
% 2.22/2.47 tff(10093,plain,
% 2.22/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 2.22/2.47 inference(monotonicity,[status(thm)],[10092])).
% 2.22/2.47 tff(10094,plain,
% 2.22/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.22/2.47 inference(transitivity,[status(thm)],[10093, 10091])).
% 2.22/2.47 tff(10095,plain,
% 2.22/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.22/2.47 inference(quant_inst,[status(thm)],[])).
% 2.22/2.47 tff(10096,plain,
% 2.22/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.22/2.47 inference(modus_ponens,[status(thm)],[10095, 10094])).
% 2.22/2.47 tff(10097,plain,
% 2.22/2.47 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[10096, 75, 1518, 1620, 1168, 707])).
% 2.22/2.47 tff(10098,plain,
% 2.22/2.47 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[750, 58, 747, 10097])).
% 2.22/2.47 tff(10099,plain,
% 2.22/2.47 (r(s(s(elem!1)), z)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[2696, 4711])).
% 2.22/2.47 tff(10100,plain,
% 2.22/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(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(elem!1)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.47 inference(rewrite,[status(thm)],[])).
% 2.22/2.47 tff(10101,plain,
% 2.22/2.47 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.47 inference(rewrite,[status(thm)],[])).
% 2.22/2.47 tff(10102,plain,
% 2.22/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(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(elem!1)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 2.22/2.47 inference(monotonicity,[status(thm)],[10101])).
% 2.22/2.47 tff(10103,plain,
% 2.22/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(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(elem!1)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.47 inference(transitivity,[status(thm)],[10102, 10100])).
% 2.22/2.47 tff(10104,plain,
% 2.22/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.47 inference(quant_inst,[status(thm)],[])).
% 2.22/2.47 tff(10105,plain,
% 2.22/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 2.22/2.47 inference(modus_ponens,[status(thm)],[10104, 10103])).
% 2.22/2.47 tff(10106,plain,
% 2.22/2.47 ($false),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[10105, 37, 10099, 10098, 8745])).
% 2.22/2.47 tff(10107,plain,((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.47 tff(10108,plain,
% 2.22/2.47 (~b(elem!1, s(s(elem!1)))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[10107, 10080, 837, 10063, 9866])).
% 2.22/2.47 tff(10109,plain,
% 2.22/2.47 (r(elem!1, s(s(elem!1)))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[1617, 10108, 5031])).
% 2.22/2.47 tff(10110,plain,
% 2.22/2.47 (b(elem!1, s(s(z))) <=> b(s(z), s(s(z)))),
% 2.22/2.47 inference(symmetry,[status(thm)],[4989])).
% 2.22/2.47 tff(10111,plain,
% 2.22/2.47 (b(elem!1, s(s(z))) <=> b(elem!1, s(elem!1))),
% 2.22/2.47 inference(monotonicity,[status(thm)],[609])).
% 2.22/2.47 tff(10112,plain,
% 2.22/2.47 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(z)))),
% 2.22/2.47 inference(symmetry,[status(thm)],[10111])).
% 2.22/2.47 tff(10113,plain,
% 2.22/2.47 (b(elem!1, s(elem!1)) <=> b(s(z), s(s(z)))),
% 2.22/2.47 inference(transitivity,[status(thm)],[10112, 10110])).
% 2.22/2.47 tff(10114,plain,
% 2.22/2.47 ((~b(elem!1, s(elem!1))) <=> (~b(s(z), s(s(z))))),
% 2.22/2.47 inference(monotonicity,[status(thm)],[10113])).
% 2.22/2.47 tff(10115,plain,
% 2.22/2.47 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.22/2.47 inference(symmetry,[status(thm)],[8931])).
% 2.22/2.47 tff(10116,plain,
% 2.22/2.47 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 2.22/2.47 inference(monotonicity,[status(thm)],[8924])).
% 2.22/2.47 tff(10117,plain,
% 2.22/2.47 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 2.22/2.47 inference(transitivity,[status(thm)],[10116, 3863])).
% 2.22/2.47 tff(10118,plain,
% 2.22/2.47 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(s(z))))))),
% 2.22/2.47 inference(monotonicity,[status(thm)],[10117])).
% 2.22/2.47 tff(10119,plain,
% 2.22/2.47 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 2.22/2.47 inference(modus_ponens,[status(thm)],[264, 10118])).
% 2.22/2.47 tff(10120,plain,
% 2.22/2.47 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(z)))), s(elem!1))),
% 2.22/2.47 inference(monotonicity,[status(thm)],[8926])).
% 2.22/2.47 tff(10121,plain,
% 2.22/2.47 (b(s(s(s(s(z)))), s(elem!1))),
% 2.22/2.47 inference(modus_ponens,[status(thm)],[4190, 10120])).
% 2.22/2.47 tff(10122,plain,
% 2.22/2.47 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 2.22/2.47 inference(monotonicity,[status(thm)],[8926])).
% 2.22/2.47 tff(10123,plain,
% 2.22/2.47 (b(s(elem!1), s(s(s(s(z)))))),
% 2.22/2.47 inference(modus_ponens,[status(thm)],[920, 10122])).
% 2.22/2.47 tff(10124,plain,
% 2.22/2.47 (~r(s(elem!1), s(s(elem!1)))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[1950, 155, 752, 1490])).
% 2.22/2.47 tff(10125,plain,
% 2.22/2.47 (b(s(elem!1), s(s(elem!1)))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[1851, 10124, 1845])).
% 2.22/2.47 tff(10126,plain,
% 2.22/2.47 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[4280, 10125, 10123, 10121])).
% 2.22/2.47 tff(10127,plain,
% 2.22/2.47 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[1660, 10126, 10119])).
% 2.22/2.47 tff(10128,plain,
% 2.22/2.47 (~r(elem!1, s(s(s(s(z)))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[3811, 10127, 1490])).
% 2.22/2.47 tff(10129,plain,
% 2.22/2.47 (b(elem!1, s(s(s(s(z)))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[278, 10128, 850])).
% 2.22/2.47 tff(10130,plain,
% 2.22/2.47 (b(elem!1, s(s(s(elem!1))))),
% 2.22/2.47 inference(modus_ponens,[status(thm)],[10129, 10115])).
% 2.22/2.47 tff(10131,plain,
% 2.22/2.47 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1)))) <=> ((~b(s(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))))))),
% 2.22/2.47 inference(rewrite,[status(thm)],[])).
% 2.22/2.47 tff(10132,plain,
% 2.22/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 2.22/2.47 inference(monotonicity,[status(thm)],[10131])).
% 2.22/2.47 tff(10133,plain,
% 2.22/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.22/2.47 inference(transitivity,[status(thm)],[10132, 5955])).
% 2.22/2.47 tff(10134,plain,
% 2.22/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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))))),
% 2.22/2.47 inference(quant_inst,[status(thm)],[])).
% 2.22/2.47 tff(10135,plain,
% 2.22/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))),
% 2.22/2.47 inference(modus_ponens,[status(thm)],[10134, 10133])).
% 2.22/2.47 tff(10136,plain,
% 2.22/2.47 (~b(elem!1, s(elem!1))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[10135, 75, 10130, 920, 4190])).
% 2.22/2.47 tff(10137,plain,
% 2.22/2.47 (~b(s(z), s(s(z)))),
% 2.22/2.47 inference(modus_ponens,[status(thm)],[10136, 10114])).
% 2.22/2.47 tff(10138,plain,
% 2.22/2.47 (r(s(z), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.22/2.47 inference(monotonicity,[status(thm)],[93])).
% 2.22/2.47 tff(10139,plain,
% 2.22/2.47 (r(elem!1, s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 2.22/2.47 inference(symmetry,[status(thm)],[10138])).
% 2.22/2.47 tff(10140,plain,
% 2.22/2.47 (r(s(z), s(s(elem!1)))),
% 2.22/2.47 inference(modus_ponens,[status(thm)],[1490, 10139])).
% 2.22/2.47 tff(10141,plain,
% 2.22/2.47 (~r(z, s(s(elem!1)))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[5301, 9023, 10140])).
% 2.22/2.47 tff(10142,plain,
% 2.22/2.47 (b(z, s(s(elem!1)))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[6314, 10141])).
% 2.22/2.47 tff(10143,plain,
% 2.22/2.47 (~r(s(elem!1), s(s(elem!1)))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[1950, 155, 1490, 752])).
% 2.22/2.47 tff(10144,plain,
% 2.22/2.47 (b(s(elem!1), s(s(elem!1)))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[1851, 10143, 1845])).
% 2.22/2.47 tff(10145,plain,
% 2.22/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 2.22/2.47 inference(rewrite,[status(thm)],[])).
% 2.22/2.47 tff(10146,plain,
% 2.22/2.47 (((~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 2.22/2.47 inference(rewrite,[status(thm)],[])).
% 2.22/2.47 tff(10147,plain,
% 2.22/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1))))))),
% 2.22/2.47 inference(monotonicity,[status(thm)],[10146])).
% 2.22/2.47 tff(10148,plain,
% 2.22/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 2.22/2.47 inference(transitivity,[status(thm)],[10147, 10145])).
% 2.22/2.47 tff(10149,plain,
% 2.22/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))),
% 2.22/2.47 inference(quant_inst,[status(thm)],[])).
% 2.22/2.47 tff(10150,plain,
% 2.22/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1))))),
% 2.22/2.47 inference(modus_ponens,[status(thm)],[10149, 10148])).
% 2.22/2.47 tff(10151,plain,
% 2.22/2.47 (~b(s(elem!1), z)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[10150, 75, 3069, 10144, 1893])).
% 2.22/2.47 tff(10152,plain,
% 2.22/2.47 (r(s(elem!1), z)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[764, 58, 554, 10151])).
% 2.22/2.47 tff(10153,plain,
% 2.22/2.47 ($false),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[2986, 37, 155, 752, 10152])).
% 2.22/2.47 tff(10154,plain,((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (s(elem!1) = s(s(elem!1))) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.47 tff(10155,plain,
% 2.22/2.47 (~b(s(s(elem!1)), s(elem!1))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[10154, 10142, 752, 155, 1490, 1845])).
% 2.22/2.47 tff(10156,plain,
% 2.22/2.47 (r(s(s(elem!1)), s(s(z)))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[4966, 10155, 909])).
% 2.22/2.47 tff(10157,plain,
% 2.22/2.47 (~r(elem!1, s(s(z)))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[1498, 10156, 1490])).
% 2.22/2.47 tff(10158,plain,
% 2.22/2.47 (~r(s(z), s(s(z)))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[9003, 10157, 93])).
% 2.22/2.47 tff(10159,plain,
% 2.22/2.47 (b(s(z), s(s(z)))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[416, 10158])).
% 2.22/2.47 tff(10160,plain,
% 2.22/2.47 ($false),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[10159, 10137])).
% 2.22/2.47 tff(10161,plain,((~r(elem!1, z)) | (~(s(z) = elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (s(elem!1) = s(s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.47 tff(10162,plain,
% 2.22/2.47 (~r(elem!1, z)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[10161, 93, 10109, 10072, 10090, 10089, 10075])).
% 2.22/2.47 tff(10163,plain,
% 2.22/2.47 (b(elem!1, z)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[387, 10162, 9867])).
% 2.22/2.47 tff(10164,plain,
% 2.22/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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, z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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, z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.22/2.47 inference(rewrite,[status(thm)],[])).
% 2.22/2.47 tff(10165,plain,
% 2.22/2.47 (((~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.22/2.47 inference(rewrite,[status(thm)],[])).
% 2.22/2.47 tff(10166,plain,
% 2.22/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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, z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 2.22/2.47 inference(monotonicity,[status(thm)],[10165])).
% 2.22/2.47 tff(10167,plain,
% 2.22/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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, z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.22/2.47 inference(transitivity,[status(thm)],[10166, 10164])).
% 2.22/2.47 tff(10168,plain,
% 2.22/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.47 inference(quant_inst,[status(thm)],[])).
% 2.22/2.47 tff(10169,plain,
% 2.22/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.22/2.47 inference(modus_ponens,[status(thm)],[10168, 10167])).
% 2.22/2.47 tff(10170,plain,
% 2.22/2.47 (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[10169, 75, 9866, 10163, 10080, 10063])).
% 2.22/2.47 tff(10171,plain,
% 2.22/2.47 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[840, 58, 837, 10170])).
% 2.22/2.47 tff(10172,plain,
% 2.22/2.47 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[2836, 75, 9866, 10163, 10080])).
% 2.22/2.47 tff(10173,plain,
% 2.22/2.47 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[750, 58, 747, 10172])).
% 2.22/2.47 tff(10174,plain,
% 2.22/2.47 (~b(s(s(elem!1)), z)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[2795, 75, 9866, 10163, 10063])).
% 2.22/2.47 tff(10175,plain,
% 2.22/2.47 (r(s(s(elem!1)), z)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[2696, 10174])).
% 2.22/2.47 tff(10176,plain,
% 2.22/2.47 ($false),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[10105, 37, 10175, 10173, 10171])).
% 2.22/2.47 tff(10177,plain,((~(s(z) = elem!1)) | r(s(z), elem!1) | b(elem!1, s(z)) | b(s(s(z)), elem!1) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.22/2.47 tff(10178,plain,
% 2.22/2.47 (~(s(z) = elem!1)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[10177, 9475, 14, 99, 13])).
% 2.22/2.47 tff(10179,plain,
% 2.22/2.47 (b(s(z), elem!1)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[601, 10178, 9475])).
% 2.22/2.47 tff(10180,plain,
% 2.22/2.47 (~(elem!1 = s(z))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[111, 10178])).
% 2.22/2.47 tff(10181,plain,
% 2.22/2.47 (r(elem!1, s(z))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[89, 10180, 14])).
% 2.22/2.47 tff(10182,plain,
% 2.22/2.47 (~r(elem!1, z)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[211, 9901, 114])).
% 2.22/2.47 tff(10183,plain,
% 2.22/2.47 (b(elem!1, z)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[387, 10182, 353])).
% 2.22/2.47 tff(10184,plain,
% 2.22/2.47 ($false),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[4527, 75, 1518, 10183, 372, 107])).
% 2.22/2.47 tff(10185,plain,((~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (elem!1 = z) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | r(s(z), elem!1) | b(elem!1, s(z)) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.22/2.48 tff(10186,plain,
% 2.22/2.48 (~b(z, s(z))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[10185, 10179, 9866, 9867, 10181, 9474, 9475, 14, 99])).
% 2.22/2.48 tff(10187,plain,
% 2.22/2.48 (r(z, s(z))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[187, 10186])).
% 2.22/2.48 tff(10188,plain,
% 2.22/2.48 (~r(elem!1, z)),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[177, 10187, 10181])).
% 2.22/2.48 tff(10189,plain,
% 2.22/2.48 (b(elem!1, z)),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[387, 10188, 9867])).
% 2.22/2.48 tff(10190,plain,
% 2.22/2.48 (~r(s(s(elem!1)), s(z))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[1966, 10189, 10063, 10187])).
% 2.22/2.48 tff(10191,plain,
% 2.22/2.48 (b(s(s(elem!1)), s(z))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[561, 10190])).
% 2.22/2.48 tff(10192,plain,
% 2.22/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)))),
% 2.22/2.48 inference(rewrite,[status(thm)],[])).
% 2.22/2.48 tff(10193,plain,
% 2.22/2.48 (((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~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(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)))),
% 2.22/2.48 inference(rewrite,[status(thm)],[])).
% 2.22/2.48 tff(10194,plain,
% 2.22/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(elem!1)), elem!1)) | (~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(X1, 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(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z))))),
% 2.22/2.48 inference(monotonicity,[status(thm)],[10193])).
% 2.22/2.48 tff(10195,plain,
% 2.22/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(elem!1)), elem!1)) | (~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(X1, 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(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)))),
% 2.22/2.48 inference(transitivity,[status(thm)],[10194, 10192])).
% 2.22/2.48 tff(10196,plain,
% 2.22/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(elem!1)), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 2.22/2.48 inference(quant_inst,[status(thm)],[])).
% 2.22/2.48 tff(10197,plain,
% 2.22/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z))),
% 2.22/2.48 inference(modus_ponens,[status(thm)],[10196, 10195])).
% 2.22/2.48 tff(10198,plain,
% 2.22/2.48 ($false),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[10197, 75, 9866, 10189, 10191, 10179, 10063])).
% 2.22/2.48 tff(10199,plain,(r(s(z), elem!1) | b(elem!1, s(z)) | b(s(s(z)), elem!1) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.22/2.48 tff(10200,plain,
% 2.22/2.48 (r(s(z), elem!1)),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[10199, 99, 14, 13])).
% 2.22/2.48 tff(10201,plain,
% 2.22/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(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))))),
% 2.22/2.48 inference(rewrite,[status(thm)],[])).
% 2.22/2.48 tff(10202,plain,
% 2.22/2.48 (((~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))))),
% 2.22/2.48 inference(rewrite,[status(thm)],[])).
% 2.22/2.48 tff(10203,plain,
% 2.22/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(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)))))),
% 2.22/2.48 inference(monotonicity,[status(thm)],[10202])).
% 2.22/2.48 tff(10204,plain,
% 2.22/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(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))))),
% 2.22/2.48 inference(transitivity,[status(thm)],[10203, 10201])).
% 2.22/2.48 tff(10205,plain,
% 2.22/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 2.22/2.48 inference(quant_inst,[status(thm)],[])).
% 2.22/2.48 tff(10206,plain,
% 2.22/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z)))),
% 2.22/2.48 inference(modus_ponens,[status(thm)],[10205, 10204])).
% 2.22/2.48 tff(10207,plain,
% 2.22/2.48 (~r(s(s(s(s(z)))), s(z))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[10206, 37, 10200, 9474])).
% 2.22/2.48 tff(10208,plain,
% 2.22/2.48 (b(s(s(s(s(z)))), s(z))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[1406, 58, 483, 10207])).
% 2.22/2.48 tff(10209,plain,
% 2.22/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(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(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.22/2.48 inference(rewrite,[status(thm)],[])).
% 2.22/2.48 tff(10210,plain,
% 2.22/2.48 (((~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(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.22/2.48 inference(rewrite,[status(thm)],[])).
% 2.22/2.48 tff(10211,plain,
% 2.22/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), 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(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))))),
% 2.22/2.48 inference(monotonicity,[status(thm)],[10210])).
% 2.22/2.48 tff(10212,plain,
% 2.22/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), 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(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.22/2.48 inference(transitivity,[status(thm)],[10211, 10209])).
% 2.22/2.48 tff(10213,plain,
% 2.22/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))))),
% 2.22/2.48 inference(quant_inst,[status(thm)],[])).
% 2.22/2.48 tff(10214,plain,
% 2.22/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))),
% 2.22/2.48 inference(modus_ponens,[status(thm)],[10213, 10212])).
% 2.22/2.48 tff(10215,plain,
% 2.22/2.48 (~r(s(z), s(s(s(s(z)))))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[10214, 37, 10200, 9474])).
% 2.22/2.48 tff(10216,plain,
% 2.22/2.48 (b(s(z), s(s(s(s(z)))))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[489, 10215])).
% 2.22/2.48 tff(10217,plain,
% 2.22/2.48 (~r(s(s(z)), elem!1)),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[596, 7114, 588])).
% 2.22/2.48 tff(10218,plain,
% 2.22/2.48 ($false),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[9876, 10217, 7114, 17])).
% 2.22/2.48 tff(10219,plain,((~(elem!1 = s(z))) | (~r(s(z), elem!1)) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.22/2.48 tff(10220,plain,
% 2.22/2.48 (~(elem!1 = s(z))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[10219, 10200, 99])).
% 2.22/2.48 tff(10221,plain,
% 2.22/2.48 (r(elem!1, s(z))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[89, 10220, 14])).
% 2.22/2.48 tff(10222,plain,
% 2.22/2.48 (~r(s(z), s(s(s(s(z)))))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[10214, 37, 588, 698])).
% 2.22/2.48 tff(10223,plain,
% 2.22/2.48 (b(s(z), s(s(s(s(z)))))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[489, 10222])).
% 2.22/2.48 tff(10224,plain,
% 2.22/2.48 (~b(s(s(s(z))), s(z))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[3531, 1061, 698, 578])).
% 2.22/2.48 tff(10225,plain,
% 2.22/2.48 ($false),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[1081, 10224, 1076])).
% 2.22/2.48 tff(10226,plain,((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.48 tff(10227,plain,
% 2.22/2.48 (~r(s(s(s(z))), elem!1)),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[10226, 10223, 698, 114])).
% 2.22/2.48 tff(10228,plain,
% 2.22/2.48 (~(s(s(s(s(z)))) = elem!1)),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[3664, 10222, 588])).
% 2.22/2.48 tff(10229,plain,
% 2.22/2.48 (~(elem!1 = s(s(s(s(z)))))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[273, 10228])).
% 2.22/2.48 tff(10230,plain,
% 2.22/2.48 (~(s(s(s(z))) = elem!1)),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[1026, 1047, 10229])).
% 2.22/2.48 tff(10231,plain,
% 2.22/2.48 (b(s(s(s(z))), elem!1)),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[1115, 10230, 10227])).
% 2.22/2.48 tff(10232,plain,
% 2.22/2.48 (b(s(elem!1), elem!1)),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[1122, 10231, 1047])).
% 2.22/2.48 tff(10233,plain,
% 2.22/2.48 (r(s(s(elem!1)), elem!1)),
% 2.22/2.48 inference(modus_ponens,[status(thm)],[698, 10025])).
% 2.22/2.48 tff(10234,plain,
% 2.22/2.48 (~r(elem!1, z)),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[4786, 10233, 114])).
% 2.22/2.48 tff(10235,plain,
% 2.22/2.48 (b(elem!1, z)),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[387, 10234, 353])).
% 2.22/2.48 tff(10236,plain,
% 2.22/2.48 (b(z, s(s(z))) <=> b(z, elem!1)),
% 2.22/2.48 inference(monotonicity,[status(thm)],[310])).
% 2.22/2.48 tff(10237,plain,
% 2.22/2.48 (b(z, elem!1) <=> b(z, s(s(z)))),
% 2.22/2.48 inference(symmetry,[status(thm)],[10236])).
% 2.22/2.48 tff(10238,plain,
% 2.22/2.48 (b(z, s(s(z)))),
% 2.22/2.48 inference(modus_ponens,[status(thm)],[1518, 10237])).
% 2.22/2.48 tff(10239,plain,
% 2.22/2.48 (b(s(s(z)), z)),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[9897, 10235, 310])).
% 2.22/2.48 tff(10240,plain,
% 2.22/2.48 (~b(s(elem!1), z)),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[10000, 10235, 10232, 10239, 10238])).
% 2.22/2.48 tff(10241,plain,
% 2.22/2.48 (r(s(elem!1), z)),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[766, 10240])).
% 2.22/2.48 tff(10242,plain,
% 2.22/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.48 inference(rewrite,[status(thm)],[])).
% 2.22/2.48 tff(10243,plain,
% 2.22/2.48 (((~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.48 inference(rewrite,[status(thm)],[])).
% 2.22/2.48 tff(10244,plain,
% 2.22/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 2.22/2.48 inference(monotonicity,[status(thm)],[10243])).
% 2.22/2.48 tff(10245,plain,
% 2.22/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.48 inference(transitivity,[status(thm)],[10244, 10242])).
% 2.22/2.48 tff(10246,plain,
% 2.22/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.48 inference(quant_inst,[status(thm)],[])).
% 2.22/2.48 tff(10247,plain,
% 2.22/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 2.22/2.48 inference(modus_ponens,[status(thm)],[10246, 10245])).
% 2.22/2.48 tff(10248,plain,
% 2.22/2.48 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[10247, 75, 1518, 1958, 1168, 921])).
% 2.22/2.48 tff(10249,plain,
% 2.22/2.48 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[793, 58, 790, 10248])).
% 2.22/2.48 tff(10250,plain,
% 2.22/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(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(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.48 inference(rewrite,[status(thm)],[])).
% 2.22/2.48 tff(10251,plain,
% 2.22/2.48 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.48 inference(rewrite,[status(thm)],[])).
% 2.22/2.48 tff(10252,plain,
% 2.22/2.48 (((~![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(s(s(s(z))))))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(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(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 2.22/2.48 inference(monotonicity,[status(thm)],[10251])).
% 2.22/2.48 tff(10253,plain,
% 2.22/2.48 (((~![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(s(s(s(z))))))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(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(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.48 inference(transitivity,[status(thm)],[10252, 10250])).
% 2.22/2.48 tff(10254,plain,
% 2.22/2.48 ((~![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(s(s(s(z))))))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.22/2.48 inference(quant_inst,[status(thm)],[])).
% 2.22/2.48 tff(10255,plain,
% 2.22/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 2.22/2.48 inference(modus_ponens,[status(thm)],[10254, 10253])).
% 2.22/2.48 tff(10256,plain,
% 2.22/2.48 ($false),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[10255, 37, 1752, 10249, 2838])).
% 2.22/2.48 tff(10257,plain,((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(elem!1), z)) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.48 tff(10258,plain,
% 2.22/2.48 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[10257, 10241, 1146, 1518, 10235, 10232])).
% 2.22/2.48 tff(10259,plain,
% 2.22/2.48 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[813, 10258, 1046])).
% 2.22/2.48 tff(10260,plain,
% 2.22/2.48 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[1219, 37, 588, 10259])).
% 2.22/2.48 tff(10261,plain,
% 2.22/2.48 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[1230, 58, 1227, 10260])).
% 2.22/2.48 tff(10262,plain,
% 2.22/2.48 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[9654, 37, 698, 10259])).
% 2.22/2.48 tff(10263,plain,
% 2.22/2.48 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[1179, 58, 1135, 10262])).
% 2.22/2.48 tff(10264,plain,
% 2.22/2.48 (~r(s(s(s(s(z)))), s(z))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[10206, 37, 588, 698])).
% 2.22/2.48 tff(10265,plain,
% 2.22/2.48 (b(s(s(s(s(z)))), s(z))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[1406, 58, 483, 10264])).
% 2.22/2.48 tff(10266,plain,
% 2.22/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.22/2.48 inference(rewrite,[status(thm)],[])).
% 2.22/2.48 tff(10267,plain,
% 2.22/2.48 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.22/2.48 inference(rewrite,[status(thm)],[])).
% 2.22/2.48 tff(10268,plain,
% 2.22/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(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(X1, 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(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 2.22/2.49 inference(monotonicity,[status(thm)],[10267])).
% 2.22/2.49 tff(10269,plain,
% 2.22/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(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(X1, 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(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.22/2.49 inference(transitivity,[status(thm)],[10268, 10266])).
% 2.22/2.49 tff(10270,plain,
% 2.22/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.22/2.49 inference(quant_inst,[status(thm)],[])).
% 2.22/2.49 tff(10271,plain,
% 2.22/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 2.22/2.49 inference(modus_ponens,[status(thm)],[10270, 10269])).
% 2.22/2.49 tff(10272,plain,
% 2.22/2.49 ($false),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[10271, 75, 10223, 10265, 10263, 10261])).
% 2.22/2.49 tff(10273,plain,((~(s(s(z)) = elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~b(z, elem!1)) | (elem!1 = z) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.49 tff(10274,plain,
% 2.22/2.49 (~(s(s(z)) = elem!1)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[10273, 10200, 9474, 9866, 9867, 10221])).
% 2.22/2.49 tff(10275,plain,
% 2.22/2.49 (r(s(s(z)), elem!1)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[104, 10274, 99])).
% 2.22/2.49 tff(10276,plain,
% 2.22/2.49 (~r(s(s(z)), s(z))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[123, 10275, 10221])).
% 2.22/2.49 tff(10277,plain,
% 2.22/2.49 (b(s(s(z)), s(z))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[153, 10276])).
% 2.22/2.49 tff(10278,plain,
% 2.22/2.49 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[3906, 10277, 10216, 10208])).
% 2.22/2.49 tff(10279,plain,
% 2.22/2.49 (r(s(s(z)), s(s(s(s(z)))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[465, 10278])).
% 2.22/2.49 tff(10280,plain,
% 2.22/2.49 ($false),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[9912, 37, 10275, 9474, 10279])).
% 2.22/2.49 tff(10281,plain,(b(s(s(z)), elem!1) | b(elem!1, s(z)) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.22/2.49 tff(10282,plain,
% 2.22/2.49 (r(z, elem!1)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[10281, 14, 99])).
% 2.22/2.49 tff(10283,plain,
% 2.22/2.49 (~(s(s(s(s(z)))) = elem!1)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[8796, 10282, 99, 14])).
% 2.22/2.49 tff(10284,plain,
% 2.22/2.49 (~(elem!1 = s(s(s(s(z)))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[273, 10283])).
% 2.22/2.49 tff(10285,plain,
% 2.22/2.49 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[10042, 37, 106, 698])).
% 2.22/2.49 tff(10286,plain,
% 2.22/2.49 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[2210, 2073, 7175, 678])).
% 2.22/2.49 tff(10287,plain,
% 2.22/2.49 ($false),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[2167, 58, 10286, 10047, 10285])).
% 2.22/2.49 tff(10288,plain,((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.49 tff(10289,plain,
% 2.22/2.49 (~r(s(s(z)), elem!1)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[10288, 10282, 9473])).
% 2.22/2.49 tff(10290,plain,
% 2.22/2.49 (s(s(z)) = elem!1),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[104, 10289, 99])).
% 2.22/2.49 tff(10291,plain,
% 2.22/2.49 (~b(s(s(z)), s(z))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[316, 10290, 14])).
% 2.22/2.49 tff(10292,plain,
% 2.22/2.49 (r(s(s(z)), s(z))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[153, 10291])).
% 2.22/2.49 tff(10293,plain,
% 2.22/2.49 (~(elem!1 = s(z))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[9876, 10292, 10289])).
% 2.22/2.49 tff(10294,plain,
% 2.22/2.49 (r(elem!1, s(z))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[89, 10293, 14])).
% 2.22/2.49 tff(10295,plain,
% 2.22/2.49 (~r(elem!1, s(s(s(s(z)))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[8127, 10294, 10282])).
% 2.22/2.49 tff(10296,plain,
% 2.22/2.49 (b(elem!1, s(s(s(s(z)))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[278, 10295, 10284])).
% 2.22/2.49 tff(10297,plain,
% 2.22/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.22/2.49 inference(rewrite,[status(thm)],[])).
% 2.22/2.49 tff(10298,plain,
% 2.22/2.49 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.22/2.49 inference(rewrite,[status(thm)],[])).
% 2.22/2.49 tff(10299,plain,
% 2.22/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), s(z))) | (~b(s(s(s(s(z)))), z))))),
% 2.22/2.49 inference(monotonicity,[status(thm)],[10298])).
% 2.22/2.49 tff(10300,plain,
% 2.22/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.22/2.49 inference(transitivity,[status(thm)],[10299, 10297])).
% 2.22/2.49 tff(10301,plain,
% 2.22/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.22/2.49 inference(quant_inst,[status(thm)],[])).
% 2.22/2.49 tff(10302,plain,
% 2.22/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))),
% 2.22/2.49 inference(modus_ponens,[status(thm)],[10301, 10300])).
% 2.22/2.49 tff(10303,plain,
% 2.22/2.49 ($false),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[10302, 75, 1360, 1239, 10265, 7175])).
% 2.22/2.49 tff(10304,plain,((~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.49 tff(10305,plain,
% 2.22/2.49 (~r(s(z), elem!1)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[10304, 10282, 9473])).
% 2.22/2.49 tff(10306,plain,
% 2.22/2.49 (~(s(z) = elem!1)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[97, 10293])).
% 2.22/2.49 tff(10307,plain,
% 2.22/2.49 (b(s(z), elem!1)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[601, 10306, 10305])).
% 2.22/2.49 tff(10308,plain,
% 2.22/2.49 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[1013, 10290])).
% 2.22/2.49 tff(10309,plain,
% 2.22/2.49 (~(s(s(elem!1)) = s(s(z)))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[5439, 10308])).
% 2.22/2.49 tff(10310,plain,
% 2.22/2.49 (~(z = elem!1)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[293, 10309])).
% 2.22/2.49 tff(10311,plain,
% 2.22/2.49 (~(elem!1 = z)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[304, 10310])).
% 2.22/2.49 tff(10312,plain,
% 2.22/2.49 (~r(z, s(z))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[367, 10294, 10282])).
% 2.22/2.49 tff(10313,plain,
% 2.22/2.49 (b(z, s(z))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[187, 10312])).
% 2.22/2.49 tff(10314,plain,
% 2.22/2.49 (~b(z, elem!1)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[10185, 10313, 99, 10311, 10294, 9473, 10307, 14, 10305])).
% 2.22/2.49 tff(10315,plain,
% 2.22/2.49 (~b(s(z), s(s(s(s(z)))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[7183, 10313, 9473, 10282])).
% 2.22/2.49 tff(10316,plain,
% 2.22/2.49 (r(s(z), s(s(s(s(z)))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[489, 10315])).
% 2.22/2.49 tff(10317,plain,
% 2.22/2.49 (~r(z, s(z))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[367, 300, 114])).
% 2.22/2.49 tff(10318,plain,
% 2.22/2.49 (b(z, s(z))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[187, 10317])).
% 2.22/2.49 tff(10319,plain,
% 2.22/2.49 (~b(s(s(s(s(z)))), s(z))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[10302, 75, 10318, 371, 7175])).
% 2.22/2.49 tff(10320,plain,
% 2.22/2.49 (r(s(s(s(s(z)))), s(z))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[1406, 58, 10319, 483])).
% 2.22/2.49 tff(10321,plain,
% 2.22/2.49 (~(z = elem!1)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[9484, 698, 9482])).
% 2.22/2.49 tff(10322,plain,
% 2.22/2.49 (r(z, elem!1)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[298, 10321, 285])).
% 2.22/2.49 tff(10323,plain,
% 2.22/2.49 (~r(z, s(s(s(s(z)))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[7164, 37, 10322, 698])).
% 2.22/2.49 tff(10324,plain,
% 2.22/2.49 ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z)))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[1515, 58, 10323])).
% 2.22/2.49 tff(10325,plain,
% 2.22/2.49 (b(z, s(s(s(s(z)))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[10324, 1503])).
% 2.22/2.49 tff(10326,plain,
% 2.22/2.49 (b(s(s(s(s(z)))), z)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[1421, 58, 1143, 9482])).
% 2.22/2.49 tff(10327,plain,
% 2.22/2.49 (~(elem!1 = z)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[304, 10321])).
% 2.22/2.49 tff(10328,plain,
% 2.22/2.49 (b(elem!1, z)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[387, 10327, 2614])).
% 2.22/2.49 tff(10329,plain,
% 2.22/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.22/2.49 inference(rewrite,[status(thm)],[])).
% 2.22/2.49 tff(10330,plain,
% 2.22/2.49 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.22/2.49 inference(rewrite,[status(thm)],[])).
% 2.22/2.49 tff(10331,plain,
% 2.22/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))))),
% 2.22/2.49 inference(monotonicity,[status(thm)],[10330])).
% 2.22/2.49 tff(10332,plain,
% 2.22/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.22/2.49 inference(transitivity,[status(thm)],[10331, 10329])).
% 2.22/2.49 tff(10333,plain,
% 2.22/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.22/2.49 inference(quant_inst,[status(thm)],[])).
% 2.22/2.49 tff(10334,plain,
% 2.22/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))),
% 2.22/2.49 inference(modus_ponens,[status(thm)],[10333, 10332])).
% 2.22/2.49 tff(10335,plain,
% 2.22/2.49 ($false),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[10334, 75, 10328, 286, 10326, 10325])).
% 2.22/2.49 tff(10336,plain,((~r(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | r(s(s(s(s(z)))), z) | r(elem!1, z) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.22/2.49 tff(10337,plain,
% 2.22/2.49 (r(elem!1, z)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[10336, 7174, 286, 698, 285])).
% 2.22/2.49 tff(10338,plain,
% 2.22/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(elem!1, 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(elem!1, s(z))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 2.22/2.49 inference(rewrite,[status(thm)],[])).
% 2.22/2.49 tff(10339,plain,
% 2.22/2.49 (((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(elem!1, s(z))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 2.22/2.49 inference(rewrite,[status(thm)],[])).
% 2.22/2.49 tff(10340,plain,
% 2.22/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z)))))),
% 2.22/2.49 inference(monotonicity,[status(thm)],[10339])).
% 2.22/2.49 tff(10341,plain,
% 2.22/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 2.22/2.49 inference(transitivity,[status(thm)],[10340, 10338])).
% 2.22/2.49 tff(10342,plain,
% 2.22/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.22/2.49 inference(quant_inst,[status(thm)],[])).
% 2.22/2.49 tff(10343,plain,
% 2.22/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z)))),
% 2.22/2.49 inference(modus_ponens,[status(thm)],[10342, 10341])).
% 2.22/2.49 tff(10344,plain,
% 2.22/2.49 ($false),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[10343, 37, 10337, 114, 698, 10320])).
% 2.22/2.49 tff(10345,plain,((~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(s(s(s(z)))))) | b(z, elem!1) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.49 tff(10346,plain,
% 2.22/2.49 (~b(s(z), z)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[10345, 10314, 9473, 10282, 10294, 10296])).
% 2.22/2.49 tff(10347,plain,
% 2.22/2.49 (r(s(z), z)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[169, 10346])).
% 2.22/2.49 tff(10348,plain,
% 2.22/2.49 (~r(s(s(s(s(z)))), z)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[2586, 10347, 10316])).
% 2.22/2.49 tff(10349,plain,
% 2.22/2.49 (~r(elem!1, z)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[162, 10347, 10294])).
% 2.22/2.49 tff(10350,plain,
% 2.22/2.49 ($false),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[10336, 10349, 10348, 9473, 10314, 10296])).
% 2.22/2.49 tff(10351,plain,(b(elem!1, s(z)) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.22/2.49 tff(10352,plain,
% 2.22/2.49 (b(elem!1, s(z))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[10351, 99])).
% 2.22/2.49 tff(10353,plain,
% 2.22/2.49 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[3884, 37, 698, 5486])).
% 2.22/2.49 tff(10354,plain,
% 2.22/2.49 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[1660, 10353, 5479])).
% 2.22/2.49 tff(10355,plain,
% 2.22/2.49 (r(s(s(s(s(z)))), z)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[9484, 288, 698])).
% 2.22/2.49 tff(10356,plain,
% 2.22/2.49 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[3872, 37, 698, 5486])).
% 2.22/2.49 tff(10357,plain,
% 2.22/2.49 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[3876, 58, 5701, 10356])).
% 2.22/2.49 tff(10358,plain,
% 2.22/2.49 (~r(s(z), s(s(s(s(z)))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[2586, 5534, 1408])).
% 2.22/2.49 tff(10359,plain,
% 2.22/2.49 (~b(s(z), s(s(s(s(z)))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[5720, 5779, 1619, 5712])).
% 2.22/2.49 tff(10360,plain,
% 2.22/2.49 ($false),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[489, 10359, 10358])).
% 2.22/2.49 tff(10361,plain,((~r(s(z), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~(z = elem!1)) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.49 tff(10362,plain,
% 2.22/2.49 (~r(s(z), elem!1)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[10361, 10357, 288, 10355, 5481, 10354])).
% 2.22/2.49 tff(10363,plain,
% 2.22/2.49 (b(s(z), elem!1)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[601, 10362, 2478])).
% 2.22/2.49 tff(10364,plain,
% 2.22/2.49 (b(s(z), z)),
% 2.22/2.49 inference(modus_ponens,[status(thm)],[10363, 9519])).
% 2.22/2.49 tff(10365,plain,
% 2.22/2.49 ((~r(s(s(s(elem!1))), elem!1)) <=> (~r(s(s(s(z))), elem!1))),
% 2.22/2.49 inference(monotonicity,[status(thm)],[3419])).
% 2.22/2.49 tff(10366,plain,
% 2.22/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.22/2.49 inference(rewrite,[status(thm)],[])).
% 2.22/2.49 tff(10367,plain,
% 2.22/2.49 (((~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(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.22/2.49 inference(rewrite,[status(thm)],[])).
% 2.22/2.49 tff(10368,plain,
% 2.22/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), 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(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1))))))),
% 2.22/2.49 inference(monotonicity,[status(thm)],[10367])).
% 2.22/2.49 tff(10369,plain,
% 2.22/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), 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(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.22/2.50 inference(transitivity,[status(thm)],[10368, 10366])).
% 2.22/2.50 tff(10370,plain,
% 2.22/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), 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)))))),
% 2.22/2.50 inference(quant_inst,[status(thm)],[])).
% 2.22/2.50 tff(10371,plain,
% 2.22/2.50 ((~![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))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 2.22/2.50 inference(modus_ponens,[status(thm)],[10370, 10369])).
% 2.22/2.50 tff(10372,plain,
% 2.22/2.50 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.22/2.50 inference(unit_resolution,[status(thm)],[10371, 37, 2647, 624])).
% 2.22/2.50 tff(10373,plain,
% 2.22/2.50 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.22/2.50 inference(modus_ponens,[status(thm)],[10372, 9478])).
% 2.22/2.50 tff(10374,plain,
% 2.22/2.50 (b(s(s(s(z))), s(s(elem!1)))),
% 2.22/2.50 inference(unit_resolution,[status(thm)],[62, 10373, 16])).
% 2.22/2.50 tff(10375,plain,
% 2.22/2.50 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.22/2.50 inference(monotonicity,[status(thm)],[3417])).
% 2.22/2.50 tff(10376,plain,
% 2.22/2.50 (r(s(s(s(s(z)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 2.22/2.50 inference(symmetry,[status(thm)],[10375])).
% 2.22/2.50 tff(10377,plain,
% 2.22/2.50 ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 2.22/2.50 inference(monotonicity,[status(thm)],[10376])).
% 2.22/2.50 tff(10378,plain,
% 2.22/2.50 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.22/2.50 inference(unit_resolution,[status(thm)],[3455, 37, 698, 624])).
% 2.22/2.50 tff(10379,plain,
% 2.22/2.50 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.22/2.50 inference(modus_ponens,[status(thm)],[10378, 10377])).
% 2.22/2.50 tff(10380,plain,
% 2.22/2.50 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.22/2.50 inference(unit_resolution,[status(thm)],[2898, 10379])).
% 2.22/2.50 tff(10381,plain,
% 2.22/2.50 (r(s(s(z)), s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(z))))),
% 2.22/2.50 inference(monotonicity,[status(thm)],[290])).
% 2.22/2.50 tff(10382,plain,
% 2.22/2.50 (r(s(s(elem!1)), s(s(s(z)))) <=> r(s(s(z)), s(s(s(z))))),
% 2.22/2.50 inference(symmetry,[status(thm)],[10381])).
% 2.22/2.50 tff(10383,plain,
% 2.22/2.50 (r(s(s(elem!1)), s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.22/2.50 inference(monotonicity,[status(thm)],[3417])).
% 2.22/2.50 tff(10384,plain,
% 2.22/2.50 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(z))))),
% 2.22/2.50 inference(symmetry,[status(thm)],[10383])).
% 2.22/2.50 tff(10385,plain,
% 2.22/2.50 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(z))))),
% 2.22/2.50 inference(transitivity,[status(thm)],[10384, 10382])).
% 2.22/2.50 tff(10386,plain,
% 2.22/2.50 ((~r(s(s(elem!1)), s(s(s(elem!1))))) <=> (~r(s(s(z)), s(s(s(z)))))),
% 2.22/2.50 inference(monotonicity,[status(thm)],[10385])).
% 2.22/2.50 tff(10387,plain,
% 2.22/2.50 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.22/2.50 inference(unit_resolution,[status(thm)],[5811, 37, 2647, 624])).
% 2.22/2.50 tff(10388,plain,
% 2.22/2.50 (~r(s(s(z)), s(s(s(z))))),
% 2.22/2.50 inference(modus_ponens,[status(thm)],[10387, 10386])).
% 2.22/2.50 tff(10389,plain,
% 2.22/2.50 (b(s(s(z)), s(s(s(z))))),
% 2.22/2.50 inference(unit_resolution,[status(thm)],[8252, 10388])).
% 2.22/2.50 tff(10390,plain,
% 2.22/2.50 (~b(s(s(s(z))), s(s(z)))),
% 2.22/2.50 inference(unit_resolution,[status(thm)],[8435, 10389, 9742, 10380])).
% 2.22/2.50 tff(10391,plain,
% 2.22/2.50 ($false),
% 2.22/2.50 inference(unit_resolution,[status(thm)],[9799, 10390, 10374, 288])).
% 2.22/2.50 tff(10392,plain,((~r(s(s(s(elem!1))), elem!1)) | (~(z = elem!1)) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.50 tff(10393,plain,
% 2.22/2.50 (~r(s(s(s(elem!1))), elem!1)),
% 2.22/2.50 inference(unit_resolution,[status(thm)],[10392, 5486, 5493, 288, 698])).
% 2.22/2.50 tff(10394,plain,
% 2.22/2.50 (~r(s(s(s(z))), elem!1)),
% 2.22/2.50 inference(modus_ponens,[status(thm)],[10393, 10365])).
% 2.22/2.50 tff(10395,plain,
% 2.22/2.50 (b(s(s(s(z))), elem!1)),
% 2.22/2.50 inference(unit_resolution,[status(thm)],[1115, 10394, 4145])).
% 2.22/2.50 tff(10396,plain,
% 2.22/2.50 (~b(s(s(s(z))), s(z))),
% 2.22/2.50 inference(unit_resolution,[status(thm)],[8081, 10395, 1391, 5501, 10364])).
% 2.22/2.50 tff(10397,plain,
% 2.22/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.50 inference(rewrite,[status(thm)],[])).
% 2.32/2.50 tff(10398,plain,
% 2.32/2.50 (((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.50 inference(rewrite,[status(thm)],[])).
% 2.32/2.50 tff(10399,plain,
% 2.32/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 2.32/2.50 inference(monotonicity,[status(thm)],[10398])).
% 2.32/2.50 tff(10400,plain,
% 2.32/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.50 inference(transitivity,[status(thm)],[10399, 10397])).
% 2.32/2.50 tff(10401,plain,
% 2.32/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.50 inference(quant_inst,[status(thm)],[])).
% 2.32/2.50 tff(10402,plain,
% 2.32/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 2.32/2.50 inference(modus_ponens,[status(thm)],[10401, 10400])).
% 2.32/2.50 tff(10403,plain,
% 2.32/2.50 ($false),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[10402, 75, 1619, 9671, 3068, 9656])).
% 2.32/2.50 tff(10404,plain,((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) | (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.50 tff(10405,plain,
% 2.32/2.50 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[10404, 10354, 698, 3989, 3959, 5486])).
% 2.32/2.50 tff(10406,plain,
% 2.32/2.50 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[813, 10405, 3966])).
% 2.32/2.50 tff(10407,plain,
% 2.32/2.50 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.32/2.50 inference(monotonicity,[status(thm)],[225])).
% 2.32/2.50 tff(10408,plain,
% 2.32/2.50 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.32/2.50 inference(symmetry,[status(thm)],[10407])).
% 2.32/2.50 tff(10409,plain,
% 2.32/2.50 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 2.32/2.50 inference(monotonicity,[status(thm)],[10408])).
% 2.32/2.50 tff(10410,plain,
% 2.32/2.50 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))),
% 2.32/2.50 inference(transitivity,[status(thm)],[10409, 2957])).
% 2.32/2.50 tff(10411,plain,
% 2.32/2.50 ((s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(z))))),
% 2.32/2.50 inference(symmetry,[status(thm)],[10410])).
% 2.32/2.50 tff(10412,plain,
% 2.32/2.50 ((~(s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(s(s(z)))))),
% 2.32/2.50 inference(monotonicity,[status(thm)],[10411])).
% 2.32/2.50 tff(10413,plain,
% 2.32/2.50 (~(s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[862, 3898])).
% 2.32/2.50 tff(10414,plain,
% 2.32/2.50 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))),
% 2.32/2.50 inference(modus_ponens,[status(thm)],[10413, 10412])).
% 2.32/2.50 tff(10415,plain,
% 2.32/2.50 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[2037, 75, 107, 1391, 1168])).
% 2.32/2.50 tff(10416,plain,
% 2.32/2.50 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[1230, 58, 1227, 10415])).
% 2.32/2.50 tff(10417,plain,
% 2.32/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, 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(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.32/2.50 inference(rewrite,[status(thm)],[])).
% 2.32/2.50 tff(10418,plain,
% 2.32/2.50 (((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.32/2.50 inference(rewrite,[status(thm)],[])).
% 2.32/2.50 tff(10419,plain,
% 2.32/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(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(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))))),
% 2.32/2.50 inference(monotonicity,[status(thm)],[10418])).
% 2.32/2.50 tff(10420,plain,
% 2.32/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(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(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.32/2.50 inference(transitivity,[status(thm)],[10419, 10417])).
% 2.32/2.50 tff(10421,plain,
% 2.32/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.32/2.50 inference(quant_inst,[status(thm)],[])).
% 2.32/2.50 tff(10422,plain,
% 2.32/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 2.32/2.50 inference(modus_ponens,[status(thm)],[10421, 10420])).
% 2.32/2.50 tff(10423,plain,
% 2.32/2.50 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[10422, 37, 1067, 10416])).
% 2.32/2.50 tff(10424,plain,
% 2.32/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.32/2.50 inference(rewrite,[status(thm)],[])).
% 2.32/2.50 tff(10425,plain,
% 2.32/2.50 (((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.32/2.50 inference(rewrite,[status(thm)],[])).
% 2.32/2.50 tff(10426,plain,
% 2.32/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))))),
% 2.32/2.50 inference(monotonicity,[status(thm)],[10425])).
% 2.32/2.50 tff(10427,plain,
% 2.32/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.32/2.50 inference(transitivity,[status(thm)],[10426, 10424])).
% 2.32/2.50 tff(10428,plain,
% 2.32/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.32/2.50 inference(quant_inst,[status(thm)],[])).
% 2.32/2.50 tff(10429,plain,
% 2.32/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 2.32/2.50 inference(modus_ponens,[status(thm)],[10428, 10427])).
% 2.32/2.50 tff(10430,plain,
% 2.32/2.50 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[10429, 75, 107, 1391, 1119, 1168])).
% 2.32/2.50 tff(10431,plain,
% 2.32/2.50 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[2930, 58, 10430])).
% 2.32/2.50 tff(10432,plain,
% 2.32/2.50 ($false),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[10431, 10423, 10414])).
% 2.32/2.50 tff(10433,plain,((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~(s(s(elem!1)) = s(s(z)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.50 tff(10434,plain,
% 2.32/2.50 (~r(s(s(s(z))), s(z))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[10433, 10395, 1391, 3839, 10406, 10363])).
% 2.32/2.50 tff(10435,plain,
% 2.32/2.50 ($false),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[1081, 10434, 10396])).
% 2.32/2.50 tff(10436,plain,(b(s(s(z)), elem!1) | (~b(elem!1, s(z))) | (~(z = elem!1)) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.50 tff(10437,plain,
% 2.32/2.50 (~(z = elem!1)),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[10436, 10352, 99, 9473])).
% 2.32/2.50 tff(10438,plain,
% 2.32/2.50 (~(s(z) = elem!1)),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[1393, 10352])).
% 2.32/2.50 tff(10439,plain,
% 2.32/2.50 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.32/2.50 inference(monotonicity,[status(thm)],[1064])).
% 2.32/2.50 tff(10440,plain,
% 2.32/2.50 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.32/2.50 inference(transitivity,[status(thm)],[10439, 269])).
% 2.32/2.50 tff(10441,plain,
% 2.32/2.50 ((s(elem!1) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(z))))),
% 2.32/2.50 inference(symmetry,[status(thm)],[10440])).
% 2.32/2.50 tff(10442,plain,
% 2.32/2.50 ((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(s(s(z)))))),
% 2.32/2.50 inference(monotonicity,[status(thm)],[10441])).
% 2.32/2.50 tff(10443,plain,
% 2.32/2.50 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[1145, 3143])).
% 2.32/2.50 tff(10444,plain,
% 2.32/2.50 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))),
% 2.32/2.50 inference(modus_ponens,[status(thm)],[10443, 10442])).
% 2.32/2.50 tff(10445,plain,
% 2.32/2.50 ((s(s(s(s(s(s(s(z))))))) = s(s(z))) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.32/2.50 inference(monotonicity,[status(thm)],[3143])).
% 2.32/2.50 tff(10446,plain,
% 2.32/2.50 ((~(s(s(s(s(s(s(s(z))))))) = s(s(z)))) <=> (~(s(s(s(s(s(s(s(z))))))) = elem!1))),
% 2.32/2.50 inference(monotonicity,[status(thm)],[10445])).
% 2.32/2.50 tff(10447,plain,
% 2.32/2.50 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.32/2.50 inference(modus_ponens,[status(thm)],[1045, 10446])).
% 2.32/2.50 tff(10448,plain,
% 2.32/2.50 (b(s(s(z)), s(z))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[6993, 588, 1391, 99])).
% 2.32/2.50 tff(10449,plain,
% 2.32/2.50 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[3906, 10265, 10448, 10223])).
% 2.32/2.50 tff(10450,plain,
% 2.32/2.50 (r(s(s(z)), s(s(s(s(z)))))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[465, 10449])).
% 2.32/2.50 tff(10451,plain,
% 2.32/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.32/2.50 inference(rewrite,[status(thm)],[])).
% 2.32/2.50 tff(10452,plain,
% 2.32/2.50 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.32/2.50 inference(rewrite,[status(thm)],[])).
% 2.32/2.50 tff(10453,plain,
% 2.32/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 2.32/2.50 inference(monotonicity,[status(thm)],[10452])).
% 2.32/2.50 tff(10454,plain,
% 2.32/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.32/2.51 inference(transitivity,[status(thm)],[10453, 10451])).
% 2.32/2.51 tff(10455,plain,
% 2.32/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))))))),
% 2.32/2.51 inference(quant_inst,[status(thm)],[])).
% 2.32/2.51 tff(10456,plain,
% 2.32/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 2.32/2.51 inference(modus_ponens,[status(thm)],[10455, 10454])).
% 2.32/2.51 tff(10457,plain,
% 2.32/2.51 (~b(elem!1, s(s(s(s(z)))))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[10456, 75, 1391, 10223, 10265])).
% 2.32/2.51 tff(10458,plain,
% 2.32/2.51 (r(elem!1, s(s(s(s(z)))))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[278, 10457, 10229])).
% 2.32/2.51 tff(10459,plain,
% 2.32/2.51 (~r(elem!1, s(s(z)))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[6546, 37, 10458, 10450])).
% 2.32/2.51 tff(10460,plain,
% 2.32/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))) | (~b(elem!1, 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(X1, 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(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.32/2.51 inference(rewrite,[status(thm)],[])).
% 2.32/2.51 tff(10461,plain,
% 2.32/2.51 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z))))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.32/2.51 inference(rewrite,[status(thm)],[])).
% 2.32/2.51 tff(10462,plain,
% 2.32/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(s(s(z))))))))),
% 2.32/2.51 inference(monotonicity,[status(thm)],[10461])).
% 2.32/2.51 tff(10463,plain,
% 2.32/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.32/2.51 inference(transitivity,[status(thm)],[10462, 10460])).
% 2.32/2.51 tff(10464,plain,
% 2.32/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))),
% 2.32/2.51 inference(quant_inst,[status(thm)],[])).
% 2.32/2.51 tff(10465,plain,
% 2.32/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(s(s(z))))))),
% 2.32/2.51 inference(modus_ponens,[status(thm)],[10464, 10463])).
% 2.32/2.51 tff(10466,plain,
% 2.32/2.51 (~b(elem!1, s(s(z)))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[10465, 75, 1391, 10448, 10223, 10265])).
% 2.32/2.51 tff(10467,plain,
% 2.32/2.51 ((elem!1 = s(s(z))) | r(elem!1, s(s(z)))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[398, 58, 10466])).
% 2.32/2.51 tff(10468,plain,
% 2.32/2.51 (elem!1 = s(s(z))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[10467, 10459])).
% 2.32/2.51 tff(10469,plain,
% 2.32/2.51 (b(z, elem!1) <=> b(z, s(s(z)))),
% 2.32/2.51 inference(monotonicity,[status(thm)],[10468])).
% 2.32/2.51 tff(10470,plain,
% 2.32/2.51 (b(z, s(s(z)))),
% 2.32/2.51 inference(modus_ponens,[status(thm)],[1518, 10469])).
% 2.32/2.51 tff(10471,plain,
% 2.32/2.51 (s(s(z)) = elem!1),
% 2.32/2.51 inference(symmetry,[status(thm)],[10468])).
% 2.32/2.51 tff(10472,plain,
% 2.32/2.51 (b(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.32/2.51 inference(monotonicity,[status(thm)],[10471])).
% 2.32/2.51 tff(10473,plain,
% 2.32/2.51 (b(s(s(s(s(s(s(s(z))))))), elem!1) <=> b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.32/2.51 inference(symmetry,[status(thm)],[10472])).
% 2.32/2.51 tff(10474,plain,
% 2.32/2.51 ((s(s(s(s(s(s(s(z))))))) = elem!1) <=> (s(s(s(s(s(s(s(z))))))) = s(s(z)))),
% 2.32/2.51 inference(monotonicity,[status(thm)],[10468])).
% 2.32/2.51 tff(10475,plain,
% 2.32/2.51 ((s(s(s(s(s(s(s(z))))))) = s(s(z))) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.32/2.51 inference(symmetry,[status(thm)],[10474])).
% 2.32/2.51 tff(10476,plain,
% 2.32/2.51 ((~(s(s(s(s(s(s(s(z))))))) = s(s(z)))) <=> (~(s(s(s(s(s(s(s(z))))))) = elem!1))),
% 2.32/2.51 inference(monotonicity,[status(thm)],[10475])).
% 2.32/2.51 tff(10477,plain,
% 2.32/2.51 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.32/2.51 inference(modus_ponens,[status(thm)],[1045, 10476])).
% 2.32/2.51 tff(10478,plain,
% 2.32/2.51 (r(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.32/2.51 inference(monotonicity,[status(thm)],[10471])).
% 2.32/2.51 tff(10479,plain,
% 2.32/2.51 ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) <=> (~r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.32/2.51 inference(monotonicity,[status(thm)],[10478])).
% 2.32/2.51 tff(10480,plain,
% 2.32/2.51 (r(s(z), elem!1) <=> r(s(z), s(s(z)))),
% 2.32/2.51 inference(monotonicity,[status(thm)],[10468])).
% 2.32/2.51 tff(10481,plain,
% 2.32/2.51 (r(s(z), s(s(z)))),
% 2.32/2.51 inference(modus_ponens,[status(thm)],[588, 10480])).
% 2.32/2.51 tff(10482,plain,
% 2.32/2.51 (~r(s(s(z)), elem!1)),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[6555, 37, 10458, 10450])).
% 2.32/2.51 tff(10483,plain,
% 2.32/2.51 (s(s(z)) = elem!1),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[104, 10482, 99])).
% 2.32/2.51 tff(10484,plain,
% 2.32/2.51 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(z)))))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[1134, 10483])).
% 2.32/2.51 tff(10485,assumption,(r(s(s(s(s(s(s(s(z))))))), s(s(z)))), introduced(assumption)).
% 2.32/2.51 tff(10486,plain,
% 2.32/2.51 (((~![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(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.32/2.51 inference(rewrite,[status(thm)],[])).
% 2.32/2.51 tff(10487,plain,
% 2.32/2.51 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.32/2.51 inference(rewrite,[status(thm)],[])).
% 2.32/2.51 tff(10488,plain,
% 2.32/2.51 (((~![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(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $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(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 2.32/2.51 inference(monotonicity,[status(thm)],[10487])).
% 2.32/2.51 tff(10489,plain,
% 2.32/2.51 (((~![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(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $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(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.32/2.51 inference(transitivity,[status(thm)],[10488, 10486])).
% 2.32/2.51 tff(10490,plain,
% 2.32/2.51 ((~![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(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.32/2.51 inference(quant_inst,[status(thm)],[])).
% 2.32/2.51 tff(10491,plain,
% 2.32/2.51 ((~![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(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.32/2.51 inference(modus_ponens,[status(thm)],[10490, 10489])).
% 2.32/2.51 tff(10492,plain,
% 2.32/2.51 ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[10491, 37, 1997])).
% 2.32/2.51 tff(10493,plain,
% 2.32/2.51 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[10492, 10485])).
% 2.32/2.51 tff(10494,plain,
% 2.32/2.51 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[1230, 58, 1227, 10493])).
% 2.32/2.51 tff(10495,assumption,(elem!1 = s(s(z))), introduced(assumption)).
% 2.32/2.51 tff(10496,plain,
% 2.32/2.51 (s(s(z)) = elem!1),
% 2.32/2.51 inference(symmetry,[status(thm)],[10495])).
% 2.32/2.51 tff(10497,plain,
% 2.32/2.51 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(z)))), elem!1)),
% 2.32/2.51 inference(monotonicity,[status(thm)],[10496])).
% 2.32/2.51 tff(10498,plain,
% 2.32/2.51 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(z)))),
% 2.32/2.51 inference(symmetry,[status(thm)],[10497])).
% 2.32/2.51 tff(10499,plain,
% 2.32/2.51 (r(s(s(s(s(z)))), s(s(z)))),
% 2.32/2.51 inference(modus_ponens,[status(thm)],[698, 10498])).
% 2.32/2.51 tff(10500,plain,
% 2.32/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(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(s(z))))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.32/2.51 inference(rewrite,[status(thm)],[])).
% 2.32/2.51 tff(10501,plain,
% 2.32/2.51 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.32/2.51 inference(rewrite,[status(thm)],[])).
% 2.32/2.51 tff(10502,plain,
% 2.32/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(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(s(z))))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 2.32/2.51 inference(monotonicity,[status(thm)],[10501])).
% 2.32/2.51 tff(10503,plain,
% 2.32/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(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(s(z))))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.32/2.51 inference(transitivity,[status(thm)],[10502, 10500])).
% 2.32/2.51 tff(10504,plain,
% 2.32/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.32/2.51 inference(quant_inst,[status(thm)],[])).
% 2.32/2.51 tff(10505,plain,
% 2.32/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 2.32/2.51 inference(modus_ponens,[status(thm)],[10504, 10503])).
% 2.32/2.51 tff(10506,plain,
% 2.32/2.51 ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[10505, 37])).
% 2.32/2.51 tff(10507,plain,
% 2.32/2.51 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[10506, 10485, 10499])).
% 2.32/2.51 tff(10508,plain,
% 2.32/2.51 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[1179, 58, 1176, 10507])).
% 2.32/2.51 tff(10509,plain,
% 2.32/2.51 ($false),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[10271, 75, 578, 982, 10508, 10494])).
% 2.32/2.51 tff(10510,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~(elem!1 = s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.51 tff(10511,plain,
% 2.32/2.51 (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[10510, 10223, 10265, 10484, 10481, 698, 10468])).
% 2.32/2.51 tff(10512,plain,
% 2.32/2.51 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.32/2.51 inference(modus_ponens,[status(thm)],[10511, 10479])).
% 2.32/2.51 tff(10513,plain,
% 2.32/2.51 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[813, 10512, 10477])).
% 2.32/2.51 tff(10514,plain,
% 2.32/2.51 (b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.32/2.51 inference(modus_ponens,[status(thm)],[10513, 10473])).
% 2.32/2.51 tff(10515,plain,
% 2.32/2.51 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(z)))),
% 2.32/2.51 inference(monotonicity,[status(thm)],[10468])).
% 2.32/2.51 tff(10516,plain,
% 2.32/2.51 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[1013, 10483])).
% 2.32/2.51 tff(10517,plain,
% 2.32/2.51 (~(s(s(s(z))) = elem!1)),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[1026, 10516, 10229])).
% 2.32/2.51 tff(10518,plain,
% 2.32/2.51 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(z)))),
% 2.32/2.51 inference(monotonicity,[status(thm)],[10495])).
% 2.32/2.51 tff(10519,plain,
% 2.32/2.51 (r(s(s(s(z))), s(s(z)))),
% 2.32/2.51 inference(modus_ponens,[status(thm)],[1061, 10518])).
% 2.32/2.51 tff(10520,plain,
% 2.32/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.32/2.51 inference(rewrite,[status(thm)],[])).
% 2.32/2.51 tff(10521,plain,
% 2.32/2.51 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.32/2.51 inference(rewrite,[status(thm)],[])).
% 2.32/2.51 tff(10522,plain,
% 2.32/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))))),
% 2.32/2.51 inference(monotonicity,[status(thm)],[10521])).
% 2.32/2.51 tff(10523,plain,
% 2.32/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.32/2.51 inference(transitivity,[status(thm)],[10522, 10520])).
% 2.32/2.51 tff(10524,plain,
% 2.32/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.32/2.51 inference(quant_inst,[status(thm)],[])).
% 2.32/2.51 tff(10525,plain,
% 2.32/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))),
% 2.32/2.51 inference(modus_ponens,[status(thm)],[10524, 10523])).
% 2.32/2.51 tff(10526,plain,
% 2.32/2.51 ($false),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[10525, 75, 3497, 578, 1053, 3489])).
% 2.32/2.51 tff(10527,plain,((~r(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (s(s(s(s(z)))) = s(s(s(z)))) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.51 tff(10528,plain,
% 2.32/2.51 ((~r(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(z))), elem!1))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[10527, 264])).
% 2.32/2.51 tff(10529,plain,
% 2.32/2.51 (~b(s(z), s(s(s(z))))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[10528, 1061, 698, 578])).
% 2.32/2.51 tff(10530,plain,
% 2.32/2.51 (r(s(z), s(s(s(z))))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[1263, 10529])).
% 2.32/2.51 tff(10531,plain,
% 2.32/2.51 (((~![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(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 2.32/2.51 inference(rewrite,[status(thm)],[])).
% 2.32/2.51 tff(10532,plain,
% 2.32/2.51 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 2.32/2.51 inference(rewrite,[status(thm)],[])).
% 2.32/2.51 tff(10533,plain,
% 2.32/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z)))))))),
% 2.32/2.51 inference(monotonicity,[status(thm)],[10532])).
% 2.32/2.51 tff(10534,plain,
% 2.32/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 2.32/2.52 inference(transitivity,[status(thm)],[10533, 10531])).
% 2.32/2.52 tff(10535,plain,
% 2.32/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 2.32/2.52 inference(quant_inst,[status(thm)],[])).
% 2.32/2.52 tff(10536,plain,
% 2.32/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z)))))),
% 2.32/2.52 inference(modus_ponens,[status(thm)],[10535, 10534])).
% 2.32/2.52 tff(10537,plain,
% 2.32/2.52 ($false),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[10536, 37, 1997, 10530, 10519])).
% 2.32/2.52 tff(10538,plain,((~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(z)))) | (~(elem!1 = s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.52 tff(10539,plain,
% 2.32/2.52 (~r(s(s(s(z))), elem!1)),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[10538, 10481, 10468, 698, 10223])).
% 2.32/2.52 tff(10540,plain,
% 2.32/2.52 (b(s(s(s(z))), elem!1)),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[1115, 10539, 10517])).
% 2.32/2.52 tff(10541,plain,
% 2.32/2.52 (b(s(s(s(z))), s(s(z)))),
% 2.32/2.52 inference(modus_ponens,[status(thm)],[10540, 10515])).
% 2.32/2.52 tff(10542,plain,
% 2.32/2.52 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[1145, 10483])).
% 2.32/2.52 tff(10543,plain,
% 2.32/2.52 (r(elem!1, z) <=> r(s(s(z)), z)),
% 2.32/2.52 inference(monotonicity,[status(thm)],[10468])).
% 2.32/2.52 tff(10544,plain,
% 2.32/2.52 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(z)))), s(elem!1))),
% 2.32/2.52 inference(monotonicity,[status(thm)],[289])).
% 2.32/2.52 tff(10545,plain,
% 2.32/2.52 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(z))),
% 2.32/2.52 inference(symmetry,[status(thm)],[10544])).
% 2.32/2.52 tff(10546,plain,
% 2.32/2.52 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 2.32/2.52 inference(monotonicity,[status(thm)],[290])).
% 2.32/2.52 tff(10547,plain,
% 2.32/2.52 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(z)), s(s(s(z))))),
% 2.32/2.52 inference(symmetry,[status(thm)],[10546])).
% 2.32/2.52 tff(10548,plain,
% 2.32/2.52 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(z))))),
% 2.32/2.52 inference(transitivity,[status(thm)],[4223, 10547])).
% 2.32/2.52 tff(10549,plain,
% 2.32/2.52 ((~b(s(s(elem!1)), s(s(s(elem!1))))) <=> (~b(s(s(z)), s(s(s(z)))))),
% 2.32/2.52 inference(monotonicity,[status(thm)],[10548])).
% 2.32/2.52 tff(10550,plain,
% 2.32/2.52 (b(s(s(z)), elem!1)),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[10436, 288, 1391, 698])).
% 2.32/2.52 tff(10551,plain,
% 2.32/2.52 (b(s(s(elem!1)), elem!1)),
% 2.32/2.52 inference(modus_ponens,[status(thm)],[10550, 3648])).
% 2.32/2.52 tff(10552,plain,
% 2.32/2.52 (b(s(s(elem!1)), z)),
% 2.32/2.52 inference(modus_ponens,[status(thm)],[10550, 5540])).
% 2.32/2.52 tff(10553,plain,
% 2.32/2.52 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.32/2.52 inference(monotonicity,[status(thm)],[3417])).
% 2.32/2.52 tff(10554,plain,
% 2.32/2.52 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 2.32/2.52 inference(modus_ponens,[status(thm)],[10380, 10553])).
% 2.32/2.52 tff(10555,plain,
% 2.32/2.52 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[3470, 37, 698, 624])).
% 2.32/2.52 tff(10556,plain,
% 2.32/2.52 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.32/2.52 inference(modus_ponens,[status(thm)],[10555, 3464])).
% 2.32/2.52 tff(10557,plain,
% 2.32/2.52 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[575, 10556])).
% 2.32/2.52 tff(10558,plain,
% 2.32/2.52 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.32/2.52 inference(modus_ponens,[status(thm)],[10557, 3832])).
% 2.32/2.52 tff(10559,plain,
% 2.32/2.52 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[1655, 468, 6060])).
% 2.32/2.52 tff(10560,plain,
% 2.32/2.52 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[1660, 10559, 5479])).
% 2.32/2.52 tff(10561,plain,
% 2.32/2.52 (~b(s(s(s(s(z)))), elem!1)),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[6070, 468, 288, 2609, 707, 371, 372, 1892])).
% 2.32/2.52 tff(10562,plain,
% 2.32/2.52 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(z))),
% 2.32/2.52 inference(monotonicity,[status(thm)],[3422])).
% 2.32/2.52 tff(10563,plain,
% 2.32/2.52 (r(s(s(elem!1)), s(z)) <=> r(s(s(elem!1)), s(elem!1))),
% 2.32/2.52 inference(symmetry,[status(thm)],[10562])).
% 2.32/2.52 tff(10564,plain,
% 2.32/2.52 (r(s(s(z)), s(elem!1)) <=> r(s(s(elem!1)), s(z))),
% 2.32/2.52 inference(symmetry,[status(thm)],[9529])).
% 2.32/2.52 tff(10565,plain,
% 2.32/2.52 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(z))),
% 2.32/2.52 inference(transitivity,[status(thm)],[5867, 10564])).
% 2.32/2.52 tff(10566,assumption,(~b(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 2.32/2.52 tff(10567,plain,
% 2.32/2.52 (r(s(s(s(s(z)))), elem!1)),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[283, 3445, 10566])).
% 2.32/2.52 tff(10568,plain,
% 2.32/2.52 (r(elem!1, s(s(s(s(z)))))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[278, 3522, 6193])).
% 2.32/2.52 tff(10569,plain,
% 2.32/2.52 (r(s(s(elem!1)), elem!1)),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[2673, 1, 5484])).
% 2.32/2.52 tff(10570,plain,
% 2.32/2.52 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(z))), elem!1)),
% 2.32/2.52 inference(symmetry,[status(thm)],[4176])).
% 2.32/2.52 tff(10571,plain,
% 2.32/2.52 ((~r(s(s(s(elem!1))), elem!1)) <=> (~r(s(s(s(z))), elem!1))),
% 2.32/2.52 inference(monotonicity,[status(thm)],[10570])).
% 2.32/2.52 tff(10572,plain,
% 2.32/2.52 (b(z, s(z)) <=> b(elem!1, s(elem!1))),
% 2.32/2.52 inference(transitivity,[status(thm)],[5495, 5733])).
% 2.32/2.52 tff(10573,plain,
% 2.32/2.52 (b(z, s(z))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[9715, 698, 288, 3195, 108])).
% 2.32/2.52 tff(10574,plain,
% 2.32/2.52 (b(elem!1, s(elem!1))),
% 2.32/2.52 inference(modus_ponens,[status(thm)],[10573, 10572])).
% 2.32/2.52 tff(10575,plain,
% 2.32/2.52 (b(elem!1, s(z))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[8118, 10573, 288])).
% 2.32/2.52 tff(10576,plain,
% 2.32/2.52 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[1660, 5062, 5479])).
% 2.32/2.52 tff(10577,plain,
% 2.32/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.32/2.52 inference(rewrite,[status(thm)],[])).
% 2.32/2.52 tff(10578,plain,
% 2.32/2.52 (((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.32/2.52 inference(rewrite,[status(thm)],[])).
% 2.32/2.52 tff(10579,plain,
% 2.32/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 2.32/2.52 inference(monotonicity,[status(thm)],[10578])).
% 2.32/2.52 tff(10580,plain,
% 2.32/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.32/2.52 inference(transitivity,[status(thm)],[10579, 10577])).
% 2.32/2.52 tff(10581,plain,
% 2.32/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.32/2.52 inference(quant_inst,[status(thm)],[])).
% 2.32/2.52 tff(10582,plain,
% 2.32/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 2.32/2.52 inference(modus_ponens,[status(thm)],[10581, 10580])).
% 2.32/2.52 tff(10583,plain,
% 2.32/2.52 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[10582, 75, 10576, 5975, 9766])).
% 2.32/2.52 tff(10584,plain,
% 2.32/2.52 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.32/2.52 inference(modus_ponens,[status(thm)],[10583, 5585])).
% 2.32/2.52 tff(10585,plain,
% 2.32/2.52 (r(s(s(s(z))), s(s(elem!1)))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[62, 10584, 16])).
% 2.32/2.52 tff(10586,plain,
% 2.32/2.52 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.32/2.52 inference(modus_ponens,[status(thm)],[10585, 5537])).
% 2.32/2.52 tff(10587,plain,
% 2.32/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(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))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.32/2.52 inference(rewrite,[status(thm)],[])).
% 2.32/2.52 tff(10588,plain,
% 2.32/2.52 (((~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(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.32/2.52 inference(rewrite,[status(thm)],[])).
% 2.32/2.52 tff(10589,plain,
% 2.32/2.52 (((~![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(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1))))))),
% 2.32/2.52 inference(monotonicity,[status(thm)],[10588])).
% 2.32/2.52 tff(10590,plain,
% 2.32/2.52 (((~![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(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.32/2.52 inference(transitivity,[status(thm)],[10589, 10587])).
% 2.32/2.52 tff(10591,plain,
% 2.32/2.52 ((~![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)))),
% 2.32/2.52 inference(quant_inst,[status(thm)],[])).
% 2.32/2.52 tff(10592,plain,
% 2.32/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 2.32/2.52 inference(modus_ponens,[status(thm)],[10591, 10590])).
% 2.32/2.52 tff(10593,plain,
% 2.32/2.52 ($false),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[10592, 37, 1490, 624, 10586])).
% 2.32/2.52 tff(10594,plain,((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~(z = elem!1)) | (s(s(s(z))) = s(s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.52 tff(10595,plain,
% 2.32/2.52 (~r(elem!1, s(s(elem!1)))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[10594, 624, 288, 6204, 10558, 10554, 3195])).
% 2.32/2.52 tff(10596,plain,
% 2.32/2.52 (b(elem!1, s(s(elem!1)))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[1617, 10595, 3432])).
% 2.32/2.52 tff(10597,plain,
% 2.32/2.52 (~r(s(z), elem!1)),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[5690, 10596, 10575, 10569])).
% 2.32/2.52 tff(10598,plain,
% 2.32/2.52 (b(s(z), elem!1)),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[601, 10597, 108])).
% 2.32/2.52 tff(10599,plain,
% 2.32/2.52 (b(s(elem!1), elem!1)),
% 2.32/2.52 inference(modus_ponens,[status(thm)],[10598, 3568])).
% 2.32/2.52 tff(10600,plain,
% 2.32/2.52 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[5209, 75, 1168, 10599, 10574])).
% 2.32/2.52 tff(10601,plain,
% 2.32/2.52 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[3010, 58, 3954, 10600])).
% 2.32/2.52 tff(10602,plain,
% 2.32/2.52 (r(s(s(s(z))), elem!1)),
% 2.32/2.52 inference(modus_ponens,[status(thm)],[624, 10570])).
% 2.32/2.52 tff(10603,plain,
% 2.32/2.52 (~(s(s(s(s(s(s(s(z))))))) = s(s(elem!1)))),
% 2.32/2.52 inference(modus_ponens,[status(thm)],[3959, 6006])).
% 2.32/2.52 tff(10604,plain,
% 2.32/2.52 (r(s(s(s(s(z)))), z)),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[9484, 698, 288])).
% 2.32/2.52 tff(10605,plain,
% 2.32/2.52 (~r(s(z), z)),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[2586, 468, 10604])).
% 2.32/2.52 tff(10606,plain,
% 2.32/2.52 (b(s(z), z)),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[169, 10605])).
% 2.32/2.52 tff(10607,plain,
% 2.32/2.52 (b(s(elem!1), elem!1)),
% 2.32/2.52 inference(modus_ponens,[status(thm)],[10606, 6057])).
% 2.32/2.52 tff(10608,plain,
% 2.32/2.52 (b(s(z), elem!1)),
% 2.32/2.52 inference(modus_ponens,[status(thm)],[10606, 6056])).
% 2.32/2.52 tff(10609,plain,
% 2.32/2.52 (~b(s(s(elem!1)), s(z))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[1638, 1620, 1391, 10608])).
% 2.32/2.52 tff(10610,plain,
% 2.32/2.52 (r(s(s(elem!1)), s(z))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[561, 10609])).
% 2.32/2.52 tff(10611,plain,
% 2.32/2.52 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[1655, 10610, 468])).
% 2.32/2.52 tff(10612,plain,
% 2.32/2.52 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[1660, 10611, 5479])).
% 2.32/2.52 tff(10613,plain,
% 2.32/2.52 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[10404, 10612, 3989, 3959, 698, 10569])).
% 2.32/2.52 tff(10614,plain,
% 2.32/2.52 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[813, 10613, 3966])).
% 2.32/2.52 tff(10615,plain,
% 2.32/2.52 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[5209, 75, 10614, 10607, 2609])).
% 2.32/2.52 tff(10616,plain,
% 2.32/2.52 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[3010, 58, 3954, 10615])).
% 2.32/2.52 tff(10617,plain,
% 2.32/2.52 (r(s(s(elem!1)), s(elem!1))),
% 2.32/2.52 inference(modus_ponens,[status(thm)],[10610, 10563])).
% 2.32/2.52 tff(10618,plain,
% 2.32/2.52 (((~![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(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.32/2.52 inference(rewrite,[status(thm)],[])).
% 2.32/2.52 tff(10619,plain,
% 2.32/2.52 (((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.32/2.52 inference(rewrite,[status(thm)],[])).
% 2.32/2.52 tff(10620,plain,
% 2.32/2.52 (((~![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(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 2.32/2.52 inference(monotonicity,[status(thm)],[10619])).
% 2.32/2.52 tff(10621,plain,
% 2.32/2.52 (((~![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(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.32/2.52 inference(transitivity,[status(thm)],[10620, 10618])).
% 2.32/2.52 tff(10622,plain,
% 2.32/2.52 ((~![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(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.32/2.52 inference(quant_inst,[status(thm)],[])).
% 2.32/2.52 tff(10623,plain,
% 2.32/2.52 ((~![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(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 2.32/2.52 inference(modus_ponens,[status(thm)],[10622, 10621])).
% 2.32/2.52 tff(10624,plain,
% 2.32/2.52 (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[10623, 37, 10617, 10616])).
% 2.32/2.52 tff(10625,plain,
% 2.32/2.52 ((s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[6017, 58, 10624])).
% 2.32/2.52 tff(10626,plain,
% 2.32/2.52 (b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[10625, 10603])).
% 2.32/2.52 tff(10627,plain,
% 2.32/2.52 ((~b(s(s(elem!1)), elem!1)) <=> (~b(s(s(elem!1)), z))),
% 2.32/2.52 inference(monotonicity,[status(thm)],[5539])).
% 2.32/2.52 tff(10628,plain,
% 2.32/2.52 (~b(s(s(elem!1)), z)),
% 2.32/2.52 inference(modus_ponens,[status(thm)],[1, 10627])).
% 2.32/2.52 tff(10629,plain,
% 2.32/2.52 (r(s(s(elem!1)), z)),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[2696, 10628])).
% 2.32/2.52 tff(10630,plain,
% 2.32/2.52 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[2707, 10629, 10604])).
% 2.32/2.52 tff(10631,plain,
% 2.32/2.52 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[3876, 58, 5701, 10630])).
% 2.32/2.52 tff(10632,plain,
% 2.32/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.32/2.52 inference(rewrite,[status(thm)],[])).
% 2.32/2.52 tff(10633,plain,
% 2.32/2.52 (((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.32/2.52 inference(rewrite,[status(thm)],[])).
% 2.32/2.52 tff(10634,plain,
% 2.32/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 2.32/2.53 inference(monotonicity,[status(thm)],[10633])).
% 2.32/2.53 tff(10635,plain,
% 2.32/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.32/2.53 inference(transitivity,[status(thm)],[10634, 10632])).
% 2.32/2.53 tff(10636,plain,
% 2.32/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.32/2.53 inference(quant_inst,[status(thm)],[])).
% 2.32/2.53 tff(10637,plain,
% 2.32/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.32/2.53 inference(modus_ponens,[status(thm)],[10636, 10635])).
% 2.32/2.53 tff(10638,plain,
% 2.32/2.53 ($false),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[10637, 75, 1620, 10612, 10614, 10631, 10626])).
% 2.32/2.53 tff(10639,plain,((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)) | (~(z = elem!1)) | b(s(s(elem!1)), elem!1) | (~r(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.53 tff(10640,plain,
% 2.32/2.53 (~r(s(z), s(s(s(s(z)))))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[10639, 10596, 698, 288, 10574, 1, 10575])).
% 2.32/2.53 tff(10641,plain,
% 2.32/2.53 (b(s(z), s(s(s(s(z)))))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[489, 10640])).
% 2.32/2.53 tff(10642,plain,
% 2.32/2.53 (~b(s(s(s(z))), s(z))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[3531, 10641, 698, 10602])).
% 2.32/2.53 tff(10643,plain,
% 2.32/2.53 (r(s(s(s(z))), s(z))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[1081, 10642])).
% 2.32/2.53 tff(10644,plain,
% 2.32/2.53 (r(s(s(s(elem!1))), s(elem!1))),
% 2.32/2.53 inference(modus_ponens,[status(thm)],[10643, 3424])).
% 2.32/2.53 tff(10645,plain,
% 2.32/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!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(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 2.32/2.53 inference(rewrite,[status(thm)],[])).
% 2.32/2.53 tff(10646,plain,
% 2.32/2.53 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 2.32/2.53 inference(rewrite,[status(thm)],[])).
% 2.32/2.53 tff(10647,plain,
% 2.32/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(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))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))))),
% 2.32/2.53 inference(monotonicity,[status(thm)],[10646])).
% 2.32/2.53 tff(10648,plain,
% 2.32/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(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))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 2.32/2.53 inference(transitivity,[status(thm)],[10647, 10645])).
% 2.32/2.53 tff(10649,plain,
% 2.32/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 2.32/2.53 inference(quant_inst,[status(thm)],[])).
% 2.32/2.53 tff(10650,plain,
% 2.32/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))),
% 2.32/2.53 inference(modus_ponens,[status(thm)],[10649, 10648])).
% 2.32/2.53 tff(10651,plain,
% 2.32/2.53 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[10650, 37, 624, 10644, 10601])).
% 2.32/2.53 tff(10652,plain,
% 2.32/2.53 (b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[874, 58, 5985, 10651])).
% 2.32/2.53 tff(10653,plain,
% 2.32/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.53 inference(rewrite,[status(thm)],[])).
% 2.32/2.53 tff(10654,plain,
% 2.32/2.53 (((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.53 inference(rewrite,[status(thm)],[])).
% 2.32/2.53 tff(10655,plain,
% 2.32/2.53 (((~![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(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))))),
% 2.32/2.53 inference(monotonicity,[status(thm)],[10654])).
% 2.32/2.53 tff(10656,plain,
% 2.32/2.53 (((~![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(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.53 inference(transitivity,[status(thm)],[10655, 10653])).
% 2.32/2.53 tff(10657,plain,
% 2.32/2.53 ((~![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(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.53 inference(quant_inst,[status(thm)],[])).
% 2.32/2.53 tff(10658,plain,
% 2.32/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))),
% 2.32/2.53 inference(modus_ponens,[status(thm)],[10657, 10656])).
% 2.32/2.53 tff(10659,plain,
% 2.32/2.53 (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[10658, 37, 10644, 10601])).
% 2.32/2.53 tff(10660,plain,
% 2.32/2.53 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[3083, 58, 3974, 10659])).
% 2.32/2.53 tff(10661,plain,
% 2.32/2.53 (~b(s(s(elem!1)), s(z))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[1638, 10598, 10575, 10596])).
% 2.32/2.53 tff(10662,plain,
% 2.32/2.53 (r(s(s(elem!1)), s(z))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[561, 10661])).
% 2.32/2.53 tff(10663,plain,
% 2.32/2.53 (r(s(s(elem!1)), s(elem!1))),
% 2.32/2.53 inference(modus_ponens,[status(thm)],[10662, 10563])).
% 2.32/2.53 tff(10664,plain,
% 2.32/2.53 (((~![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(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.53 inference(rewrite,[status(thm)],[])).
% 2.32/2.53 tff(10665,plain,
% 2.32/2.53 (((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.53 inference(rewrite,[status(thm)],[])).
% 2.32/2.53 tff(10666,plain,
% 2.32/2.53 (((~![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(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 2.32/2.53 inference(monotonicity,[status(thm)],[10665])).
% 2.32/2.53 tff(10667,plain,
% 2.32/2.53 (((~![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(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, 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(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.53 inference(transitivity,[status(thm)],[10666, 10664])).
% 2.32/2.53 tff(10668,plain,
% 2.32/2.53 ((~![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(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.53 inference(quant_inst,[status(thm)],[])).
% 2.32/2.53 tff(10669,plain,
% 2.32/2.53 ((~![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(s(s(s(z))))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 2.32/2.53 inference(modus_ponens,[status(thm)],[10668, 10667])).
% 2.32/2.53 tff(10670,plain,
% 2.32/2.53 (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[10669, 37, 10663, 10601])).
% 2.32/2.53 tff(10671,plain,
% 2.32/2.53 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[840, 58, 3959, 10670])).
% 2.32/2.53 tff(10672,plain,
% 2.32/2.53 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(z))))),
% 2.32/2.53 inference(monotonicity,[status(thm)],[3418])).
% 2.32/2.53 tff(10673,plain,
% 2.32/2.53 ((~r(s(s(elem!1)), s(s(s(elem!1))))) <=> (~r(s(s(elem!1)), s(s(s(z)))))),
% 2.32/2.53 inference(monotonicity,[status(thm)],[10672])).
% 2.32/2.53 tff(10674,plain,
% 2.32/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, 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(elem!1)), s(s(s(elem!1))))))),
% 2.32/2.53 inference(rewrite,[status(thm)],[])).
% 2.32/2.53 tff(10675,plain,
% 2.32/2.53 (((~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(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.32/2.53 inference(rewrite,[status(thm)],[])).
% 2.32/2.53 tff(10676,plain,
% 2.32/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 2.32/2.53 inference(monotonicity,[status(thm)],[10675])).
% 2.32/2.53 tff(10677,plain,
% 2.32/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.32/2.53 inference(transitivity,[status(thm)],[10676, 10674])).
% 2.32/2.53 tff(10678,plain,
% 2.32/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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))))))),
% 2.32/2.53 inference(quant_inst,[status(thm)],[])).
% 2.32/2.53 tff(10679,plain,
% 2.32/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.32/2.53 inference(modus_ponens,[status(thm)],[10678, 10677])).
% 2.32/2.53 tff(10680,plain,
% 2.32/2.53 ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[10679, 37])).
% 2.32/2.53 tff(10681,plain,
% 2.32/2.53 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[10680, 10644, 10663])).
% 2.32/2.53 tff(10682,plain,
% 2.32/2.53 (~r(s(s(elem!1)), s(s(s(z))))),
% 2.32/2.53 inference(modus_ponens,[status(thm)],[10681, 10673])).
% 2.32/2.53 tff(10683,plain,
% 2.32/2.53 (b(s(s(elem!1)), s(s(s(z))))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[1936, 10682, 4222])).
% 2.32/2.53 tff(10684,plain,
% 2.32/2.53 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.32/2.53 inference(modus_ponens,[status(thm)],[10683, 9847])).
% 2.32/2.53 tff(10685,plain,
% 2.32/2.53 ($false),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[5833, 75, 10684, 10671, 10660, 10652])).
% 2.32/2.53 tff(10686,plain,((~r(s(s(s(elem!1))), elem!1)) | (~(z = elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (s(z) = elem!1) | b(s(s(elem!1)), elem!1) | (~r(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.53 tff(10687,plain,
% 2.32/2.53 (~r(s(s(s(elem!1))), elem!1)),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[10686, 1168, 288, 698, 108, 1, 3195])).
% 2.32/2.53 tff(10688,plain,
% 2.32/2.53 (~r(s(s(s(z))), elem!1)),
% 2.32/2.53 inference(modus_ponens,[status(thm)],[10687, 10571])).
% 2.32/2.53 tff(10689,plain,
% 2.32/2.53 (b(s(s(s(z))), elem!1)),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[1115, 10688, 4145])).
% 2.32/2.53 tff(10690,plain,
% 2.32/2.53 ((~b(s(s(elem!1)), elem!1)) <=> (~b(s(s(z)), elem!1))),
% 2.32/2.53 inference(monotonicity,[status(thm)],[3649])).
% 2.32/2.53 tff(10691,plain,
% 2.32/2.53 (~b(s(s(z)), elem!1)),
% 2.32/2.53 inference(modus_ponens,[status(thm)],[1, 10690])).
% 2.32/2.53 tff(10692,plain,
% 2.32/2.53 (r(s(s(z)), elem!1)),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[104, 10691, 5480])).
% 2.32/2.53 tff(10693,plain,
% 2.32/2.53 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[3884, 37, 698, 10569])).
% 2.32/2.53 tff(10694,plain,
% 2.32/2.53 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[1660, 10693, 5479])).
% 2.32/2.53 tff(10695,plain,
% 2.32/2.53 (~r(s(z), elem!1)),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[10361, 10694, 10631, 10604, 288, 10692])).
% 2.32/2.53 tff(10696,plain,
% 2.32/2.53 (b(s(z), elem!1)),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[601, 10695, 108])).
% 2.32/2.53 tff(10697,plain,
% 2.32/2.53 (~r(s(s(s(z))), s(z))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[10433, 10696, 3839, 10575, 10689, 1168])).
% 2.32/2.53 tff(10698,plain,
% 2.32/2.53 (b(s(s(s(z))), s(z))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[1081, 10697])).
% 2.32/2.53 tff(10699,plain,
% 2.32/2.53 (b(s(s(s(elem!1))), s(elem!1))),
% 2.32/2.53 inference(modus_ponens,[status(thm)],[10698, 4187])).
% 2.32/2.53 tff(10700,plain,
% 2.32/2.53 (b(s(s(s(elem!1))), elem!1)),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[3370, 10687, 5477])).
% 2.32/2.53 tff(10701,plain,
% 2.32/2.53 (b(s(elem!1), elem!1)),
% 2.32/2.53 inference(modus_ponens,[status(thm)],[10696, 3568])).
% 2.32/2.53 tff(10702,plain,
% 2.32/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.32/2.53 inference(rewrite,[status(thm)],[])).
% 2.32/2.53 tff(10703,plain,
% 2.32/2.53 (((~b(elem!1, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.32/2.53 inference(rewrite,[status(thm)],[])).
% 2.32/2.53 tff(10704,plain,
% 2.32/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1))), s(elem!1))) | (~b(s(elem!1), 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(X1, 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), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1))))),
% 2.32/2.53 inference(monotonicity,[status(thm)],[10703])).
% 2.32/2.53 tff(10705,plain,
% 2.32/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1))), s(elem!1))) | (~b(s(elem!1), 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(X1, 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), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.32/2.53 inference(transitivity,[status(thm)],[10704, 10702])).
% 2.32/2.53 tff(10706,plain,
% 2.32/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1))), s(elem!1))) | (~b(s(elem!1), 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)))),
% 2.32/2.53 inference(quant_inst,[status(thm)],[])).
% 2.32/2.53 tff(10707,plain,
% 2.32/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1))),
% 2.32/2.53 inference(modus_ponens,[status(thm)],[10706, 10705])).
% 2.32/2.53 tff(10708,plain,
% 2.32/2.53 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[10707, 75, 10701, 10700, 10574])).
% 2.32/2.53 tff(10709,plain,
% 2.32/2.53 ($false),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[10708, 10699])).
% 2.32/2.53 tff(10710,plain,((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~(z = elem!1)) | (s(z) = elem!1) | (~r(s(s(s(s(z)))), elem!1)) | b(s(s(elem!1)), elem!1) | (~r(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.53 tff(10711,plain,
% 2.32/2.53 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[10710, 1, 108, 698, 288, 3195])).
% 2.32/2.53 tff(10712,plain,
% 2.32/2.53 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[813, 10711, 3966])).
% 2.32/2.53 tff(10713,plain,
% 2.32/2.53 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[10404, 10712, 3989, 3959, 698, 10569])).
% 2.32/2.53 tff(10714,plain,
% 2.32/2.53 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[1660, 10713, 5479])).
% 2.32/2.53 tff(10715,plain,
% 2.32/2.53 ($false),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[3934, 37, 3195, 10714, 10569])).
% 2.32/2.53 tff(10716,plain,(b(s(s(elem!1)), elem!1) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (s(z) = elem!1) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.53 tff(10717,plain,
% 2.32/2.53 (b(s(s(elem!1)), elem!1)),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[10716, 10568, 10567, 108, 288])).
% 2.32/2.53 tff(10718,plain,
% 2.32/2.53 (b(s(s(z)), elem!1)),
% 2.32/2.53 inference(modus_ponens,[status(thm)],[10717, 3649])).
% 2.32/2.53 tff(10719,plain,
% 2.32/2.53 (b(z, s(z))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[9715, 10567, 288, 10568, 108])).
% 2.32/2.53 tff(10720,plain,
% 2.32/2.53 (b(elem!1, s(z))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[8118, 10719, 288])).
% 2.32/2.53 tff(10721,plain,
% 2.32/2.53 (r(s(s(s(s(z)))), z)),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[9484, 10567, 288])).
% 2.32/2.53 tff(10722,plain,
% 2.32/2.53 (b(s(s(elem!1)), elem!1)),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[10716, 3195, 698, 108, 288])).
% 2.32/2.53 tff(10723,plain,
% 2.32/2.53 (~r(elem!1, s(s(elem!1)))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[3811, 1647, 3195])).
% 2.32/2.53 tff(10724,plain,
% 2.32/2.53 (b(elem!1, s(s(elem!1)))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[1617, 10723, 3432])).
% 2.32/2.53 tff(10725,plain,
% 2.32/2.53 (b(s(s(elem!1)), elem!1) <=> b(s(s(z)), z)),
% 2.32/2.53 inference(transitivity,[status(thm)],[3649, 5545])).
% 2.32/2.53 tff(10726,plain,
% 2.32/2.53 (b(s(s(z)), z)),
% 2.32/2.53 inference(modus_ponens,[status(thm)],[10722, 10725])).
% 2.32/2.53 tff(10727,plain,
% 2.32/2.53 (b(z, s(s(z)))),
% 2.32/2.53 inference(modus_ponens,[status(thm)],[10724, 5549])).
% 2.32/2.53 tff(10728,plain,
% 2.32/2.53 (~b(s(z), s(s(z)))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[410, 10727, 10573, 10726])).
% 2.32/2.53 tff(10729,plain,
% 2.32/2.53 (r(s(z), s(s(z)))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[416, 10728])).
% 2.32/2.53 tff(10730,plain,
% 2.32/2.53 (r(s(elem!1), s(s(elem!1)))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[3414, 10729, 288])).
% 2.32/2.53 tff(10731,plain,
% 2.32/2.53 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[1179, 58, 3989, 9655])).
% 2.32/2.53 tff(10732,plain,
% 2.32/2.53 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[9670, 58, 9712, 9663])).
% 2.32/2.53 tff(10733,assumption,(b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))), introduced(assumption)).
% 2.32/2.53 tff(10734,assumption,(b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 2.32/2.53 tff(10735,plain,
% 2.32/2.53 (~r(s(z), s(s(s(s(z)))))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[1655, 6172, 1647])).
% 2.32/2.54 tff(10736,plain,
% 2.32/2.54 (b(s(z), s(s(s(s(z)))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[489, 10735])).
% 2.32/2.54 tff(10737,plain,
% 2.32/2.54 (b(s(elem!1), s(s(s(s(z)))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[3857, 10736, 288])).
% 2.32/2.54 tff(10738,plain,
% 2.32/2.54 (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[9677, 75, 10737, 10734, 10733])).
% 2.32/2.54 tff(10739,plain,
% 2.32/2.54 (r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[3010, 58, 3954, 10738])).
% 2.32/2.54 tff(10740,plain,
% 2.32/2.54 (~r(s(s(s(z))), elem!1)),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[3531, 984, 578, 698])).
% 2.32/2.54 tff(10741,plain,
% 2.32/2.54 (b(s(s(s(z))), elem!1)),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[1115, 10740, 1031])).
% 2.32/2.54 tff(10742,plain,
% 2.32/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 2.32/2.54 inference(rewrite,[status(thm)],[])).
% 2.32/2.54 tff(10743,plain,
% 2.32/2.54 (((~b(elem!1, s(z))) | (~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(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 2.32/2.54 inference(rewrite,[status(thm)],[])).
% 2.32/2.54 tff(10744,plain,
% 2.32/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z)))))),
% 2.32/2.54 inference(monotonicity,[status(thm)],[10743])).
% 2.32/2.54 tff(10745,plain,
% 2.32/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 2.32/2.54 inference(transitivity,[status(thm)],[10744, 10742])).
% 2.32/2.54 tff(10746,plain,
% 2.32/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))),
% 2.32/2.54 inference(quant_inst,[status(thm)],[])).
% 2.32/2.54 tff(10747,plain,
% 2.32/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z)))),
% 2.32/2.54 inference(modus_ponens,[status(thm)],[10746, 10745])).
% 2.32/2.54 tff(10748,plain,
% 2.32/2.54 ($false),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[10747, 75, 107, 1391, 10741, 984])).
% 2.32/2.54 tff(10749,plain,((~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (s(s(s(z))) = elem!1) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.54 tff(10750,plain,
% 2.32/2.54 (~b(s(s(s(z))), s(z))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[10749, 10736, 1391, 107, 4145, 698])).
% 2.32/2.54 tff(10751,plain,
% 2.32/2.54 (r(s(s(s(z))), s(z))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[1081, 10750])).
% 2.32/2.54 tff(10752,plain,
% 2.32/2.54 (r(s(s(s(elem!1))), s(elem!1))),
% 2.32/2.54 inference(modus_ponens,[status(thm)],[10751, 3424])).
% 2.32/2.54 tff(10753,plain,
% 2.32/2.54 (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[10658, 37, 10752, 10739])).
% 2.32/2.54 tff(10754,plain,
% 2.32/2.54 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[3083, 58, 3974, 10753])).
% 2.32/2.54 tff(10755,plain,
% 2.32/2.54 (r(s(s(elem!1)), s(elem!1))),
% 2.32/2.54 inference(modus_ponens,[status(thm)],[6172, 10563])).
% 2.32/2.54 tff(10756,plain,
% 2.32/2.54 (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[10669, 37, 10755, 10739])).
% 2.32/2.54 tff(10757,plain,
% 2.32/2.54 (b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[840, 58, 3959, 10756])).
% 2.32/2.54 tff(10758,plain,
% 2.32/2.54 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[10680, 10752, 10755])).
% 2.32/2.54 tff(10759,plain,
% 2.32/2.54 (~r(s(s(elem!1)), s(s(s(z))))),
% 2.32/2.54 inference(modus_ponens,[status(thm)],[10758, 10673])).
% 2.32/2.54 tff(10760,plain,
% 2.32/2.54 (b(s(s(elem!1)), s(s(s(z))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[1936, 10759, 4222])).
% 2.32/2.54 tff(10761,plain,
% 2.32/2.54 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.32/2.54 inference(modus_ponens,[status(thm)],[10760, 9847])).
% 2.32/2.54 tff(10762,plain,
% 2.32/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.54 inference(rewrite,[status(thm)],[])).
% 2.32/2.54 tff(10763,plain,
% 2.32/2.54 (((~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.54 inference(rewrite,[status(thm)],[])).
% 2.32/2.54 tff(10764,plain,
% 2.32/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 2.32/2.54 inference(monotonicity,[status(thm)],[10763])).
% 2.32/2.54 tff(10765,plain,
% 2.32/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.54 inference(transitivity,[status(thm)],[10764, 10762])).
% 2.32/2.54 tff(10766,plain,
% 2.32/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.32/2.54 inference(quant_inst,[status(thm)],[])).
% 2.32/2.54 tff(10767,plain,
% 2.32/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 2.32/2.54 inference(modus_ponens,[status(thm)],[10766, 10765])).
% 2.32/2.54 tff(10768,plain,
% 2.32/2.54 ($false),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[10767, 75, 10761, 10734, 10733, 10757, 10754])).
% 2.32/2.54 tff(10769,plain,((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~(z = elem!1)) | (~b(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.54 tff(10770,plain,
% 2.32/2.54 (~b(s(z), elem!1)),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[10769, 10732, 10731, 288, 1391, 698, 1647, 1620])).
% 2.32/2.54 tff(10771,plain,
% 2.32/2.54 (r(s(z), elem!1)),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[601, 10770, 108])).
% 2.32/2.54 tff(10772,plain,
% 2.32/2.54 (r(s(z), z)),
% 2.32/2.54 inference(modus_ponens,[status(thm)],[10771, 5533])).
% 2.32/2.54 tff(10773,plain,
% 2.32/2.54 (~r(s(z), s(s(s(s(z)))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[2586, 10772, 10604])).
% 2.32/2.54 tff(10774,plain,
% 2.32/2.54 (r(s(elem!1), elem!1)),
% 2.32/2.54 inference(modus_ponens,[status(thm)],[10771, 4002])).
% 2.32/2.54 tff(10775,plain,
% 2.32/2.54 (~b(s(elem!1), s(s(s(s(z)))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[9679, 10774, 3954, 3989, 1918, 738, 698])).
% 2.32/2.54 tff(10776,plain,
% 2.32/2.54 (~b(s(z), s(s(s(s(z)))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[3857, 10775, 288])).
% 2.32/2.54 tff(10777,plain,
% 2.32/2.54 ($false),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[489, 10776, 10773])).
% 2.32/2.54 tff(10778,plain,((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~(z = elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(z)))), elem!1)) | (s(z) = elem!1) | (~b(elem!1, s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.54 tff(10779,plain,
% 2.32/2.54 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[10778, 10730, 288, 698, 108, 10575, 1647, 10724])).
% 2.32/2.54 tff(10780,plain,
% 2.32/2.54 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[813, 10779, 3966])).
% 2.32/2.54 tff(10781,plain,
% 2.32/2.54 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[6013, 75, 10724, 10780, 10722])).
% 2.32/2.54 tff(10782,plain,
% 2.32/2.54 ((s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[6017, 58, 10781])).
% 2.32/2.54 tff(10783,plain,
% 2.32/2.54 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[10782, 10603])).
% 2.32/2.54 tff(10784,plain,
% 2.32/2.54 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[6025, 37, 10730, 10783])).
% 2.32/2.54 tff(10785,plain,
% 2.32/2.54 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[3010, 58, 3954, 10784])).
% 2.32/2.54 tff(10786,plain,
% 2.32/2.54 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[6033, 37, 10730, 10783])).
% 2.32/2.54 tff(10787,plain,
% 2.32/2.54 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[793, 58, 3961, 10786])).
% 2.32/2.54 tff(10788,plain,
% 2.32/2.54 ($false),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[6041, 75, 10780, 10787, 10574, 10785])).
% 2.32/2.54 tff(10789,plain,((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~(z = elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (s(z) = elem!1) | (~r(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.54 tff(10790,plain,
% 2.32/2.54 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[10789, 288, 10567, 108, 10568])).
% 2.32/2.54 tff(10791,plain,
% 2.32/2.54 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[1660, 10790, 5479])).
% 2.32/2.54 tff(10792,plain,
% 2.32/2.54 (b(elem!1, s(z))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[8118, 372, 288])).
% 2.32/2.54 tff(10793,plain,
% 2.32/2.54 (r(z, s(s(elem!1)))),
% 2.32/2.54 inference(modus_ponens,[status(thm)],[1490, 5983])).
% 2.32/2.54 tff(10794,plain,
% 2.32/2.54 (~r(s(z), s(s(s(s(z)))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[2586, 5534, 10604])).
% 2.32/2.54 tff(10795,plain,
% 2.32/2.54 (b(s(z), s(s(s(s(z)))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[489, 10794])).
% 2.32/2.54 tff(10796,plain,
% 2.32/2.54 (b(s(elem!1), s(s(s(s(z)))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[3857, 10795, 288])).
% 2.32/2.54 tff(10797,plain,
% 2.32/2.54 (~r(s(z), s(s(elem!1)))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[5301, 5534, 2364])).
% 2.32/2.54 tff(10798,plain,
% 2.32/2.54 (b(s(z), s(s(elem!1)))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[1890, 10797])).
% 2.32/2.54 tff(10799,plain,
% 2.32/2.54 (b(s(elem!1), s(s(elem!1)))),
% 2.32/2.54 inference(modus_ponens,[status(thm)],[10798, 4147])).
% 2.32/2.54 tff(10800,plain,
% 2.32/2.54 (~r(s(s(s(s(z)))), s(elem!1))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[9641, 37, 698, 4003])).
% 2.32/2.54 tff(10801,plain,
% 2.32/2.54 (b(s(s(s(s(z)))), s(elem!1))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[4263, 58, 4260, 10800])).
% 2.32/2.54 tff(10802,plain,
% 2.32/2.54 ($false),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[4280, 10801, 10799, 1619, 10796])).
% 2.32/2.54 tff(10803,plain,((~r(s(z), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~(z = elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.54 tff(10804,plain,
% 2.32/2.54 (~r(s(z), elem!1)),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[10803, 10793, 288, 1619, 698])).
% 2.32/2.54 tff(10805,plain,
% 2.32/2.54 (b(s(z), elem!1)),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[601, 10804, 108])).
% 2.32/2.54 tff(10806,plain,
% 2.32/2.54 (b(s(z), z)),
% 2.32/2.54 inference(modus_ponens,[status(thm)],[10805, 9519])).
% 2.32/2.54 tff(10807,plain,
% 2.32/2.54 (~b(s(s(z)), s(z))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[7565, 10806, 10792, 372, 3650])).
% 2.32/2.54 tff(10808,plain,
% 2.32/2.54 (r(s(s(z)), s(z))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[153, 10807])).
% 2.32/2.54 tff(10809,plain,
% 2.32/2.54 (r(s(s(elem!1)), s(z))),
% 2.32/2.54 inference(modus_ponens,[status(thm)],[10808, 10565])).
% 2.32/2.54 tff(10810,plain,
% 2.32/2.54 (r(s(s(elem!1)), s(elem!1))),
% 2.32/2.54 inference(modus_ponens,[status(thm)],[10809, 10563])).
% 2.32/2.54 tff(10811,plain,
% 2.32/2.54 (b(elem!1, s(elem!1))),
% 2.32/2.54 inference(modus_ponens,[status(thm)],[372, 10572])).
% 2.32/2.54 tff(10812,plain,
% 2.32/2.54 (b(s(elem!1), elem!1)),
% 2.32/2.54 inference(modus_ponens,[status(thm)],[10805, 3568])).
% 2.32/2.54 tff(10813,plain,
% 2.32/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.54 inference(rewrite,[status(thm)],[])).
% 2.32/2.54 tff(10814,plain,
% 2.32/2.54 (((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.54 inference(rewrite,[status(thm)],[])).
% 2.32/2.54 tff(10815,plain,
% 2.32/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 2.32/2.54 inference(monotonicity,[status(thm)],[10814])).
% 2.32/2.54 tff(10816,plain,
% 2.32/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.54 inference(transitivity,[status(thm)],[10815, 10813])).
% 2.32/2.54 tff(10817,plain,
% 2.32/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.32/2.54 inference(quant_inst,[status(thm)],[])).
% 2.32/2.54 tff(10818,plain,
% 2.32/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 2.32/2.54 inference(modus_ponens,[status(thm)],[10817, 10816])).
% 2.32/2.54 tff(10819,plain,
% 2.32/2.54 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[10818, 75, 1619, 9671, 9656])).
% 2.32/2.54 tff(10820,plain,
% 2.32/2.54 ((s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[6017, 58, 10819])).
% 2.32/2.54 tff(10821,plain,
% 2.32/2.54 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[10820, 6007])).
% 2.32/2.54 tff(10822,plain,
% 2.32/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.32/2.54 inference(rewrite,[status(thm)],[])).
% 2.32/2.54 tff(10823,plain,
% 2.32/2.54 (((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.32/2.55 inference(rewrite,[status(thm)],[])).
% 2.32/2.55 tff(10824,plain,
% 2.32/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(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(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 2.32/2.55 inference(monotonicity,[status(thm)],[10823])).
% 2.32/2.55 tff(10825,plain,
% 2.32/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(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(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.32/2.55 inference(transitivity,[status(thm)],[10824, 10822])).
% 2.32/2.55 tff(10826,plain,
% 2.32/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.32/2.55 inference(quant_inst,[status(thm)],[])).
% 2.32/2.55 tff(10827,plain,
% 2.32/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 2.32/2.55 inference(modus_ponens,[status(thm)],[10826, 10825])).
% 2.32/2.55 tff(10828,plain,
% 2.32/2.55 ($false),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[10827, 37, 1490, 738, 10821])).
% 2.32/2.55 tff(10829,plain,((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.55 tff(10830,plain,
% 2.32/2.55 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[10829, 1490, 3959, 1619, 3989, 698])).
% 2.32/2.55 tff(10831,plain,
% 2.32/2.55 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[813, 10830, 3966])).
% 2.32/2.55 tff(10832,plain,
% 2.32/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.32/2.55 inference(rewrite,[status(thm)],[])).
% 2.32/2.55 tff(10833,plain,
% 2.32/2.55 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.32/2.55 inference(rewrite,[status(thm)],[])).
% 2.32/2.55 tff(10834,plain,
% 2.32/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 2.32/2.55 inference(monotonicity,[status(thm)],[10833])).
% 2.32/2.55 tff(10835,plain,
% 2.32/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.32/2.55 inference(transitivity,[status(thm)],[10834, 10832])).
% 2.32/2.55 tff(10836,plain,
% 2.32/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.55 inference(quant_inst,[status(thm)],[])).
% 2.32/2.55 tff(10837,plain,
% 2.32/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(s(z))))))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.32/2.55 inference(modus_ponens,[status(thm)],[10836, 10835])).
% 2.32/2.55 tff(10838,plain,
% 2.32/2.55 (~b(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[10837, 75, 10831, 10812, 707, 10811])).
% 2.32/2.55 tff(10839,plain,
% 2.32/2.55 (r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[840, 58, 3959, 10838])).
% 2.32/2.55 tff(10840,plain,
% 2.32/2.55 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[5193, 75, 10831, 10812, 10811])).
% 2.32/2.55 tff(10841,plain,
% 2.32/2.55 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[793, 58, 3961, 10840])).
% 2.32/2.55 tff(10842,plain,
% 2.32/2.55 (((~![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(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.55 inference(rewrite,[status(thm)],[])).
% 2.32/2.55 tff(10843,plain,
% 2.32/2.55 (((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.55 inference(rewrite,[status(thm)],[])).
% 2.32/2.55 tff(10844,plain,
% 2.32/2.55 (((~![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(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(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(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))))),
% 2.32/2.55 inference(monotonicity,[status(thm)],[10843])).
% 2.32/2.55 tff(10845,plain,
% 2.32/2.55 (((~![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(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(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(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.55 inference(transitivity,[status(thm)],[10844, 10842])).
% 2.32/2.55 tff(10846,plain,
% 2.32/2.55 ((~![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(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.32/2.55 inference(quant_inst,[status(thm)],[])).
% 2.32/2.55 tff(10847,plain,
% 2.32/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(z)))))))))),
% 2.32/2.55 inference(modus_ponens,[status(thm)],[10846, 10845])).
% 2.32/2.55 tff(10848,plain,
% 2.32/2.55 ($false),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[10847, 37, 10841, 10839, 10810])).
% 2.32/2.55 tff(10849,plain,((~r(elem!1, s(s(elem!1)))) | (~(z = elem!1)) | (~b(z, s(z))) | (~b(s(s(elem!1)), elem!1)) | (s(z) = elem!1) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.55 tff(10850,plain,
% 2.32/2.55 (~r(elem!1, s(s(elem!1)))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[10849, 288, 10719, 10717, 108, 10791, 10567])).
% 2.32/2.55 tff(10851,plain,
% 2.32/2.55 (b(elem!1, s(s(elem!1)))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[1617, 10850, 3432])).
% 2.32/2.55 tff(10852,plain,
% 2.32/2.55 (b(s(s(z)), z)),
% 2.32/2.55 inference(modus_ponens,[status(thm)],[10717, 10725])).
% 2.32/2.55 tff(10853,plain,
% 2.32/2.55 (b(z, s(s(z)))),
% 2.32/2.55 inference(modus_ponens,[status(thm)],[10851, 5549])).
% 2.32/2.55 tff(10854,plain,
% 2.32/2.55 (~b(s(z), s(s(z)))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[410, 10853, 10719, 10852])).
% 2.32/2.55 tff(10855,plain,
% 2.32/2.55 (r(s(z), s(s(z)))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[416, 10854])).
% 2.32/2.55 tff(10856,plain,
% 2.32/2.55 (r(s(elem!1), s(s(elem!1)))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[3414, 10855, 288])).
% 2.32/2.55 tff(10857,plain,
% 2.32/2.55 (b(elem!1, s(elem!1))),
% 2.32/2.55 inference(modus_ponens,[status(thm)],[10719, 10572])).
% 2.32/2.55 tff(10858,plain,
% 2.32/2.55 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[6043, 10857, 3954, 3961, 10856, 3959, 10851, 10717])).
% 2.32/2.55 tff(10859,plain,
% 2.32/2.55 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[813, 10858, 3966])).
% 2.32/2.55 tff(10860,plain,
% 2.32/2.55 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[9654, 37, 10567, 10859])).
% 2.32/2.55 tff(10861,plain,
% 2.32/2.55 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[1179, 58, 3989, 10860])).
% 2.32/2.55 tff(10862,plain,
% 2.32/2.55 (~r(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[9662, 37, 10567, 10859])).
% 2.32/2.55 tff(10863,plain,
% 2.32/2.55 (b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[9670, 58, 9712, 10862])).
% 2.32/2.55 tff(10864,plain,
% 2.32/2.55 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[10818, 75, 10791, 10863, 10861])).
% 2.32/2.55 tff(10865,plain,
% 2.32/2.55 ((s(s(s(s(s(s(s(z))))))) = s(s(elem!1))) | r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[6017, 58, 10864])).
% 2.32/2.55 tff(10866,plain,
% 2.32/2.55 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[10865, 10603])).
% 2.32/2.55 tff(10867,plain,
% 2.32/2.55 (~r(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[6025, 37, 10856, 10866])).
% 2.32/2.55 tff(10868,plain,
% 2.32/2.55 (b(s(s(s(s(s(s(s(z))))))), s(elem!1))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[3010, 58, 3954, 10867])).
% 2.32/2.55 tff(10869,plain,
% 2.32/2.55 (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[6033, 37, 10856, 10866])).
% 2.32/2.55 tff(10870,plain,
% 2.32/2.55 (b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[793, 58, 3961, 10869])).
% 2.32/2.55 tff(10871,plain,
% 2.32/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.55 inference(rewrite,[status(thm)],[])).
% 2.32/2.55 tff(10872,plain,
% 2.32/2.55 (((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(z))))))) <=> ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.55 inference(rewrite,[status(thm)],[])).
% 2.32/2.55 tff(10873,plain,
% 2.32/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 2.32/2.55 inference(monotonicity,[status(thm)],[10872])).
% 2.32/2.55 tff(10874,plain,
% 2.32/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.55 inference(transitivity,[status(thm)],[10873, 10871])).
% 2.32/2.55 tff(10875,plain,
% 2.32/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.32/2.55 inference(quant_inst,[status(thm)],[])).
% 2.32/2.55 tff(10876,plain,
% 2.32/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 2.32/2.55 inference(modus_ponens,[status(thm)],[10875, 10874])).
% 2.32/2.55 tff(10877,plain,
% 2.32/2.55 (~b(s(elem!1), s(s(s(s(z)))))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[10876, 75, 10870, 10863, 10868])).
% 2.32/2.55 tff(10878,plain,
% 2.32/2.55 (~b(s(z), s(s(s(s(z)))))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[3857, 10877, 288])).
% 2.32/2.55 tff(10879,plain,
% 2.32/2.55 (r(s(z), s(s(s(s(z)))))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[489, 10878])).
% 2.32/2.55 tff(10880,plain,
% 2.32/2.55 (~r(s(z), z)),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[2586, 10879, 10721])).
% 2.32/2.55 tff(10881,plain,
% 2.32/2.55 (b(s(z), z)),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[169, 10880])).
% 2.32/2.55 tff(10882,plain,
% 2.32/2.55 (~b(s(s(z)), s(z))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[7565, 10881, 10720, 10719, 10718])).
% 2.32/2.55 tff(10883,plain,
% 2.32/2.55 (r(s(s(z)), s(z))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[153, 10882])).
% 2.32/2.55 tff(10884,plain,
% 2.32/2.55 (r(s(s(elem!1)), s(z))),
% 2.32/2.55 inference(modus_ponens,[status(thm)],[10883, 10565])).
% 2.32/2.55 tff(10885,plain,
% 2.32/2.55 (r(s(s(elem!1)), s(elem!1))),
% 2.32/2.55 inference(modus_ponens,[status(thm)],[10884, 10563])).
% 2.32/2.55 tff(10886,plain,
% 2.32/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.55 inference(rewrite,[status(thm)],[])).
% 2.32/2.55 tff(10887,plain,
% 2.32/2.55 (((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(elem!1)))) <=> ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.55 inference(rewrite,[status(thm)],[])).
% 2.32/2.55 tff(10888,plain,
% 2.32/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))))),
% 2.32/2.55 inference(monotonicity,[status(thm)],[10887])).
% 2.32/2.55 tff(10889,plain,
% 2.32/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.55 inference(transitivity,[status(thm)],[10888, 10886])).
% 2.32/2.55 tff(10890,plain,
% 2.32/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 2.32/2.56 inference(quant_inst,[status(thm)],[])).
% 2.32/2.56 tff(10891,plain,
% 2.32/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(s(z)))))))))),
% 2.32/2.56 inference(modus_ponens,[status(thm)],[10890, 10889])).
% 2.32/2.56 tff(10892,plain,
% 2.32/2.56 (~b(s(s(s(s(z)))), s(elem!1))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[10891, 75, 10870, 10863, 10868])).
% 2.32/2.56 tff(10893,plain,
% 2.32/2.56 (r(s(s(s(s(z)))), s(elem!1))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[4263, 58, 10892, 4260])).
% 2.32/2.56 tff(10894,plain,
% 2.32/2.56 (b(s(s(z)), s(s(s(s(z)))))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[3926, 10791, 3839])).
% 2.32/2.56 tff(10895,plain,
% 2.32/2.56 ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1)))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[5879, 37, 4249])).
% 2.32/2.56 tff(10896,plain,
% 2.32/2.56 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[10895, 5873])).
% 2.32/2.56 tff(10897,plain,
% 2.32/2.56 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[3876, 58, 5701, 10896])).
% 2.32/2.56 tff(10898,plain,
% 2.32/2.56 (b(s(s(s(s(z)))), s(s(z)))),
% 2.32/2.56 inference(modus_ponens,[status(thm)],[10897, 9741])).
% 2.32/2.56 tff(10899,assumption,(r(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 2.32/2.56 tff(10900,plain,
% 2.32/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), 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(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 2.32/2.56 inference(rewrite,[status(thm)],[])).
% 2.32/2.56 tff(10901,plain,
% 2.32/2.56 (((~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 2.32/2.56 inference(rewrite,[status(thm)],[])).
% 2.32/2.56 tff(10902,plain,
% 2.32/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1)))))),
% 2.32/2.56 inference(monotonicity,[status(thm)],[10901])).
% 2.32/2.56 tff(10903,plain,
% 2.32/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 2.32/2.56 inference(transitivity,[status(thm)],[10902, 10900])).
% 2.32/2.56 tff(10904,plain,
% 2.32/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.32/2.56 inference(quant_inst,[status(thm)],[])).
% 2.32/2.56 tff(10905,plain,
% 2.32/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 2.32/2.56 inference(modus_ponens,[status(thm)],[10904, 10903])).
% 2.32/2.56 tff(10906,plain,
% 2.32/2.56 ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[10905, 37, 698, 4249])).
% 2.32/2.56 tff(10907,plain,
% 2.32/2.56 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[10906, 10899])).
% 2.32/2.56 tff(10908,plain,
% 2.32/2.56 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.32/2.56 inference(modus_ponens,[status(thm)],[10907, 3464])).
% 2.32/2.56 tff(10909,plain,
% 2.32/2.56 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[575, 10908])).
% 2.32/2.56 tff(10910,plain,
% 2.32/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.32/2.56 inference(rewrite,[status(thm)],[])).
% 2.32/2.56 tff(10911,plain,
% 2.32/2.56 (((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.32/2.56 inference(rewrite,[status(thm)],[])).
% 2.32/2.56 tff(10912,plain,
% 2.32/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1))))))),
% 2.32/2.56 inference(monotonicity,[status(thm)],[10911])).
% 2.32/2.56 tff(10913,plain,
% 2.32/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.32/2.56 inference(transitivity,[status(thm)],[10912, 10910])).
% 2.32/2.56 tff(10914,plain,
% 2.32/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.32/2.56 inference(quant_inst,[status(thm)],[])).
% 2.32/2.56 tff(10915,plain,
% 2.32/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 2.32/2.56 inference(modus_ponens,[status(thm)],[10914, 10913])).
% 2.32/2.56 tff(10916,plain,
% 2.32/2.56 ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[10915, 37, 5873])).
% 2.32/2.56 tff(10917,plain,
% 2.32/2.56 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[10916, 10899])).
% 2.32/2.56 tff(10918,plain,
% 2.32/2.56 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.32/2.56 inference(modus_ponens,[status(thm)],[10917, 9478])).
% 2.32/2.56 tff(10919,plain,
% 2.32/2.56 (b(s(s(s(z))), s(s(elem!1)))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[62, 10918, 16])).
% 2.32/2.56 tff(10920,plain,
% 2.32/2.56 (b(s(s(s(z))), s(s(z)))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[9799, 10919, 288])).
% 2.32/2.56 tff(10921,plain,
% 2.32/2.56 ($false),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[1163, 10920, 10909, 895, 10898])).
% 2.32/2.56 tff(10922,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~(z = elem!1)) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.56 tff(10923,plain,
% 2.32/2.56 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[10922, 10894, 288, 6204, 10567, 10893, 10885])).
% 2.32/2.56 tff(10924,plain,
% 2.32/2.56 (~r(s(s(s(z))), s(z))),
% 2.32/2.56 inference(modus_ponens,[status(thm)],[10923, 5583])).
% 2.32/2.56 tff(10925,plain,
% 2.32/2.56 (b(s(s(s(z))), s(z))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[1081, 10924])).
% 2.32/2.56 tff(10926,plain,
% 2.32/2.56 (b(s(s(s(elem!1))), s(elem!1))),
% 2.32/2.56 inference(modus_ponens,[status(thm)],[10925, 4187])).
% 2.32/2.56 tff(10927,plain,
% 2.32/2.56 (b(elem!1, s(s(z)))),
% 2.32/2.56 inference(modus_ponens,[status(thm)],[10851, 4269])).
% 2.32/2.56 tff(10928,plain,
% 2.32/2.56 (b(s(z), elem!1)),
% 2.32/2.56 inference(modus_ponens,[status(thm)],[10881, 6056])).
% 2.32/2.56 tff(10929,plain,
% 2.32/2.56 (~b(s(s(s(z))), elem!1)),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[9577, 10925, 10718, 10928, 10927])).
% 2.32/2.56 tff(10930,plain,
% 2.32/2.56 (r(s(s(s(z))), elem!1)),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[1115, 10929, 4145])).
% 2.32/2.56 tff(10931,plain,
% 2.32/2.56 (r(s(s(s(elem!1))), elem!1)),
% 2.32/2.56 inference(modus_ponens,[status(thm)],[10930, 4176])).
% 2.32/2.56 tff(10932,plain,
% 2.32/2.56 (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[4183, 37, 10859, 10931])).
% 2.32/2.56 tff(10933,plain,
% 2.32/2.56 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[3083, 58, 3974, 10932])).
% 2.32/2.56 tff(10934,plain,
% 2.32/2.56 (b(s(elem!1), elem!1)),
% 2.32/2.56 inference(modus_ponens,[status(thm)],[10881, 6057])).
% 2.32/2.56 tff(10935,plain,
% 2.32/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.32/2.56 inference(rewrite,[status(thm)],[])).
% 2.32/2.56 tff(10936,plain,
% 2.32/2.56 (((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.32/2.56 inference(rewrite,[status(thm)],[])).
% 2.32/2.56 tff(10937,plain,
% 2.32/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))))),
% 2.32/2.56 inference(monotonicity,[status(thm)],[10936])).
% 2.32/2.56 tff(10938,plain,
% 2.32/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))))),
% 2.32/2.56 inference(transitivity,[status(thm)],[10937, 10935])).
% 2.32/2.56 tff(10939,plain,
% 2.32/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.56 inference(quant_inst,[status(thm)],[])).
% 2.32/2.56 tff(10940,plain,
% 2.32/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(elem!1)))),
% 2.32/2.56 inference(modus_ponens,[status(thm)],[10939, 10938])).
% 2.32/2.56 tff(10941,plain,
% 2.32/2.56 ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(z)))))))))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[10940, 75, 10934, 10857, 10868])).
% 2.32/2.56 tff(10942,plain,
% 2.32/2.56 ($false),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[10941, 10933, 10926])).
% 2.32/2.56 tff(10943,plain,((~(z = elem!1)) | (s(z) = elem!1) | b(s(s(s(s(z)))), elem!1) | b(elem!1, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.56 tff(10944,plain,
% 2.32/2.56 (b(elem!1, s(s(s(s(z)))))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[10943, 10561, 288, 108])).
% 2.32/2.56 tff(10945,plain,
% 2.32/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.32/2.56 inference(rewrite,[status(thm)],[])).
% 2.32/2.56 tff(10946,plain,
% 2.32/2.56 (((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.32/2.56 inference(rewrite,[status(thm)],[])).
% 2.32/2.56 tff(10947,plain,
% 2.32/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 2.32/2.56 inference(monotonicity,[status(thm)],[10946])).
% 2.32/2.56 tff(10948,plain,
% 2.32/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.32/2.56 inference(transitivity,[status(thm)],[10947, 10945])).
% 2.32/2.56 tff(10949,plain,
% 2.32/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), elem!1)))),
% 2.32/2.56 inference(quant_inst,[status(thm)],[])).
% 2.32/2.56 tff(10950,plain,
% 2.32/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 2.32/2.56 inference(modus_ponens,[status(thm)],[10949, 10948])).
% 2.32/2.56 tff(10951,plain,
% 2.32/2.56 ($false),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[10950, 75, 10944, 10560, 707, 5975, 9766])).
% 2.32/2.56 tff(10952,plain,((~r(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~(z = elem!1)) | (s(z) = elem!1) | (~b(elem!1, s(elem!1))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.56 tff(10953,plain,
% 2.32/2.56 (~r(s(z), s(s(s(s(z)))))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[10952, 10558, 10551, 10554, 288, 2478, 5734, 371, 5501, 10552])).
% 2.32/2.56 tff(10954,plain,
% 2.32/2.56 (b(s(z), s(s(s(s(z)))))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[489, 10953])).
% 2.32/2.56 tff(10955,plain,
% 2.32/2.56 (b(s(elem!1), s(s(s(s(z)))))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[3857, 10954, 288])).
% 2.32/2.56 tff(10956,plain,
% 2.32/2.56 (~b(s(s(s(s(z)))), elem!1)),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[6050, 10954, 1391, 288])).
% 2.32/2.56 tff(10957,plain,
% 2.32/2.56 (b(elem!1, s(s(s(s(z)))))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[10943, 10956, 288, 2478])).
% 2.32/2.56 tff(10958,plain,
% 2.32/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.32/2.56 inference(rewrite,[status(thm)],[])).
% 2.32/2.56 tff(10959,plain,
% 2.32/2.56 (((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.32/2.56 inference(rewrite,[status(thm)],[])).
% 2.32/2.56 tff(10960,plain,
% 2.32/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 2.32/2.57 inference(monotonicity,[status(thm)],[10959])).
% 2.32/2.57 tff(10961,plain,
% 2.32/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.32/2.57 inference(transitivity,[status(thm)],[10960, 10958])).
% 2.32/2.57 tff(10962,plain,
% 2.32/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), elem!1)))),
% 2.32/2.57 inference(quant_inst,[status(thm)],[])).
% 2.32/2.57 tff(10963,plain,
% 2.32/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 2.32/2.57 inference(modus_ponens,[status(thm)],[10962, 10961])).
% 2.32/2.57 tff(10964,plain,
% 2.32/2.57 ($false),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[10963, 75, 10957, 921, 10558, 10554, 10955])).
% 2.32/2.57 tff(10965,plain,((~r(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~(z = elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.57 tff(10966,plain,
% 2.32/2.57 (~r(s(s(s(elem!1))), elem!1)),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[10965, 3569, 288, 1391, 9520, 698])).
% 2.32/2.57 tff(10967,plain,
% 2.32/2.57 (b(s(s(s(elem!1))), elem!1)),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[3370, 10966, 5477])).
% 2.32/2.57 tff(10968,plain,
% 2.32/2.57 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[5079, 10967, 5734, 10551, 3569])).
% 2.32/2.57 tff(10969,plain,
% 2.32/2.57 (~b(s(s(z)), s(s(s(z))))),
% 2.32/2.57 inference(modus_ponens,[status(thm)],[10968, 10549])).
% 2.32/2.57 tff(10970,plain,
% 2.32/2.57 (~b(s(s(z)), s(z))),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[7565, 9520, 1391, 5501, 10550])).
% 2.32/2.57 tff(10971,plain,
% 2.32/2.57 (r(s(s(z)), s(z))),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[153, 10970])).
% 2.32/2.57 tff(10972,plain,
% 2.32/2.57 (~r(s(s(s(z))), elem!1)),
% 2.32/2.57 inference(modus_ponens,[status(thm)],[10966, 10365])).
% 2.32/2.57 tff(10973,plain,
% 2.32/2.57 (b(s(s(s(z))), elem!1)),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[1115, 10972, 4145])).
% 2.32/2.57 tff(10974,plain,
% 2.32/2.57 (~b(s(s(s(z))), s(z))),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[8081, 10973, 1391, 5501, 9520])).
% 2.32/2.57 tff(10975,plain,
% 2.32/2.57 (r(s(s(s(z))), s(z))),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[1081, 10974])).
% 2.32/2.57 tff(10976,plain,
% 2.32/2.57 (~r(s(s(z)), s(s(s(z))))),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[6502, 10975, 10971])).
% 2.32/2.57 tff(10977,plain,
% 2.32/2.57 (b(s(s(z)), s(s(s(z))))),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[8252, 10976])).
% 2.32/2.57 tff(10978,plain,
% 2.32/2.57 ($false),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[10977, 10969])).
% 2.32/2.57 tff(10979,plain,((~b(s(z), elem!1)) | (~(z = elem!1)) | (~b(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.57 tff(10980,plain,
% 2.32/2.57 (~b(s(z), elem!1)),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[10979, 288, 1391, 698])).
% 2.32/2.57 tff(10981,plain,
% 2.32/2.57 (r(s(z), elem!1)),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[601, 10980, 2478])).
% 2.32/2.57 tff(10982,plain,
% 2.32/2.57 (r(s(elem!1), elem!1)),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[4005, 10981, 288])).
% 2.32/2.57 tff(10983,plain,
% 2.32/2.57 (~r(s(s(s(s(z)))), s(elem!1))),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[9641, 37, 698, 10982])).
% 2.32/2.57 tff(10984,plain,
% 2.32/2.57 (b(s(s(s(s(z)))), s(elem!1))),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[4263, 58, 4260, 10983])).
% 2.32/2.57 tff(10985,plain,
% 2.32/2.57 (b(s(s(s(s(z)))), s(z))),
% 2.32/2.57 inference(modus_ponens,[status(thm)],[10984, 10545])).
% 2.32/2.57 tff(10986,plain,
% 2.32/2.57 (r(s(z), z)),
% 2.32/2.57 inference(modus_ponens,[status(thm)],[10982, 9500])).
% 2.32/2.57 tff(10987,plain,
% 2.32/2.57 (~r(s(z), s(s(s(s(z)))))),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[2586, 10986, 10355])).
% 2.32/2.57 tff(10988,plain,
% 2.32/2.57 (b(s(z), s(s(s(s(z)))))),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[489, 10987])).
% 2.32/2.57 tff(10989,plain,
% 2.32/2.57 (~b(s(s(s(s(z)))), elem!1)),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[6050, 10988, 1391, 288])).
% 2.32/2.57 tff(10990,plain,
% 2.32/2.57 (b(elem!1, s(s(s(s(z)))))),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[10943, 10989, 288, 2478])).
% 2.32/2.57 tff(10991,plain,
% 2.32/2.57 (b(s(elem!1), s(s(s(s(z)))))),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[3857, 10988, 288])).
% 2.32/2.57 tff(10992,plain,
% 2.32/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, 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(X1, 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(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.32/2.57 inference(rewrite,[status(thm)],[])).
% 2.32/2.57 tff(10993,plain,
% 2.32/2.57 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.32/2.57 inference(rewrite,[status(thm)],[])).
% 2.32/2.57 tff(10994,plain,
% 2.32/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 2.32/2.57 inference(monotonicity,[status(thm)],[10993])).
% 2.32/2.57 tff(10995,plain,
% 2.32/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 2.32/2.57 inference(transitivity,[status(thm)],[10994, 10992])).
% 2.32/2.57 tff(10996,plain,
% 2.32/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(elem!1))))),
% 2.32/2.57 inference(quant_inst,[status(thm)],[])).
% 2.32/2.57 tff(10997,plain,
% 2.32/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 2.32/2.57 inference(modus_ponens,[status(thm)],[10996, 10995])).
% 2.32/2.57 tff(10998,plain,
% 2.32/2.57 ($false),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[10997, 75, 578, 286, 982, 3862, 2609])).
% 2.32/2.57 tff(10999,plain,((~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.57 tff(11000,plain,
% 2.32/2.57 (~b(s(s(s(s(z)))), s(z))),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[10999, 10991, 10990, 10988, 5734])).
% 2.32/2.57 tff(11001,plain,
% 2.32/2.57 ($false),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[11000, 10985])).
% 2.32/2.57 tff(11002,plain,((~(z = elem!1)) | (~b(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.57 tff(11003,plain,
% 2.32/2.57 (~(z = elem!1)),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[11002, 1391, 698])).
% 2.32/2.57 tff(11004,plain,
% 2.32/2.57 (~(elem!1 = z)),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[304, 11003])).
% 2.32/2.57 tff(11005,plain,
% 2.32/2.57 (b(s(elem!1), elem!1)),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[1122, 10540, 10516])).
% 2.32/2.57 tff(11006,plain,
% 2.32/2.57 (r(elem!1, z) <=> r(s(s(z)), z)),
% 2.32/2.57 inference(monotonicity,[status(thm)],[10495])).
% 2.32/2.57 tff(11007,plain,
% 2.32/2.57 (b(z, elem!1) <=> b(z, s(s(z)))),
% 2.32/2.57 inference(monotonicity,[status(thm)],[10495])).
% 2.32/2.57 tff(11008,plain,
% 2.32/2.57 (b(z, s(s(z)))),
% 2.32/2.57 inference(modus_ponens,[status(thm)],[1518, 11007])).
% 2.32/2.57 tff(11009,plain,
% 2.32/2.57 (~r(s(s(z)), z)),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[2015, 1561, 1997])).
% 2.32/2.57 tff(11010,plain,
% 2.32/2.57 (b(s(s(z)), z)),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[202, 11009])).
% 2.32/2.57 tff(11011,plain,
% 2.32/2.57 ((s(s(s(s(s(s(s(z))))))) = elem!1) <=> (s(s(s(s(s(s(s(z))))))) = s(s(z)))),
% 2.32/2.57 inference(monotonicity,[status(thm)],[10495])).
% 2.32/2.57 tff(11012,plain,
% 2.32/2.57 ((s(s(s(s(s(s(s(z))))))) = s(s(z))) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.32/2.57 inference(symmetry,[status(thm)],[11011])).
% 2.32/2.57 tff(11013,plain,
% 2.32/2.57 ((~(s(s(s(s(s(s(s(z))))))) = s(s(z)))) <=> (~(s(s(s(s(s(s(s(z))))))) = elem!1))),
% 2.32/2.57 inference(monotonicity,[status(thm)],[11012])).
% 2.32/2.57 tff(11014,plain,
% 2.32/2.57 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.32/2.57 inference(modus_ponens,[status(thm)],[1045, 11013])).
% 2.32/2.57 tff(11015,plain,
% 2.32/2.57 (r(s(s(s(s(s(s(s(z))))))), s(s(z))) <=> r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.32/2.57 inference(monotonicity,[status(thm)],[10496])).
% 2.32/2.57 tff(11016,plain,
% 2.32/2.57 (r(s(s(s(s(s(s(s(z))))))), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.32/2.57 inference(symmetry,[status(thm)],[11015])).
% 2.32/2.57 tff(11017,plain,
% 2.32/2.57 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.32/2.57 inference(modus_ponens,[status(thm)],[738, 11016])).
% 2.32/2.57 tff(11018,plain,
% 2.32/2.57 (((~![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(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.32/2.57 inference(rewrite,[status(thm)],[])).
% 2.32/2.57 tff(11019,plain,
% 2.32/2.57 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.32/2.57 inference(rewrite,[status(thm)],[])).
% 2.32/2.57 tff(11020,plain,
% 2.32/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), z)) | (~r(s(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), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 2.32/2.57 inference(monotonicity,[status(thm)],[11019])).
% 2.32/2.57 tff(11021,plain,
% 2.32/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), z)) | (~r(s(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), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.32/2.57 inference(transitivity,[status(thm)],[11020, 11018])).
% 2.32/2.57 tff(11022,plain,
% 2.32/2.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.32/2.57 inference(quant_inst,[status(thm)],[])).
% 2.32/2.57 tff(11023,plain,
% 2.32/2.57 ((~![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(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.32/2.57 inference(modus_ponens,[status(thm)],[11022, 11021])).
% 2.32/2.57 tff(11024,plain,
% 2.32/2.57 ((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[11023, 37, 1561, 1997])).
% 2.32/2.57 tff(11025,plain,
% 2.32/2.57 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[11024, 11017])).
% 2.32/2.57 tff(11026,plain,
% 2.32/2.57 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[1230, 58, 1227, 11025])).
% 2.32/2.57 tff(11027,plain,
% 2.32/2.57 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[10506, 11017, 10499])).
% 2.32/2.57 tff(11028,plain,
% 2.32/2.57 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[1179, 58, 1176, 11027])).
% 2.32/2.57 tff(11029,plain,
% 2.32/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 2.32/2.57 inference(rewrite,[status(thm)],[])).
% 2.32/2.57 tff(11030,plain,
% 2.32/2.57 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 2.32/2.57 inference(rewrite,[status(thm)],[])).
% 2.32/2.57 tff(11031,plain,
% 2.32/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z))))))),
% 2.32/2.57 inference(monotonicity,[status(thm)],[11030])).
% 2.32/2.57 tff(11032,plain,
% 2.32/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 2.32/2.57 inference(transitivity,[status(thm)],[11031, 11029])).
% 2.32/2.57 tff(11033,plain,
% 2.32/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 2.32/2.57 inference(quant_inst,[status(thm)],[])).
% 2.32/2.57 tff(11034,plain,
% 2.32/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z))))),
% 2.32/2.57 inference(modus_ponens,[status(thm)],[11033, 11032])).
% 2.32/2.57 tff(11035,plain,
% 2.32/2.57 (~b(s(s(s(z))), z)),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[11034, 75, 370, 11010, 1155])).
% 2.32/2.57 tff(11036,plain,
% 2.32/2.57 (r(s(s(s(z))), z)),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[1334, 58, 221, 11035])).
% 2.32/2.57 tff(11037,plain,
% 2.32/2.57 (~r(s(z), s(s(s(z))))),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[4652, 37, 1561, 11036])).
% 2.32/2.57 tff(11038,plain,
% 2.32/2.57 (b(s(z), s(s(s(z))))),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[1263, 11037])).
% 2.32/2.57 tff(11039,plain,
% 2.32/2.57 (~r(s(s(s(z))), s(z))),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[4131, 37, 1561, 11036])).
% 2.32/2.57 tff(11040,plain,
% 2.32/2.57 (b(s(s(s(z))), s(z))),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[1081, 11039])).
% 2.32/2.57 tff(11041,plain,
% 2.32/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.32/2.57 inference(rewrite,[status(thm)],[])).
% 2.32/2.57 tff(11042,plain,
% 2.32/2.57 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))) <=> ((~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(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.32/2.57 inference(rewrite,[status(thm)],[])).
% 2.32/2.57 tff(11043,plain,
% 2.32/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 2.32/2.57 inference(monotonicity,[status(thm)],[11042])).
% 2.32/2.57 tff(11044,plain,
% 2.32/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.32/2.57 inference(transitivity,[status(thm)],[11043, 11041])).
% 2.32/2.57 tff(11045,plain,
% 2.32/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.32/2.58 inference(quant_inst,[status(thm)],[])).
% 2.32/2.58 tff(11046,plain,
% 2.32/2.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 2.32/2.58 inference(modus_ponens,[status(thm)],[11045, 11044])).
% 2.32/2.58 tff(11047,plain,
% 2.32/2.58 ($false),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[11046, 75, 11040, 11038, 982, 11028, 11026])).
% 2.32/2.58 tff(11048,plain,((~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~(elem!1 = s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.58 tff(11049,plain,
% 2.32/2.58 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[11048, 1561, 1176, 982, 1997, 698, 10495, 11008, 1155])).
% 2.32/2.58 tff(11050,plain,
% 2.32/2.58 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[813, 11049, 11014])).
% 2.32/2.58 tff(11051,plain,
% 2.32/2.58 (~b(s(elem!1), z)),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[10000, 1958, 921, 401, 370])).
% 2.32/2.58 tff(11052,plain,
% 2.32/2.58 (~r(s(elem!1), z)),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[10257, 1958, 1518, 790, 1168, 921])).
% 2.32/2.58 tff(11053,plain,
% 2.32/2.58 ($false),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[766, 11052, 11051])).
% 2.32/2.58 tff(11054,plain,((~b(elem!1, z)) | (~b(z, elem!1)) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), z)) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.58 tff(11055,plain,
% 2.32/2.58 (~b(elem!1, z)),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[11054, 11050, 790, 1518, 921, 11010, 11008])).
% 2.32/2.58 tff(11056,plain,
% 2.32/2.58 (r(elem!1, z)),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[387, 11055, 353])).
% 2.32/2.58 tff(11057,plain,
% 2.32/2.58 (r(s(s(z)), z)),
% 2.32/2.58 inference(modus_ponens,[status(thm)],[11056, 11006])).
% 2.32/2.58 tff(11058,plain,
% 2.32/2.58 ($false),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[11009, 11057])).
% 2.32/2.58 tff(11059,plain,((~r(s(z), z)) | (~(elem!1 = s(s(z)))) | (elem!1 = z) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.58 tff(11060,plain,
% 2.32/2.58 (~r(s(z), z)),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[11059, 10468, 11004, 10542, 1518, 11005, 10484, 10265, 10481, 698, 10541])).
% 2.32/2.58 tff(11061,plain,
% 2.32/2.58 (b(s(z), z)),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[169, 11060])).
% 2.32/2.58 tff(11062,plain,
% 2.32/2.58 (~b(elem!1, z)),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[6636, 11061, 1391, 1518])).
% 2.32/2.58 tff(11063,plain,
% 2.32/2.58 (r(elem!1, z)),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[387, 11062, 11004])).
% 2.32/2.58 tff(11064,plain,
% 2.32/2.58 (r(s(s(z)), z)),
% 2.32/2.58 inference(modus_ponens,[status(thm)],[11063, 10543])).
% 2.32/2.58 tff(11065,plain,
% 2.32/2.58 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[8352, 6494, 467])).
% 2.32/2.58 tff(11066,plain,
% 2.32/2.58 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[575, 11065])).
% 2.32/2.58 tff(11067,plain,
% 2.32/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(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(X1, 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(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.32/2.58 inference(rewrite,[status(thm)],[])).
% 2.32/2.58 tff(11068,plain,
% 2.32/2.58 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.32/2.58 inference(rewrite,[status(thm)],[])).
% 2.32/2.58 tff(11069,plain,
% 2.32/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))))),
% 2.32/2.58 inference(monotonicity,[status(thm)],[11068])).
% 2.32/2.58 tff(11070,plain,
% 2.32/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.32/2.58 inference(transitivity,[status(thm)],[11069, 11067])).
% 2.32/2.58 tff(11071,plain,
% 2.32/2.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 2.32/2.58 inference(quant_inst,[status(thm)],[])).
% 2.32/2.58 tff(11072,plain,
% 2.32/2.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))),
% 2.32/2.58 inference(modus_ponens,[status(thm)],[11071, 11070])).
% 2.32/2.58 tff(11073,plain,
% 2.32/2.58 (~b(s(z), s(s(s(z))))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[11072, 75, 578, 11066, 982])).
% 2.32/2.58 tff(11074,plain,
% 2.32/2.58 (r(s(z), s(s(s(z))))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[1263, 11073])).
% 2.32/2.58 tff(11075,plain,
% 2.32/2.58 (((~![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)), z)) | (~r(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(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 2.32/2.58 inference(rewrite,[status(thm)],[])).
% 2.32/2.58 tff(11076,plain,
% 2.32/2.58 (((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 2.32/2.58 inference(rewrite,[status(thm)],[])).
% 2.32/2.58 tff(11077,plain,
% 2.32/2.58 (((~![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(z))))) | (~r(s(z), s(s(s(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), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))))),
% 2.32/2.58 inference(monotonicity,[status(thm)],[11076])).
% 2.32/2.58 tff(11078,plain,
% 2.32/2.58 (((~![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(z))))) | (~r(s(z), s(s(s(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), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 2.32/2.58 inference(transitivity,[status(thm)],[11077, 11075])).
% 2.32/2.58 tff(11079,plain,
% 2.32/2.58 ((~![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(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))),
% 2.32/2.58 inference(quant_inst,[status(thm)],[])).
% 2.32/2.58 tff(11080,plain,
% 2.32/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))),
% 2.32/2.58 inference(modus_ponens,[status(thm)],[11079, 11078])).
% 2.32/2.58 tff(11081,plain,
% 2.32/2.58 ($false),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[11080, 37, 1997, 320, 11074, 6494])).
% 2.32/2.58 tff(11082,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.58 tff(11083,plain,
% 2.32/2.58 (~r(s(s(z)), s(s(s(z))))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[11082, 10481, 11064, 10223, 10265, 10450])).
% 2.32/2.58 tff(11084,plain,
% 2.32/2.58 (b(s(s(z)), s(s(s(z))))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[8252, 11083])).
% 2.32/2.58 tff(11085,plain,
% 2.32/2.58 (s(elem!1) = s(s(s(z)))),
% 2.32/2.58 inference(monotonicity,[status(thm)],[10495])).
% 2.32/2.58 tff(11086,plain,
% 2.32/2.58 (s(s(s(z))) = s(elem!1)),
% 2.32/2.58 inference(symmetry,[status(thm)],[11085])).
% 2.32/2.58 tff(11087,plain,
% 2.32/2.58 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (s(s(s(s(s(s(s(z))))))) = s(elem!1))),
% 2.32/2.58 inference(monotonicity,[status(thm)],[11086])).
% 2.32/2.58 tff(11088,plain,
% 2.32/2.58 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.32/2.58 inference(transitivity,[status(thm)],[11087, 269])).
% 2.32/2.58 tff(11089,plain,
% 2.32/2.58 ((s(elem!1) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(z))))),
% 2.32/2.58 inference(symmetry,[status(thm)],[11088])).
% 2.32/2.58 tff(11090,plain,
% 2.32/2.58 ((~(s(elem!1) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(s(s(z)))))),
% 2.32/2.58 inference(monotonicity,[status(thm)],[11089])).
% 2.32/2.58 tff(11091,plain,
% 2.32/2.58 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))),
% 2.32/2.58 inference(modus_ponens,[status(thm)],[790, 11090])).
% 2.32/2.58 tff(11092,assumption,(b(s(s(s(s(s(s(s(z))))))), s(s(z)))), introduced(assumption)).
% 2.32/2.58 tff(11093,plain,
% 2.32/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(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(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(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(s(s(s(z))))))), s(s(z)))))),
% 2.32/2.58 inference(rewrite,[status(thm)],[])).
% 2.32/2.58 tff(11094,plain,
% 2.32/2.58 (((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z))) <=> ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(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(s(s(s(z))))))), s(s(z)))))),
% 2.32/2.58 inference(rewrite,[status(thm)],[])).
% 2.32/2.58 tff(11095,plain,
% 2.32/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(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(s(s(s(z))))))), s(s(z))))))),
% 2.32/2.58 inference(monotonicity,[status(thm)],[11094])).
% 2.32/2.58 tff(11096,plain,
% 2.32/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(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(s(s(s(z))))))), s(s(z)))))),
% 2.32/2.58 inference(transitivity,[status(thm)],[11095, 11093])).
% 2.32/2.58 tff(11097,plain,
% 2.32/2.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.32/2.58 inference(quant_inst,[status(thm)],[])).
% 2.32/2.58 tff(11098,plain,
% 2.32/2.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(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(s(s(s(z))))))), s(s(z))))),
% 2.32/2.58 inference(modus_ponens,[status(thm)],[11097, 11096])).
% 2.32/2.58 tff(11099,plain,
% 2.32/2.58 ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[11098, 75, 370, 1155, 8218])).
% 2.32/2.58 tff(11100,plain,
% 2.32/2.58 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[11099, 11092])).
% 2.32/2.58 tff(11101,plain,
% 2.32/2.58 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[750, 58, 747, 11100])).
% 2.32/2.58 tff(11102,plain,
% 2.32/2.58 (((~![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(s(s(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(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(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.32/2.58 inference(rewrite,[status(thm)],[])).
% 2.32/2.58 tff(11103,plain,
% 2.32/2.58 (((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.32/2.58 inference(rewrite,[status(thm)],[])).
% 2.32/2.58 tff(11104,plain,
% 2.32/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(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(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))))),
% 2.32/2.58 inference(monotonicity,[status(thm)],[11103])).
% 2.32/2.58 tff(11105,plain,
% 2.32/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(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(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.32/2.58 inference(transitivity,[status(thm)],[11104, 11102])).
% 2.32/2.59 tff(11106,plain,
% 2.32/2.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.32/2.59 inference(quant_inst,[status(thm)],[])).
% 2.32/2.59 tff(11107,plain,
% 2.32/2.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 2.32/2.59 inference(modus_ponens,[status(thm)],[11106, 11105])).
% 2.32/2.59 tff(11108,plain,
% 2.32/2.59 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[11107, 37, 6472, 11101])).
% 2.32/2.59 tff(11109,plain,
% 2.32/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.32/2.59 inference(rewrite,[status(thm)],[])).
% 2.32/2.59 tff(11110,plain,
% 2.32/2.59 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.32/2.59 inference(rewrite,[status(thm)],[])).
% 2.32/2.59 tff(11111,plain,
% 2.32/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))))),
% 2.32/2.59 inference(monotonicity,[status(thm)],[11110])).
% 2.32/2.59 tff(11112,plain,
% 2.32/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.32/2.59 inference(transitivity,[status(thm)],[11111, 11109])).
% 2.32/2.59 tff(11113,plain,
% 2.32/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.32/2.59 inference(quant_inst,[status(thm)],[])).
% 2.32/2.59 tff(11114,plain,
% 2.32/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 2.32/2.59 inference(modus_ponens,[status(thm)],[11113, 11112])).
% 2.32/2.59 tff(11115,plain,
% 2.32/2.59 ((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[11114, 75, 1155, 8218])).
% 2.32/2.59 tff(11116,plain,
% 2.32/2.59 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[11115, 11092])).
% 2.32/2.59 tff(11117,plain,
% 2.32/2.59 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[2930, 58, 11116])).
% 2.32/2.59 tff(11118,plain,
% 2.32/2.59 ($false),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[11117, 11108, 11091])).
% 2.32/2.59 tff(11119,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(z))), z)) | (s(elem!1) = s(s(s(s(s(s(s(z)))))))) | (~(elem!1 = s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.59 tff(11120,plain,
% 2.32/2.59 (~r(s(s(s(z))), z)),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[11119, 11084, 10542, 10468, 10541, 10514, 10470])).
% 2.32/2.59 tff(11121,plain,
% 2.32/2.59 (~(elem!1 = s(s(s(z))))),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[1033, 10517])).
% 2.32/2.59 tff(11122,plain,
% 2.32/2.59 (r(elem!1, s(s(s(z)))) <=> r(s(s(z)), s(s(s(z))))),
% 2.32/2.59 inference(monotonicity,[status(thm)],[10495])).
% 2.32/2.59 tff(11123,plain,
% 2.32/2.59 (r(s(s(z)), s(s(s(z))))),
% 2.32/2.59 inference(modus_ponens,[status(thm)],[1266, 11122])).
% 2.32/2.59 tff(11124,plain,
% 2.32/2.59 ($false),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[8249, 11123])).
% 2.32/2.59 tff(11125,plain,((~r(elem!1, s(s(s(z))))) | r(s(s(z)), s(s(s(z)))) | (~(elem!1 = s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.59 tff(11126,plain,
% 2.32/2.59 (~r(elem!1, s(s(s(z))))),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[11125, 11083, 10468])).
% 2.32/2.59 tff(11127,plain,
% 2.32/2.59 (b(elem!1, s(s(s(z))))),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[1279, 11126, 11121])).
% 2.32/2.59 tff(11128,plain,
% 2.32/2.59 (~b(s(s(s(z))), z)),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[6760, 11127, 1518, 10540])).
% 2.32/2.59 tff(11129,plain,
% 2.32/2.59 ($false),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[1334, 58, 221, 11128, 11120])).
% 2.32/2.59 tff(11130,plain,((~r(s(z), elem!1)) | (~b(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.32/2.59 tff(11131,plain,
% 2.32/2.59 (~r(s(z), elem!1)),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[11130, 1518, 9473, 99, 10352])).
% 2.32/2.59 tff(11132,plain,
% 2.32/2.59 (b(s(z), elem!1)),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[601, 11131, 10438])).
% 2.32/2.59 tff(11133,plain,
% 2.32/2.59 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[8644, 8515])).
% 2.32/2.59 tff(11134,assumption,(r(s(s(s(s(s(s(s(z))))))), z)), introduced(assumption)).
% 2.32/2.59 tff(11135,plain,
% 2.32/2.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(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), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.59 inference(rewrite,[status(thm)],[])).
% 2.32/2.59 tff(11136,plain,
% 2.32/2.59 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.59 inference(rewrite,[status(thm)],[])).
% 2.32/2.59 tff(11137,plain,
% 2.32/2.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.32/2.59 inference(monotonicity,[status(thm)],[11136])).
% 2.32/2.59 tff(11138,plain,
% 2.32/2.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.59 inference(transitivity,[status(thm)],[11137, 11135])).
% 2.32/2.59 tff(11139,plain,
% 2.32/2.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.32/2.59 inference(quant_inst,[status(thm)],[])).
% 2.32/2.59 tff(11140,plain,
% 2.32/2.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.32/2.59 inference(modus_ponens,[status(thm)],[11139, 11138])).
% 2.32/2.59 tff(11141,plain,
% 2.32/2.59 ($false),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[11140, 37, 1561, 8647, 11134])).
% 2.32/2.59 tff(11142,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.59 tff(11143,plain,
% 2.32/2.59 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[11142, 11133, 3185])).
% 2.32/2.59 tff(11144,plain,
% 2.32/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.32/2.59 inference(rewrite,[status(thm)],[])).
% 2.32/2.59 tff(11145,plain,
% 2.32/2.59 (((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z))) <=> ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.32/2.59 inference(rewrite,[status(thm)],[])).
% 2.32/2.59 tff(11146,plain,
% 2.32/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 2.32/2.59 inference(monotonicity,[status(thm)],[11145])).
% 2.32/2.59 tff(11147,plain,
% 2.32/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.32/2.59 inference(transitivity,[status(thm)],[11146, 11144])).
% 2.32/2.59 tff(11148,plain,
% 2.32/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.32/2.59 inference(quant_inst,[status(thm)],[])).
% 2.32/2.59 tff(11149,plain,
% 2.32/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.32/2.59 inference(modus_ponens,[status(thm)],[11148, 11147])).
% 2.32/2.59 tff(11150,plain,
% 2.32/2.59 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[11149, 75, 1518, 107, 1391, 1168])).
% 2.32/2.59 tff(11151,plain,
% 2.32/2.59 ($false),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[750, 58, 747, 11150, 11143])).
% 2.32/2.59 tff(11152,plain,((~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.59 tff(11153,plain,
% 2.32/2.59 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[11152, 11132, 10352, 1518])).
% 2.32/2.59 tff(11154,plain,
% 2.32/2.59 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[813, 11153, 10447])).
% 2.32/2.59 tff(11155,plain,
% 2.32/2.59 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[9654, 37, 9473, 11154])).
% 2.32/2.59 tff(11156,plain,
% 2.32/2.59 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(z)))))),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[1134, 3143])).
% 2.32/2.59 tff(11157,plain,
% 2.32/2.59 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[1179, 58, 11156, 11155])).
% 2.32/2.59 tff(11158,plain,
% 2.32/2.59 ((s(s(z)) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 2.32/2.59 inference(monotonicity,[status(thm)],[3143])).
% 2.32/2.59 tff(11159,plain,
% 2.32/2.59 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 2.32/2.59 inference(transitivity,[status(thm)],[11158, 1028])).
% 2.32/2.59 tff(11160,plain,
% 2.32/2.59 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = elem!1))),
% 2.32/2.59 inference(monotonicity,[status(thm)],[11159])).
% 2.32/2.59 tff(11161,plain,
% 2.32/2.59 (~(s(s(s(z))) = elem!1)),
% 2.32/2.59 inference(modus_ponens,[status(thm)],[1556, 11160])).
% 2.32/2.59 tff(11162,plain,
% 2.32/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), z)))),
% 2.32/2.59 inference(rewrite,[status(thm)],[])).
% 2.32/2.59 tff(11163,plain,
% 2.32/2.59 (((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), z)))),
% 2.32/2.59 inference(rewrite,[status(thm)],[])).
% 2.32/2.59 tff(11164,plain,
% 2.32/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), z))))),
% 2.32/2.59 inference(monotonicity,[status(thm)],[11163])).
% 2.32/2.59 tff(11165,plain,
% 2.32/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), z)))),
% 2.32/2.59 inference(transitivity,[status(thm)],[11164, 11162])).
% 2.32/2.59 tff(11166,plain,
% 2.32/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))),
% 2.32/2.59 inference(quant_inst,[status(thm)],[])).
% 2.32/2.59 tff(11167,plain,
% 2.32/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), z))),
% 2.32/2.59 inference(modus_ponens,[status(thm)],[11166, 11165])).
% 2.32/2.59 tff(11168,plain,
% 2.32/2.59 (~b(s(s(s(z))), z)),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[11167, 75, 1518, 107, 1391, 1119])).
% 2.32/2.59 tff(11169,plain,
% 2.32/2.59 (r(s(s(s(z))), z)),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[1334, 58, 221, 11168])).
% 2.32/2.59 tff(11170,plain,
% 2.32/2.59 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 2.32/2.59 inference(rewrite,[status(thm)],[])).
% 2.32/2.59 tff(11171,plain,
% 2.32/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))), elem!1)) | (~b(elem!1, 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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z)))))),
% 2.32/2.59 inference(monotonicity,[status(thm)],[11170])).
% 2.32/2.59 tff(11172,plain,
% 2.32/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))), elem!1)) | (~b(elem!1, 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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 2.32/2.59 inference(transitivity,[status(thm)],[11171, 10742])).
% 2.32/2.59 tff(11173,plain,
% 2.32/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 2.32/2.59 inference(quant_inst,[status(thm)],[])).
% 2.32/2.59 tff(11174,plain,
% 2.32/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z)))),
% 2.32/2.59 inference(modus_ponens,[status(thm)],[11173, 11172])).
% 2.32/2.59 tff(11175,plain,
% 2.32/2.59 (~b(s(s(s(z))), s(z))),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[11174, 75, 107, 1391, 1119])).
% 2.32/2.59 tff(11176,plain,
% 2.32/2.59 (r(s(s(s(z))), s(z))),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[1081, 11175])).
% 2.32/2.59 tff(11177,plain,
% 2.32/2.59 ($false),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[6259, 37, 506, 11176, 11169])).
% 2.32/2.59 tff(11178,plain,((~b(s(s(s(z))), elem!1)) | (~r(z, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.59 tff(11179,plain,
% 2.32/2.59 (~b(s(s(s(z))), elem!1)),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[11178, 11132, 10352, 506, 1518])).
% 2.32/2.59 tff(11180,plain,
% 2.32/2.59 (r(s(s(s(z))), elem!1)),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[1115, 11179, 11161])).
% 2.42/2.60 tff(11181,plain,
% 2.42/2.60 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[3487, 37, 11180, 9473])).
% 2.42/2.60 tff(11182,plain,
% 2.42/2.60 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[575, 11181])).
% 2.42/2.60 tff(11183,plain,
% 2.42/2.60 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[3495, 37, 11180, 9473])).
% 2.42/2.60 tff(11184,plain,
% 2.42/2.60 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[2898, 11183])).
% 2.42/2.60 tff(11185,plain,
% 2.42/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.42/2.60 inference(rewrite,[status(thm)],[])).
% 2.42/2.60 tff(11186,plain,
% 2.42/2.60 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(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(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.42/2.60 inference(rewrite,[status(thm)],[])).
% 2.42/2.60 tff(11187,plain,
% 2.42/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 2.42/2.60 inference(monotonicity,[status(thm)],[11186])).
% 2.42/2.60 tff(11188,plain,
% 2.42/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.42/2.60 inference(transitivity,[status(thm)],[11187, 11185])).
% 2.42/2.60 tff(11189,plain,
% 2.42/2.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.42/2.60 inference(quant_inst,[status(thm)],[])).
% 2.42/2.60 tff(11190,plain,
% 2.42/2.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 2.42/2.60 inference(modus_ponens,[status(thm)],[11189, 11188])).
% 2.42/2.60 tff(11191,plain,
% 2.42/2.60 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[11190, 75, 11184, 11182, 11157])).
% 2.42/2.60 tff(11192,plain,
% 2.42/2.60 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[2926, 37, 11180, 11154])).
% 2.42/2.60 tff(11193,plain,
% 2.42/2.60 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[2930, 58, 11192])).
% 2.42/2.60 tff(11194,plain,
% 2.42/2.60 ($false),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[11193, 11191, 10444])).
% 2.42/2.60 tff(11195,plain,((~b(z, elem!1)) | (~(s(s(elem!1)) = s(s(s(s(z)))))) | (~r(z, s(z))) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.42/2.60 tff(11196,plain,
% 2.42/2.60 (~b(z, elem!1)),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[11195, 1020, 506, 99])).
% 2.42/2.60 tff(11197,plain,
% 2.42/2.60 (r(z, elem!1)),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[298, 11196, 10437])).
% 2.42/2.60 tff(11198,plain,
% 2.42/2.60 (~r(s(z), elem!1)),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[10304, 11197, 9473])).
% 2.42/2.60 tff(11199,plain,
% 2.42/2.60 ((s(s(z)) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(z)))))),
% 2.42/2.60 inference(monotonicity,[status(thm)],[3143])).
% 2.42/2.60 tff(11200,plain,
% 2.42/2.60 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(elem!1 = s(s(s(s(z))))))),
% 2.42/2.60 inference(monotonicity,[status(thm)],[11199])).
% 2.42/2.60 tff(11201,plain,
% 2.42/2.60 (~(elem!1 = s(s(s(s(z)))))),
% 2.42/2.60 inference(modus_ponens,[status(thm)],[459, 11200])).
% 2.42/2.60 tff(11202,plain,
% 2.42/2.60 (~(s(s(z)) = s(elem!1))),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[3261, 10438])).
% 2.42/2.60 tff(11203,plain,
% 2.42/2.60 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[4541, 11202])).
% 2.42/2.60 tff(11204,plain,
% 2.42/2.60 (~(s(s(s(z))) = elem!1)),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[1026, 1047, 860])).
% 2.42/2.60 tff(11205,plain,
% 2.42/2.60 ((~r(s(elem!1), elem!1)) <=> (~r(s(s(s(z))), elem!1))),
% 2.42/2.60 inference(monotonicity,[status(thm)],[8318])).
% 2.42/2.60 tff(11206,plain,
% 2.42/2.60 (((~![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(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.42/2.60 inference(rewrite,[status(thm)],[])).
% 2.42/2.60 tff(11207,plain,
% 2.42/2.60 (((~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.42/2.60 inference(rewrite,[status(thm)],[])).
% 2.42/2.60 tff(11208,plain,
% 2.42/2.60 (((~![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(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 2.42/2.60 inference(monotonicity,[status(thm)],[11207])).
% 2.42/2.60 tff(11209,plain,
% 2.42/2.60 (((~![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(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.42/2.60 inference(transitivity,[status(thm)],[11208, 11206])).
% 2.42/2.60 tff(11210,plain,
% 2.42/2.60 ((~![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(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 2.42/2.60 inference(quant_inst,[status(thm)],[])).
% 2.42/2.60 tff(11211,plain,
% 2.42/2.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(z))))))),
% 2.42/2.60 inference(modus_ponens,[status(thm)],[11210, 11209])).
% 2.42/2.60 tff(11212,plain,
% 2.42/2.60 (~r(s(elem!1), s(s(s(s(z)))))),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[11211, 37, 698, 752])).
% 2.42/2.60 tff(11213,plain,
% 2.42/2.60 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.42/2.60 inference(modus_ponens,[status(thm)],[11212, 8460])).
% 2.42/2.60 tff(11214,plain,
% 2.42/2.60 (r(z, s(s(elem!1))) <=> r(z, s(s(s(s(z)))))),
% 2.42/2.60 inference(monotonicity,[status(thm)],[1047])).
% 2.42/2.60 tff(11215,plain,
% 2.42/2.60 (r(z, s(s(s(s(z))))) <=> r(z, s(s(elem!1)))),
% 2.42/2.60 inference(symmetry,[status(thm)],[11214])).
% 2.42/2.60 tff(11216,plain,
% 2.42/2.60 ((~r(z, s(s(s(s(z)))))) <=> (~r(z, s(s(elem!1))))),
% 2.42/2.60 inference(monotonicity,[status(thm)],[11215])).
% 2.42/2.60 tff(11217,plain,
% 2.42/2.60 (~r(z, s(s(elem!1)))),
% 2.42/2.60 inference(modus_ponens,[status(thm)],[7165, 11216])).
% 2.42/2.60 tff(11218,plain,
% 2.42/2.60 (b(s(s(elem!1)), z) <=> b(s(s(s(s(z)))), z)),
% 2.42/2.60 inference(monotonicity,[status(thm)],[1047])).
% 2.42/2.60 tff(11219,plain,
% 2.42/2.60 (b(s(s(s(s(z)))), z) <=> b(s(s(elem!1)), z)),
% 2.42/2.60 inference(symmetry,[status(thm)],[11218])).
% 2.42/2.60 tff(11220,plain,
% 2.42/2.60 (b(s(s(elem!1)), z)),
% 2.42/2.60 inference(modus_ponens,[status(thm)],[7175, 11219])).
% 2.42/2.60 tff(11221,plain,
% 2.42/2.60 (b(s(s(s(z))), z)),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[1098, 767, 1047])).
% 2.42/2.60 tff(11222,plain,
% 2.42/2.60 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[5576, 11221, 11220, 11217])).
% 2.42/2.60 tff(11223,plain,
% 2.42/2.60 (r(s(s(s(z))), s(s(elem!1)))),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[62, 11222, 16])).
% 2.42/2.60 tff(11224,plain,
% 2.42/2.60 ($false),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[11223, 11213])).
% 2.42/2.60 tff(11225,plain,((~r(s(elem!1), elem!1)) | (~(s(s(z)) = elem!1)) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.60 tff(11226,plain,
% 2.42/2.60 (~r(s(elem!1), elem!1)),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[11225, 310, 16, 698, 300])).
% 2.42/2.60 tff(11227,plain,
% 2.42/2.60 (~r(s(s(s(z))), elem!1)),
% 2.42/2.60 inference(modus_ponens,[status(thm)],[11226, 11205])).
% 2.42/2.60 tff(11228,plain,
% 2.42/2.60 (b(s(s(s(z))), elem!1)),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[1115, 11227, 11204])).
% 2.42/2.60 tff(11229,plain,
% 2.42/2.60 (b(s(elem!1), elem!1)),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[1122, 11228, 1047])).
% 2.42/2.60 tff(11230,plain,
% 2.42/2.60 ((s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(s(s(z))))))))),
% 2.42/2.60 inference(monotonicity,[status(thm)],[1047])).
% 2.42/2.60 tff(11231,plain,
% 2.42/2.60 ((s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(s(z)))))),
% 2.42/2.60 inference(transitivity,[status(thm)],[11230, 9664])).
% 2.42/2.60 tff(11232,plain,
% 2.42/2.60 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) <=> (s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 2.42/2.60 inference(symmetry,[status(thm)],[11231])).
% 2.42/2.60 tff(11233,plain,
% 2.42/2.60 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(z)))))) <=> (~(s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))))),
% 2.42/2.60 inference(monotonicity,[status(thm)],[11232])).
% 2.42/2.60 tff(11234,plain,
% 2.42/2.60 (~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 2.42/2.60 inference(modus_ponens,[status(thm)],[1135, 11233])).
% 2.42/2.60 tff(11235,plain,
% 2.42/2.60 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[5185, 10233, 300, 11234])).
% 2.42/2.60 tff(11236,plain,
% 2.42/2.60 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[813, 11235, 1046])).
% 2.42/2.60 tff(11237,plain,
% 2.42/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.42/2.60 inference(rewrite,[status(thm)],[])).
% 2.42/2.60 tff(11238,plain,
% 2.42/2.60 (((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.42/2.60 inference(rewrite,[status(thm)],[])).
% 2.42/2.60 tff(11239,plain,
% 2.42/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))))),
% 2.42/2.60 inference(monotonicity,[status(thm)],[11238])).
% 2.42/2.60 tff(11240,plain,
% 2.42/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.42/2.60 inference(transitivity,[status(thm)],[11239, 11237])).
% 2.42/2.60 tff(11241,plain,
% 2.42/2.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))))),
% 2.42/2.60 inference(quant_inst,[status(thm)],[])).
% 2.42/2.60 tff(11242,plain,
% 2.42/2.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(s(z)))))))))),
% 2.42/2.60 inference(modus_ponens,[status(thm)],[11241, 11240])).
% 2.42/2.60 tff(11243,plain,
% 2.42/2.60 (~b(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[11242, 75, 107, 1391, 11236, 11229])).
% 2.42/2.60 tff(11244,plain,
% 2.42/2.60 (r(s(elem!1), s(s(s(s(s(s(s(z))))))))),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[793, 58, 1146, 11243])).
% 2.42/2.60 tff(11245,plain,
% 2.42/2.60 ((s(s(s(s(s(s(s(z))))))) = s(z)) <=> (s(z) = s(s(s(s(s(s(s(z))))))))),
% 2.42/2.60 inference(symmetry,[status(thm)],[7909])).
% 2.42/2.60 tff(11246,plain,
% 2.42/2.60 ((~(s(s(s(s(s(s(s(z))))))) = s(z))) <=> (~(s(z) = s(s(s(s(s(s(s(z)))))))))),
% 2.42/2.60 inference(monotonicity,[status(thm)],[11245])).
% 2.42/2.60 tff(11247,plain,
% 2.42/2.60 (~(s(z) = s(s(s(s(s(s(s(z))))))))),
% 2.42/2.60 inference(modus_ponens,[status(thm)],[1227, 11246])).
% 2.42/2.60 tff(11248,plain,
% 2.42/2.60 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[8514, 75, 107, 1391, 11236])).
% 2.42/2.60 tff(11249,plain,
% 2.42/2.60 ((s(z) = s(s(s(s(s(s(s(z)))))))) | r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[8518, 58, 11248])).
% 2.42/2.60 tff(11250,plain,
% 2.42/2.60 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[11249, 11247])).
% 2.42/2.60 tff(11251,plain,
% 2.42/2.60 (r(s(z), s(s(s(z)))) <=> r(s(z), s(elem!1))),
% 2.42/2.60 inference(monotonicity,[status(thm)],[1008])).
% 2.42/2.60 tff(11252,plain,
% 2.42/2.60 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(z))))),
% 2.42/2.60 inference(monotonicity,[status(thm)],[1127])).
% 2.42/2.60 tff(11253,plain,
% 2.42/2.60 ((~b(s(z), s(elem!1))) <=> (~b(s(z), s(s(s(z)))))),
% 2.42/2.60 inference(monotonicity,[status(thm)],[11252])).
% 2.42/2.60 tff(11254,plain,
% 2.42/2.60 (~b(s(z), s(elem!1))),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[8549, 75, 107, 1391, 11229])).
% 2.42/2.60 tff(11255,plain,
% 2.42/2.60 (~b(s(z), s(s(s(z))))),
% 2.42/2.60 inference(modus_ponens,[status(thm)],[11254, 11253])).
% 2.42/2.60 tff(11256,plain,
% 2.42/2.60 (r(s(z), s(s(s(z))))),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[1263, 11255])).
% 2.42/2.60 tff(11257,plain,
% 2.42/2.60 (r(s(z), s(elem!1))),
% 2.42/2.60 inference(modus_ponens,[status(thm)],[11256, 11251])).
% 2.42/2.60 tff(11258,plain,
% 2.42/2.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(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(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.42/2.60 inference(rewrite,[status(thm)],[])).
% 2.42/2.60 tff(11259,plain,
% 2.42/2.60 (((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.42/2.60 inference(rewrite,[status(thm)],[])).
% 2.42/2.60 tff(11260,plain,
% 2.42/2.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.42/2.60 inference(monotonicity,[status(thm)],[11259])).
% 2.42/2.60 tff(11261,plain,
% 2.42/2.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.42/2.60 inference(transitivity,[status(thm)],[11260, 11258])).
% 2.42/2.60 tff(11262,plain,
% 2.42/2.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(elem!1))))),
% 2.42/2.60 inference(quant_inst,[status(thm)],[])).
% 2.42/2.60 tff(11263,plain,
% 2.42/2.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(s(s(z))))))))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.42/2.60 inference(modus_ponens,[status(thm)],[11262, 11261])).
% 2.42/2.60 tff(11264,plain,
% 2.42/2.60 ($false),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[11263, 37, 11257, 11250, 11244])).
% 2.42/2.60 tff(11265,plain,((~(s(s(z)) = elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (elem!1 = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.60 tff(11266,plain,
% 2.42/2.60 (~b(s(z), elem!1)),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[11265, 11197, 9473, 10352, 11203, 3143, 11201])).
% 2.42/2.60 tff(11267,plain,
% 2.42/2.60 ($false),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[601, 11266, 11198, 10438])).
% 2.42/2.60 tff(11268,plain,((~(s(s(elem!1)) = s(s(s(s(z)))))) | (~r(z, s(z))) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.42/2.60 tff(11269,plain,
% 2.42/2.60 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[11268, 506, 99])).
% 2.42/2.60 tff(11270,plain,
% 2.42/2.60 (~(s(s(elem!1)) = s(s(z)))),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[237, 10437])).
% 2.42/2.60 tff(11271,plain,
% 2.42/2.60 (~(s(s(z)) = elem!1)),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[1013, 11269])).
% 2.42/2.60 tff(11272,plain,
% 2.42/2.60 (r(s(s(z)), elem!1)),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[104, 11271, 99])).
% 2.42/2.60 tff(11273,plain,
% 2.42/2.61 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[9912, 37, 106, 9473])).
% 2.42/2.61 tff(11274,plain,
% 2.42/2.61 (b(s(s(z)), s(s(s(s(z)))))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[465, 11273])).
% 2.42/2.61 tff(11275,plain,
% 2.42/2.61 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[10042, 37, 106, 9473])).
% 2.42/2.61 tff(11276,plain,
% 2.42/2.61 (b(s(s(s(s(z)))), s(s(z)))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[2167, 58, 10047, 11275])).
% 2.42/2.61 tff(11277,plain,
% 2.42/2.61 (r(s(s(elem!1)), s(s(z)))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[10059, 2647, 9473, 266, 1011, 11276, 11274])).
% 2.42/2.61 tff(11278,plain,
% 2.42/2.61 ($false),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[2661, 37, 106, 11277, 2647])).
% 2.42/2.61 tff(11279,plain,((~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (s(s(elem!1)) = s(s(z))) | (s(s(elem!1)) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.61 tff(11280,plain,
% 2.42/2.61 (~r(s(s(elem!1)), elem!1)),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[11279, 11272, 11270, 11269])).
% 2.42/2.61 tff(11281,plain,
% 2.42/2.61 (s(s(elem!1)) = elem!1),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[2673, 11280, 1])).
% 2.42/2.61 tff(11282,plain,
% 2.42/2.61 (elem!1 = s(s(elem!1))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[2555, 11281])).
% 2.42/2.61 tff(11283,plain,
% 2.42/2.61 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(s(elem!1)))),
% 2.42/2.61 inference(monotonicity,[status(thm)],[11282])).
% 2.42/2.61 tff(11284,plain,
% 2.42/2.61 (r(s(s(z)), s(s(elem!1)))),
% 2.42/2.61 inference(modus_ponens,[status(thm)],[11272, 11283])).
% 2.42/2.61 tff(11285,plain,
% 2.42/2.61 (~r(z, elem!1)),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[10288, 11272, 9473])).
% 2.42/2.61 tff(11286,plain,
% 2.42/2.61 (b(z, elem!1)),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[298, 11285, 10437])).
% 2.42/2.61 tff(11287,plain,
% 2.42/2.61 (~r(z, elem!1)),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[10288, 2545, 9473])).
% 2.42/2.61 tff(11288,plain,
% 2.42/2.61 (b(z, elem!1)),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[298, 11287, 10437])).
% 2.42/2.61 tff(11289,plain,
% 2.42/2.61 (~r(s(z), elem!1)),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[11130, 11288, 9473, 99, 10352])).
% 2.42/2.61 tff(11290,plain,
% 2.42/2.61 (b(s(z), elem!1)),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[601, 11289, 10438])).
% 2.42/2.61 tff(11291,plain,
% 2.42/2.61 (~b(elem!1, s(s(elem!1)))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[6176, 11290, 10352, 11288])).
% 2.42/2.61 tff(11292,plain,
% 2.42/2.61 (s(s(z)) = elem!1),
% 2.42/2.61 inference(modus_ponens,[status(thm)],[10495, 306])).
% 2.42/2.61 tff(11293,plain,
% 2.42/2.61 ($false),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[15, 11292])).
% 2.42/2.61 tff(11294,plain,((~(elem!1 = s(s(z)))) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.42/2.61 tff(11295,plain,
% 2.42/2.61 (~(elem!1 = s(s(z)))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[11294, 2219])).
% 2.42/2.61 tff(11296,plain,
% 2.42/2.61 (~b(elem!1, s(s(z)))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[6362, 75, 11290, 10352, 309])).
% 2.42/2.61 tff(11297,plain,
% 2.42/2.61 ((elem!1 = s(s(z))) | r(elem!1, s(s(z)))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[398, 58, 11296])).
% 2.42/2.61 tff(11298,plain,
% 2.42/2.61 (r(elem!1, s(s(z)))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[11297, 11295])).
% 2.42/2.61 tff(11299,plain,
% 2.42/2.61 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[9912, 37, 2545, 9473])).
% 2.42/2.61 tff(11300,plain,
% 2.42/2.61 (b(s(s(z)), s(s(s(s(z)))))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[465, 11299])).
% 2.42/2.61 tff(11301,plain,
% 2.42/2.61 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[10042, 37, 2545, 9473])).
% 2.42/2.61 tff(11302,plain,
% 2.42/2.61 (b(s(s(s(s(z)))), s(s(z)))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[2167, 58, 10047, 11301])).
% 2.42/2.61 tff(11303,plain,
% 2.42/2.61 (r(s(s(elem!1)), elem!1)),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[2673, 7695, 1])).
% 2.42/2.61 tff(11304,plain,
% 2.42/2.61 (r(elem!1, s(s(elem!1)))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[1617, 1630, 3685])).
% 2.42/2.61 tff(11305,plain,
% 2.42/2.61 (~r(s(s(elem!1)), s(s(z)))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[1498, 11304, 1489])).
% 2.42/2.61 tff(11306,plain,
% 2.42/2.61 ($false),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[10059, 11305, 11303, 9473, 266, 1011, 1154, 895])).
% 2.42/2.61 tff(11307,plain,((elem!1 = s(s(elem!1))) | (s(s(elem!1)) = s(s(z))) | (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(s(z)))))) | (~r(elem!1, s(s(z)))) | b(s(s(elem!1)), elem!1) | b(elem!1, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.61 tff(11308,plain,
% 2.42/2.61 (elem!1 = s(s(elem!1))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[11307, 1011, 11270, 11302, 11300, 11298, 1, 11291])).
% 2.42/2.61 tff(11309,plain,
% 2.42/2.61 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(s(elem!1)))),
% 2.42/2.61 inference(monotonicity,[status(thm)],[11308])).
% 2.42/2.61 tff(11310,plain,
% 2.42/2.61 (r(s(s(z)), s(s(elem!1)))),
% 2.42/2.61 inference(modus_ponens,[status(thm)],[2545, 11309])).
% 2.42/2.61 tff(11311,plain,
% 2.42/2.61 (~b(s(s(s(z))), elem!1)),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[11178, 11290, 10352, 506, 11288])).
% 2.42/2.61 tff(11312,plain,
% 2.42/2.61 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[3632, 11308, 11311])).
% 2.42/2.61 tff(11313,plain,
% 2.42/2.61 (r(s(s(s(z))), s(s(elem!1)))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[62, 11312, 11203])).
% 2.42/2.61 tff(11314,plain,
% 2.42/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.42/2.61 inference(rewrite,[status(thm)],[])).
% 2.42/2.61 tff(11315,plain,
% 2.42/2.61 (((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.42/2.61 inference(rewrite,[status(thm)],[])).
% 2.42/2.61 tff(11316,plain,
% 2.42/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1))))))),
% 2.42/2.61 inference(monotonicity,[status(thm)],[11315])).
% 2.42/2.61 tff(11317,plain,
% 2.42/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.42/2.61 inference(transitivity,[status(thm)],[11316, 11314])).
% 2.42/2.61 tff(11318,plain,
% 2.42/2.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.42/2.61 inference(quant_inst,[status(thm)],[])).
% 2.42/2.61 tff(11319,plain,
% 2.42/2.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1))))),
% 2.42/2.61 inference(modus_ponens,[status(thm)],[11318, 11317])).
% 2.42/2.61 tff(11320,plain,
% 2.42/2.61 (~r(s(s(s(z))), s(s(z)))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[11319, 37, 11313, 11310])).
% 2.42/2.61 tff(11321,plain,
% 2.42/2.61 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.42/2.61 inference(monotonicity,[status(thm)],[11308])).
% 2.42/2.61 tff(11322,plain,
% 2.42/2.61 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.42/2.61 inference(modus_ponens,[status(thm)],[9473, 11321])).
% 2.42/2.61 tff(11323,plain,
% 2.42/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.42/2.61 inference(rewrite,[status(thm)],[])).
% 2.42/2.61 tff(11324,plain,
% 2.42/2.61 (((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.42/2.61 inference(rewrite,[status(thm)],[])).
% 2.42/2.61 tff(11325,plain,
% 2.42/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(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(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1))))))),
% 2.42/2.61 inference(monotonicity,[status(thm)],[11324])).
% 2.42/2.61 tff(11326,plain,
% 2.42/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(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(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.42/2.61 inference(transitivity,[status(thm)],[11325, 11323])).
% 2.42/2.61 tff(11327,plain,
% 2.42/2.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.42/2.61 inference(quant_inst,[status(thm)],[])).
% 2.42/2.61 tff(11328,plain,
% 2.42/2.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 2.42/2.61 inference(modus_ponens,[status(thm)],[11327, 11326])).
% 2.42/2.61 tff(11329,plain,
% 2.42/2.61 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[11328, 37, 11313, 11322])).
% 2.42/2.61 tff(11330,plain,
% 2.42/2.61 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[2898, 11329])).
% 2.42/2.61 tff(11331,plain,
% 2.42/2.61 (~r(s(s(z)), s(s(s(z))))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[8023, 37, 11313, 11310])).
% 2.42/2.61 tff(11332,plain,
% 2.42/2.61 (b(s(s(z)), s(s(s(z))))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[8252, 11331])).
% 2.42/2.61 tff(11333,plain,
% 2.42/2.61 (~b(s(s(s(z))), s(s(z)))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[8435, 11332, 11302, 11330])).
% 2.42/2.61 tff(11334,plain,
% 2.42/2.61 ($false),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[2173, 58, 11333, 11320, 8230])).
% 2.42/2.61 tff(11335,plain,((s(s(elem!1)) = s(s(s(s(z))))) | b(s(s(elem!1)), elem!1) | (~b(s(s(z)), s(z))) | (~r(z, s(z))) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.42/2.61 tff(11336,plain,
% 2.42/2.61 (~b(s(s(z)), s(z))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[11335, 11269, 1, 506, 99])).
% 2.42/2.61 tff(11337,plain,
% 2.42/2.61 (~r(s(z), elem!1)),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[6993, 11336, 99, 10352])).
% 2.42/2.61 tff(11338,plain,
% 2.42/2.61 (b(s(z), elem!1)),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[601, 11337, 10438])).
% 2.42/2.61 tff(11339,plain,
% 2.42/2.61 (~b(s(s(s(z))), elem!1)),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[11178, 11338, 10352, 506, 11286])).
% 2.42/2.61 tff(11340,plain,
% 2.42/2.61 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[3632, 11282, 11339])).
% 2.42/2.61 tff(11341,plain,
% 2.42/2.61 (r(s(s(s(z))), s(s(elem!1)))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[62, 11340, 11203])).
% 2.42/2.61 tff(11342,plain,
% 2.42/2.61 (r(s(s(z)), s(z))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[153, 11336])).
% 2.42/2.61 tff(11343,plain,
% 2.42/2.61 (~r(s(s(s(z))), s(s(z)))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[8237, 37, 11342, 11341, 11284])).
% 2.42/2.61 tff(11344,plain,
% 2.42/2.61 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.42/2.61 inference(monotonicity,[status(thm)],[11282])).
% 2.42/2.61 tff(11345,plain,
% 2.42/2.61 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.42/2.61 inference(modus_ponens,[status(thm)],[9473, 11344])).
% 2.42/2.61 tff(11346,plain,
% 2.42/2.61 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[11328, 37, 11341, 11345])).
% 2.42/2.61 tff(11347,plain,
% 2.42/2.61 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[2898, 11346])).
% 2.42/2.61 tff(11348,plain,
% 2.42/2.61 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[10042, 37, 11272, 9473])).
% 2.42/2.61 tff(11349,plain,
% 2.42/2.61 (b(s(s(s(s(z)))), s(s(z)))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[2167, 58, 10047, 11348])).
% 2.42/2.61 tff(11350,plain,
% 2.42/2.61 (~r(s(s(z)), s(s(s(z))))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[8023, 37, 11341, 11284])).
% 2.42/2.61 tff(11351,plain,
% 2.42/2.61 (b(s(s(z)), s(s(s(z))))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[8252, 11350])).
% 2.42/2.61 tff(11352,plain,
% 2.42/2.61 (~b(s(s(s(z))), s(s(z)))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[8435, 11351, 11349, 11347])).
% 2.42/2.61 tff(11353,plain,
% 2.42/2.61 ($false),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[2173, 58, 11352, 11343, 8230])).
% 2.42/2.61 tff(11354,plain,((~r(z, s(z))) | b(s(s(elem!1)), elem!1) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.42/2.61 tff(11355,plain,
% 2.42/2.61 (~r(z, s(z))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[11354, 99, 1])).
% 2.42/2.61 tff(11356,plain,
% 2.42/2.61 (b(z, s(z))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[187, 11355])).
% 2.42/2.61 tff(11357,plain,
% 2.42/2.61 (~r(s(s(elem!1)), elem!1)),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[11279, 2545, 11270, 1011])).
% 2.42/2.61 tff(11358,plain,
% 2.42/2.61 (s(s(elem!1)) = elem!1),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[2673, 11357, 1])).
% 2.42/2.61 tff(11359,plain,
% 2.42/2.61 (b(s(s(elem!1)), s(z)) <=> b(elem!1, s(z))),
% 2.42/2.61 inference(monotonicity,[status(thm)],[11358])).
% 2.42/2.61 tff(11360,plain,
% 2.42/2.61 (b(elem!1, s(z)) <=> b(s(s(elem!1)), s(z))),
% 2.42/2.61 inference(symmetry,[status(thm)],[11359])).
% 2.42/2.61 tff(11361,plain,
% 2.42/2.61 (b(s(s(elem!1)), s(z))),
% 2.42/2.61 inference(modus_ponens,[status(thm)],[10352, 11360])).
% 2.42/2.61 tff(11362,plain,
% 2.42/2.61 (elem!1 = s(s(elem!1))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[2555, 11358])).
% 2.42/2.61 tff(11363,plain,
% 2.42/2.61 (b(z, s(s(elem!1))) <=> b(z, elem!1)),
% 2.42/2.61 inference(monotonicity,[status(thm)],[2323])).
% 2.42/2.61 tff(11364,plain,
% 2.42/2.61 (b(z, elem!1) <=> b(z, s(s(elem!1)))),
% 2.42/2.61 inference(symmetry,[status(thm)],[11363])).
% 2.42/2.61 tff(11365,plain,
% 2.42/2.61 (b(z, s(s(elem!1)))),
% 2.42/2.61 inference(modus_ponens,[status(thm)],[1518, 11364])).
% 2.42/2.61 tff(11366,plain,
% 2.42/2.61 (r(s(z), elem!1) <=> r(s(z), s(s(elem!1)))),
% 2.42/2.61 inference(monotonicity,[status(thm)],[1602])).
% 2.42/2.61 tff(11367,plain,
% 2.42/2.61 ((~r(s(z), elem!1)) <=> (~r(s(z), s(s(elem!1))))),
% 2.42/2.61 inference(monotonicity,[status(thm)],[11366])).
% 2.42/2.61 tff(11368,plain,
% 2.42/2.61 (~r(s(z), s(s(elem!1)))),
% 2.42/2.61 inference(modus_ponens,[status(thm)],[9475, 11367])).
% 2.42/2.61 tff(11369,plain,
% 2.42/2.61 (b(s(z), s(s(elem!1)))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[1890, 11368])).
% 2.42/2.61 tff(11370,plain,
% 2.42/2.61 ($false),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[7150, 75, 1457, 372, 11369, 11365])).
% 2.42/2.61 tff(11371,plain,((~(elem!1 = s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, elem!1)) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.42/2.61 tff(11372,plain,
% 2.42/2.61 (~b(s(s(elem!1)), s(z))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[11371, 11362, 11356, 11289, 11288])).
% 2.42/2.61 tff(11373,plain,
% 2.42/2.61 ($false),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[11372, 11361])).
% 2.42/2.61 tff(11374,plain,((s(s(elem!1)) = s(s(s(s(z))))) | b(s(s(z)), elem!1) | b(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.42/2.61 tff(11375,plain,
% 2.42/2.61 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[11374, 99, 1])).
% 2.42/2.61 tff(11376,plain,
% 2.42/2.61 (s(s(z)) = elem!1),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[1425, 11375])).
% 2.42/2.61 tff(11377,plain,
% 2.42/2.61 (~r(z, elem!1)),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[11265, 107, 9473, 1391, 5493, 310, 8398])).
% 2.42/2.61 tff(11378,plain,
% 2.42/2.61 (b(z, elem!1)),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[298, 11377, 235])).
% 2.42/2.61 tff(11379,plain,
% 2.42/2.61 (b(z, s(s(z)))),
% 2.42/2.61 inference(modus_ponens,[status(thm)],[11378, 10237])).
% 2.42/2.61 tff(11380,plain,
% 2.42/2.61 (~b(z, s(s(z)))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[1780, 107, 1391, 372, 8291])).
% 2.42/2.61 tff(11381,plain,
% 2.42/2.61 ($false),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[11380, 11379])).
% 2.42/2.61 tff(11382,plain,((~b(s(z), elem!1)) | (~(s(s(z)) = elem!1)) | (z = elem!1) | (~b(elem!1, s(z))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.61 tff(11383,plain,
% 2.42/2.61 (~b(s(z), elem!1)),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[11382, 11376, 10437, 10352, 11356])).
% 2.42/2.61 tff(11384,plain,
% 2.42/2.61 (r(s(z), elem!1)),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[601, 11383, 10438])).
% 2.42/2.61 tff(11385,plain,
% 2.42/2.61 (~r(z, elem!1)),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[10304, 11384, 9473])).
% 2.42/2.61 tff(11386,plain,
% 2.42/2.61 (~b(z, elem!1)),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[11130, 11384, 9473, 99, 10352])).
% 2.42/2.61 tff(11387,plain,
% 2.42/2.61 ($false),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[298, 11386, 11385, 10437])).
% 2.42/2.61 tff(11388,plain,(b(s(s(z)), elem!1) | b(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.42/2.61 tff(11389,plain,
% 2.42/2.61 (b(s(s(z)), elem!1)),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[11388, 1])).
% 2.42/2.61 tff(11390,plain,
% 2.42/2.61 (b(s(s(z)), elem!1)),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[10281, 14, 13])).
% 2.42/2.61 tff(11391,plain,
% 2.42/2.61 (b(s(elem!1), z) <=> b(s(s(z)), z)),
% 2.42/2.61 inference(monotonicity,[status(thm)],[18])).
% 2.42/2.61 tff(11392,plain,
% 2.42/2.61 (b(s(s(z)), z) <=> b(s(elem!1), z)),
% 2.42/2.61 inference(symmetry,[status(thm)],[11391])).
% 2.42/2.61 tff(11393,plain,
% 2.42/2.61 ((~b(s(s(z)), z)) <=> (~b(s(elem!1), z))),
% 2.42/2.61 inference(monotonicity,[status(thm)],[11392])).
% 2.42/2.61 tff(11394,plain,
% 2.42/2.61 (r(s(s(s(elem!1))), elem!1)),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[702, 8607, 9474])).
% 2.42/2.61 tff(11395,plain,
% 2.42/2.61 (~r(z, s(z))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[2724, 8607, 13])).
% 2.42/2.61 tff(11396,plain,
% 2.42/2.61 (b(z, s(z))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[187, 11395])).
% 2.42/2.61 tff(11397,plain,
% 2.42/2.61 (r(s(s(s(z))), z) <=> r(s(s(elem!1)), z)),
% 2.42/2.61 inference(monotonicity,[status(thm)],[7111])).
% 2.42/2.61 tff(11398,plain,
% 2.42/2.61 (r(s(s(elem!1)), z) <=> r(s(s(s(z))), z)),
% 2.42/2.61 inference(symmetry,[status(thm)],[11397])).
% 2.42/2.61 tff(11399,plain,
% 2.42/2.61 ((elem!1 = s(s(elem!1))) <=> (s(z) = s(s(elem!1)))),
% 2.42/2.61 inference(monotonicity,[status(thm)],[17])).
% 2.42/2.61 tff(11400,plain,
% 2.42/2.61 ((elem!1 = s(s(elem!1))) <=> (s(s(elem!1)) = s(z))),
% 2.42/2.61 inference(transitivity,[status(thm)],[11399, 1882])).
% 2.42/2.61 tff(11401,plain,
% 2.42/2.61 ((s(s(elem!1)) = s(z)) <=> (elem!1 = s(s(elem!1)))),
% 2.42/2.61 inference(symmetry,[status(thm)],[11400])).
% 2.42/2.61 tff(11402,plain,
% 2.42/2.61 ((~(s(s(elem!1)) = s(z))) <=> (~(elem!1 = s(s(elem!1))))),
% 2.42/2.61 inference(monotonicity,[status(thm)],[11401])).
% 2.42/2.61 tff(11403,plain,
% 2.42/2.61 (~(elem!1 = s(s(elem!1)))),
% 2.42/2.61 inference(modus_ponens,[status(thm)],[556, 11402])).
% 2.42/2.61 tff(11404,plain,
% 2.42/2.61 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[719, 8607])).
% 2.42/2.61 tff(11405,plain,
% 2.42/2.61 (b(s(s(s(s(s(s(s(z))))))), s(z)) <=> b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.42/2.61 inference(monotonicity,[status(thm)],[8682])).
% 2.42/2.61 tff(11406,plain,
% 2.42/2.61 ((~b(s(s(s(s(s(s(s(z))))))), s(z))) <=> (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.42/2.61 inference(monotonicity,[status(thm)],[11405])).
% 2.42/2.61 tff(11407,plain,
% 2.42/2.61 (b(s(s(z)), s(z))),
% 2.42/2.61 inference(modus_ponens,[status(thm)],[964, 354])).
% 2.42/2.61 tff(11408,plain,
% 2.42/2.61 (r(elem!1, z) <=> r(s(z), z)),
% 2.42/2.61 inference(monotonicity,[status(thm)],[17])).
% 2.42/2.61 tff(11409,plain,
% 2.42/2.61 (r(s(z), z)),
% 2.42/2.61 inference(modus_ponens,[status(thm)],[155, 11408])).
% 2.42/2.61 tff(11410,plain,
% 2.42/2.61 (~r(s(z), s(s(z)))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[2015, 320, 1561])).
% 2.42/2.61 tff(11411,plain,
% 2.42/2.61 (b(s(z), s(s(z)))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[416, 11410])).
% 2.42/2.61 tff(11412,plain,
% 2.42/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.42/2.61 inference(rewrite,[status(thm)],[])).
% 2.42/2.61 tff(11413,plain,
% 2.42/2.61 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(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(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.42/2.61 inference(rewrite,[status(thm)],[])).
% 2.42/2.61 tff(11414,plain,
% 2.42/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))))),
% 2.42/2.61 inference(monotonicity,[status(thm)],[11413])).
% 2.42/2.61 tff(11415,plain,
% 2.42/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.42/2.61 inference(transitivity,[status(thm)],[11414, 11412])).
% 2.42/2.61 tff(11416,plain,
% 2.42/2.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.42/2.61 inference(quant_inst,[status(thm)],[])).
% 2.42/2.61 tff(11417,plain,
% 2.42/2.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 2.42/2.61 inference(modus_ponens,[status(thm)],[11416, 11415])).
% 2.42/2.61 tff(11418,plain,
% 2.42/2.61 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[11417, 75, 309, 11411, 8629])).
% 2.42/2.61 tff(11419,plain,
% 2.42/2.61 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[9447, 58, 1045, 11418])).
% 2.42/2.61 tff(11420,plain,
% 2.42/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.42/2.61 inference(rewrite,[status(thm)],[])).
% 2.42/2.61 tff(11421,plain,
% 2.42/2.61 (((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.42/2.61 inference(rewrite,[status(thm)],[])).
% 2.42/2.61 tff(11422,plain,
% 2.42/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 2.42/2.62 inference(monotonicity,[status(thm)],[11421])).
% 2.42/2.62 tff(11423,plain,
% 2.42/2.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.42/2.62 inference(transitivity,[status(thm)],[11422, 11420])).
% 2.42/2.62 tff(11424,plain,
% 2.42/2.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.42/2.62 inference(quant_inst,[status(thm)],[])).
% 2.42/2.62 tff(11425,plain,
% 2.42/2.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.42/2.62 inference(modus_ponens,[status(thm)],[11424, 11423])).
% 2.42/2.62 tff(11426,plain,
% 2.42/2.62 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[11425, 75, 372, 309, 11411, 8629])).
% 2.42/2.62 tff(11427,plain,
% 2.42/2.62 (r(s(s(s(s(s(s(s(z))))))), z)),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[750, 58, 747, 11426])).
% 2.42/2.62 tff(11428,plain,
% 2.42/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 2.42/2.62 inference(rewrite,[status(thm)],[])).
% 2.42/2.62 tff(11429,plain,
% 2.42/2.62 (((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z))))) <=> ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 2.42/2.62 inference(rewrite,[status(thm)],[])).
% 2.42/2.62 tff(11430,plain,
% 2.42/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z))))),
% 2.42/2.62 inference(monotonicity,[status(thm)],[11429])).
% 2.42/2.62 tff(11431,plain,
% 2.42/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 2.42/2.62 inference(transitivity,[status(thm)],[11430, 11428])).
% 2.42/2.62 tff(11432,plain,
% 2.42/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.42/2.62 inference(quant_inst,[status(thm)],[])).
% 2.42/2.62 tff(11433,plain,
% 2.42/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), z))),
% 2.42/2.62 inference(modus_ponens,[status(thm)],[11432, 11431])).
% 2.42/2.62 tff(11434,plain,
% 2.42/2.62 ($false),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[11433, 37, 320, 11427, 11419])).
% 2.42/2.62 tff(11435,plain,((~r(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.62 tff(11436,plain,
% 2.42/2.62 (~r(s(s(z)), z)),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[11435, 8629, 309, 372, 1561])).
% 2.42/2.62 tff(11437,plain,
% 2.42/2.62 (b(s(s(z)), z)),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[202, 11436])).
% 2.42/2.62 tff(11438,plain,
% 2.42/2.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.42/2.62 inference(rewrite,[status(thm)],[])).
% 2.42/2.62 tff(11439,plain,
% 2.42/2.62 (((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))) <=> ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.42/2.62 inference(rewrite,[status(thm)],[])).
% 2.42/2.62 tff(11440,plain,
% 2.42/2.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.42/2.62 inference(monotonicity,[status(thm)],[11439])).
% 2.42/2.62 tff(11441,plain,
% 2.42/2.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.42/2.62 inference(transitivity,[status(thm)],[11440, 11438])).
% 2.42/2.62 tff(11442,plain,
% 2.42/2.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.42/2.62 inference(quant_inst,[status(thm)],[])).
% 2.42/2.62 tff(11443,plain,
% 2.42/2.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.42/2.62 inference(modus_ponens,[status(thm)],[11442, 11441])).
% 2.42/2.62 tff(11444,plain,
% 2.42/2.62 ($false),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[11443, 75, 372, 309, 401, 8629, 8631])).
% 2.42/2.62 tff(11445,plain,((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.62 tff(11446,plain,
% 2.42/2.62 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[11445, 11437, 309, 372, 8629])).
% 2.42/2.62 tff(11447,plain,
% 2.42/2.62 ((s(z) = s(s(s(s(s(s(s(z)))))))) | r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[8518, 58, 11446])).
% 2.42/2.62 tff(11448,plain,
% 2.42/2.62 (r(s(z), s(s(s(s(s(s(s(z))))))))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[11447, 11247])).
% 2.42/2.62 tff(11449,plain,
% 2.42/2.62 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[11142, 8647, 1561])).
% 2.42/2.62 tff(11450,plain,
% 2.42/2.62 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[750, 58, 747, 11449])).
% 2.42/2.62 tff(11451,plain,
% 2.42/2.62 (r(s(z), s(elem!1)) <=> r(s(z), s(s(z)))),
% 2.42/2.62 inference(monotonicity,[status(thm)],[18])).
% 2.42/2.62 tff(11452,plain,
% 2.42/2.62 (r(s(z), s(s(z))) <=> r(s(z), s(elem!1))),
% 2.42/2.62 inference(symmetry,[status(thm)],[11451])).
% 2.42/2.62 tff(11453,plain,
% 2.42/2.62 (r(s(z), s(elem!1))),
% 2.42/2.62 inference(modus_ponens,[status(thm)],[1997, 11452])).
% 2.42/2.62 tff(11454,assumption,(r(z, s(elem!1))), introduced(assumption)).
% 2.42/2.62 tff(11455,plain,
% 2.42/2.62 (((~![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(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), z)) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))))),
% 2.42/2.62 inference(rewrite,[status(thm)],[])).
% 2.42/2.62 tff(11456,plain,
% 2.42/2.62 (((~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))))),
% 2.42/2.62 inference(rewrite,[status(thm)],[])).
% 2.42/2.62 tff(11457,plain,
% 2.42/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(z, 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(elem!1))) | (~r(s(z), s(elem!1)))))),
% 2.42/2.62 inference(monotonicity,[status(thm)],[11456])).
% 2.42/2.62 tff(11458,plain,
% 2.42/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(z, 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(elem!1))) | (~r(s(z), s(elem!1))))),
% 2.42/2.62 inference(transitivity,[status(thm)],[11457, 11455])).
% 2.42/2.62 tff(11459,plain,
% 2.42/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(z), z)))),
% 2.42/2.62 inference(quant_inst,[status(thm)],[])).
% 2.42/2.62 tff(11460,plain,
% 2.42/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1)))),
% 2.42/2.62 inference(modus_ponens,[status(thm)],[11459, 11458])).
% 2.42/2.62 tff(11461,plain,
% 2.42/2.62 ($false),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[11460, 37, 1561, 1753, 11454])).
% 2.42/2.62 tff(11462,plain,((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.62 tff(11463,plain,
% 2.42/2.62 (~r(z, s(elem!1))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[11462, 11453, 1561])).
% 2.42/2.62 tff(11464,plain,
% 2.42/2.62 (r(z, s(elem!1)) <=> r(z, s(s(z)))),
% 2.42/2.62 inference(monotonicity,[status(thm)],[18])).
% 2.42/2.62 tff(11465,plain,
% 2.42/2.62 (r(z, s(s(z))) <=> r(z, s(elem!1))),
% 2.42/2.62 inference(symmetry,[status(thm)],[11464])).
% 2.42/2.62 tff(11466,plain,
% 2.42/2.62 (r(z, s(elem!1))),
% 2.42/2.62 inference(modus_ponens,[status(thm)],[331, 11465])).
% 2.42/2.62 tff(11467,assumption,(~r(z, s(elem!1))), introduced(assumption)).
% 2.42/2.62 tff(11468,plain,
% 2.42/2.62 ($false),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[11467, 11466])).
% 2.42/2.62 tff(11469,plain,((~r(z, s(s(z)))) | r(z, s(elem!1)) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.62 tff(11470,plain,
% 2.42/2.62 (~r(z, s(s(z)))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[11469, 11463, 17])).
% 2.42/2.62 tff(11471,plain,
% 2.42/2.62 (b(z, s(s(z)))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[351, 11470])).
% 2.42/2.62 tff(11472,plain,
% 2.42/2.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.42/2.62 inference(rewrite,[status(thm)],[])).
% 2.42/2.62 tff(11473,plain,
% 2.42/2.62 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.42/2.62 inference(rewrite,[status(thm)],[])).
% 2.42/2.62 tff(11474,plain,
% 2.42/2.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))), s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))))),
% 2.42/2.62 inference(monotonicity,[status(thm)],[11473])).
% 2.42/2.62 tff(11475,plain,
% 2.42/2.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))), s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))))),
% 2.42/2.62 inference(transitivity,[status(thm)],[11474, 11472])).
% 2.42/2.62 tff(11476,plain,
% 2.42/2.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))), s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 2.42/2.62 inference(quant_inst,[status(thm)],[])).
% 2.42/2.62 tff(11477,plain,
% 2.42/2.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 2.42/2.62 inference(modus_ponens,[status(thm)],[11476, 11475])).
% 2.42/2.62 tff(11478,plain,
% 2.42/2.62 ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(z))))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[11477, 75, 372, 401, 8629])).
% 2.42/2.62 tff(11479,plain,
% 2.42/2.62 (~b(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[11478, 11471, 11450])).
% 2.42/2.62 tff(11480,plain,
% 2.42/2.62 (r(s(s(s(s(s(s(s(z))))))), s(s(z)))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[9447, 58, 1045, 11479])).
% 2.42/2.62 tff(11481,plain,
% 2.42/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.42/2.63 inference(rewrite,[status(thm)],[])).
% 2.42/2.63 tff(11482,plain,
% 2.42/2.63 (((~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.42/2.63 inference(rewrite,[status(thm)],[])).
% 2.42/2.63 tff(11483,plain,
% 2.42/2.63 (((~![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(s(z))))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $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(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 2.42/2.63 inference(monotonicity,[status(thm)],[11482])).
% 2.42/2.63 tff(11484,plain,
% 2.42/2.63 (((~![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(s(z))))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $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(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.42/2.63 inference(transitivity,[status(thm)],[11483, 11481])).
% 2.42/2.63 tff(11485,plain,
% 2.42/2.63 ((~![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(s(z))))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 2.42/2.63 inference(quant_inst,[status(thm)],[])).
% 2.42/2.63 tff(11486,plain,
% 2.42/2.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 2.42/2.63 inference(modus_ponens,[status(thm)],[11485, 11484])).
% 2.42/2.63 tff(11487,plain,
% 2.42/2.63 ($false),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[11486, 37, 1997, 8647, 11480])).
% 2.42/2.63 tff(11488,plain,((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~(elem!1 = s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.63 tff(11489,plain,
% 2.42/2.63 (~r(s(z), s(s(z)))),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[11488, 11448, 372, 11437, 8629, 17, 1561])).
% 2.42/2.63 tff(11490,plain,
% 2.42/2.63 (b(s(z), s(s(z)))),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[416, 11489])).
% 2.42/2.63 tff(11491,plain,
% 2.42/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 2.42/2.63 inference(rewrite,[status(thm)],[])).
% 2.42/2.63 tff(11492,plain,
% 2.42/2.63 (((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 2.42/2.63 inference(rewrite,[status(thm)],[])).
% 2.42/2.63 tff(11493,plain,
% 2.42/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))))),
% 2.42/2.63 inference(monotonicity,[status(thm)],[11492])).
% 2.42/2.63 tff(11494,plain,
% 2.42/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 2.42/2.63 inference(transitivity,[status(thm)],[11493, 11491])).
% 2.42/2.63 tff(11495,plain,
% 2.42/2.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.42/2.63 inference(quant_inst,[status(thm)],[])).
% 2.42/2.63 tff(11496,plain,
% 2.42/2.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))),
% 2.42/2.63 inference(modus_ponens,[status(thm)],[11495, 11494])).
% 2.42/2.63 tff(11497,plain,
% 2.42/2.63 ($false),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[11496, 75, 372, 309, 11490, 11437])).
% 2.42/2.63 tff(11498,plain,((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~(elem!1 = s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.63 tff(11499,plain,
% 2.42/2.63 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[11498, 11409, 11407, 17, 372])).
% 2.42/2.63 tff(11500,plain,
% 2.42/2.63 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.42/2.63 inference(modus_ponens,[status(thm)],[11499, 11406])).
% 2.42/2.63 tff(11501,plain,
% 2.42/2.63 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[813, 11500, 11404])).
% 2.42/2.63 tff(11502,plain,
% 2.42/2.63 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 2.42/2.63 inference(monotonicity,[status(thm)],[8602])).
% 2.42/2.63 tff(11503,plain,
% 2.42/2.63 ((s(s(elem!1)) = s(s(s(s(z))))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 2.42/2.63 inference(symmetry,[status(thm)],[11502])).
% 2.42/2.63 tff(11504,plain,
% 2.42/2.63 ((~(s(s(elem!1)) = s(s(s(s(z)))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 2.42/2.63 inference(monotonicity,[status(thm)],[11503])).
% 2.42/2.63 tff(11505,plain,
% 2.42/2.63 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 2.42/2.63 inference(monotonicity,[status(thm)],[7111])).
% 2.42/2.63 tff(11506,plain,
% 2.42/2.63 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 2.42/2.63 inference(transitivity,[status(thm)],[11505, 3863])).
% 2.42/2.63 tff(11507,plain,
% 2.42/2.63 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(s(z))))))),
% 2.42/2.63 inference(monotonicity,[status(thm)],[11506])).
% 2.42/2.63 tff(11508,plain,
% 2.42/2.63 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 2.42/2.63 inference(modus_ponens,[status(thm)],[264, 11507])).
% 2.42/2.63 tff(11509,plain,
% 2.42/2.63 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.42/2.63 inference(modus_ponens,[status(thm)],[11508, 11504])).
% 2.42/2.63 tff(11510,plain,
% 2.42/2.63 ((s(s(elem!1)) = s(z)) <=> (s(s(elem!1)) = elem!1)),
% 2.42/2.63 inference(transitivity,[status(thm)],[11401, 4928])).
% 2.42/2.63 tff(11511,plain,
% 2.42/2.63 ((~(s(s(elem!1)) = s(z))) <=> (~(s(s(elem!1)) = elem!1))),
% 2.42/2.63 inference(monotonicity,[status(thm)],[11510])).
% 2.42/2.63 tff(11512,plain,
% 2.42/2.63 (~(s(s(elem!1)) = elem!1)),
% 2.42/2.63 inference(modus_ponens,[status(thm)],[556, 11511])).
% 2.42/2.63 tff(11513,plain,
% 2.42/2.63 (r(s(s(elem!1)), elem!1)),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[2673, 1, 11512])).
% 2.42/2.63 tff(11514,plain,
% 2.42/2.63 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[5835, 11513, 624, 8625, 738, 8679])).
% 2.42/2.63 tff(11515,plain,
% 2.42/2.63 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), elem!1)),
% 2.42/2.63 inference(monotonicity,[status(thm)],[8682])).
% 2.42/2.63 tff(11516,plain,
% 2.42/2.63 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(z))),
% 2.42/2.63 inference(symmetry,[status(thm)],[11515])).
% 2.42/2.63 tff(11517,plain,
% 2.42/2.63 (r(s(s(s(elem!1))), s(z))),
% 2.42/2.63 inference(modus_ponens,[status(thm)],[624, 11516])).
% 2.42/2.63 tff(11518,plain,
% 2.42/2.63 (r(s(s(s(z))), s(z)) <=> r(s(s(elem!1)), s(z))),
% 2.42/2.63 inference(monotonicity,[status(thm)],[7111])).
% 2.42/2.63 tff(11519,plain,
% 2.42/2.63 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(z))),
% 2.42/2.63 inference(monotonicity,[status(thm)],[17])).
% 2.42/2.63 tff(11520,plain,
% 2.42/2.63 (r(s(s(s(z))), elem!1) <=> r(s(s(elem!1)), s(z))),
% 2.42/2.63 inference(transitivity,[status(thm)],[11519, 11518])).
% 2.42/2.63 tff(11521,plain,
% 2.42/2.63 ((s(s(s(z))) = elem!1) <=> (s(s(s(z))) = s(z))),
% 2.42/2.63 inference(monotonicity,[status(thm)],[17])).
% 2.42/2.63 tff(11522,plain,
% 2.42/2.63 ((s(s(s(z))) = s(z)) <=> (s(s(s(z))) = elem!1)),
% 2.42/2.63 inference(symmetry,[status(thm)],[11521])).
% 2.42/2.63 tff(11523,plain,
% 2.42/2.63 ((~(s(s(s(z))) = s(z))) <=> (~(s(s(s(z))) = elem!1))),
% 2.42/2.63 inference(monotonicity,[status(thm)],[11522])).
% 2.42/2.63 tff(11524,plain,
% 2.42/2.63 (~(s(s(s(z))) = elem!1)),
% 2.42/2.63 inference(modus_ponens,[status(thm)],[457, 11523])).
% 2.42/2.63 tff(11525,plain,
% 2.42/2.63 (b(s(s(s(z))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 2.42/2.63 inference(monotonicity,[status(thm)],[7111])).
% 2.42/2.63 tff(11526,plain,
% 2.42/2.63 (b(s(s(s(z))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 2.42/2.63 inference(transitivity,[status(thm)],[3638, 11525, 7110])).
% 2.42/2.63 tff(11527,plain,
% 2.42/2.63 (b(s(s(elem!1)), elem!1)),
% 2.42/2.63 inference(modus_ponens,[status(thm)],[1119, 11526])).
% 2.42/2.63 tff(11528,plain,
% 2.42/2.63 ($false),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[1, 11527])).
% 2.42/2.63 tff(11529,plain,((~b(s(s(s(z))), elem!1)) | b(s(s(elem!1)), elem!1) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.63 tff(11530,plain,
% 2.42/2.63 (~b(s(s(s(z))), elem!1)),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[11529, 1, 17])).
% 2.42/2.63 tff(11531,plain,
% 2.42/2.63 (r(s(s(s(z))), elem!1)),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[1115, 11530, 11524])).
% 2.42/2.63 tff(11532,plain,
% 2.42/2.63 (r(s(s(elem!1)), s(z))),
% 2.42/2.63 inference(modus_ponens,[status(thm)],[11531, 11520])).
% 2.42/2.63 tff(11533,plain,
% 2.42/2.63 (((~![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(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))))),
% 2.42/2.63 inference(rewrite,[status(thm)],[])).
% 2.42/2.63 tff(11534,plain,
% 2.42/2.63 (((~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))))),
% 2.42/2.63 inference(rewrite,[status(thm)],[])).
% 2.42/2.63 tff(11535,plain,
% 2.42/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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)))))),
% 2.42/2.63 inference(monotonicity,[status(thm)],[11534])).
% 2.42/2.63 tff(11536,plain,
% 2.42/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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))))),
% 2.42/2.63 inference(transitivity,[status(thm)],[11535, 11533])).
% 2.42/2.63 tff(11537,plain,
% 2.42/2.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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))))))),
% 2.42/2.63 inference(quant_inst,[status(thm)],[])).
% 2.42/2.63 tff(11538,plain,
% 2.42/2.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))),
% 2.42/2.63 inference(modus_ponens,[status(thm)],[11537, 11536])).
% 2.42/2.63 tff(11539,plain,
% 2.42/2.63 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[11538, 37, 11532, 11517])).
% 2.42/2.63 tff(11540,plain,
% 2.42/2.63 ($false),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[5815, 58, 11539, 11514, 11509])).
% 2.42/2.63 tff(11541,plain,(b(s(s(elem!1)), elem!1) | (~(elem!1 = s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.63 tff(11542,plain,
% 2.42/2.63 (b(s(s(elem!1)), elem!1)),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[11541, 11501, 624, 17])).
% 2.42/2.63 tff(11543,plain,
% 2.42/2.63 (~b(elem!1, s(s(elem!1)))),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[4730, 11542, 1518, 964, 266])).
% 2.42/2.63 tff(11544,plain,
% 2.42/2.63 (r(elem!1, s(s(elem!1)))),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[1617, 11543, 11403])).
% 2.42/2.63 tff(11545,plain,
% 2.42/2.63 (r(s(z), s(s(elem!1)))),
% 2.42/2.63 inference(modus_ponens,[status(thm)],[11544, 8608])).
% 2.42/2.63 tff(11546,plain,
% 2.42/2.63 (~r(z, s(s(elem!1)))),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[5301, 11545, 11409])).
% 2.42/2.63 tff(11547,plain,
% 2.42/2.63 (b(z, s(s(elem!1)))),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[6314, 11546])).
% 2.42/2.63 tff(11548,plain,
% 2.42/2.63 (b(s(s(s(z))), elem!1) <=> b(s(s(elem!1)), s(z))),
% 2.42/2.63 inference(transitivity,[status(thm)],[3638, 11525])).
% 2.42/2.63 tff(11549,plain,
% 2.42/2.63 (b(s(s(s(z))), elem!1)),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[3645, 11542, 17])).
% 2.42/2.63 tff(11550,plain,
% 2.42/2.63 (b(s(s(elem!1)), s(z))),
% 2.42/2.63 inference(modus_ponens,[status(thm)],[11549, 11548])).
% 2.42/2.63 tff(11551,plain,
% 2.42/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))))),
% 2.42/2.63 inference(rewrite,[status(thm)],[])).
% 2.42/2.63 tff(11552,plain,
% 2.42/2.63 (((~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))))),
% 2.42/2.63 inference(rewrite,[status(thm)],[])).
% 2.42/2.63 tff(11553,plain,
% 2.42/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z)))))),
% 2.42/2.63 inference(monotonicity,[status(thm)],[11552])).
% 2.42/2.63 tff(11554,plain,
% 2.42/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))))),
% 2.42/2.63 inference(transitivity,[status(thm)],[11553, 11551])).
% 2.42/2.63 tff(11555,plain,
% 2.42/2.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))),
% 2.42/2.63 inference(quant_inst,[status(thm)],[])).
% 2.42/2.63 tff(11556,plain,
% 2.42/2.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z)))),
% 2.42/2.63 inference(modus_ponens,[status(thm)],[11555, 11554])).
% 2.42/2.63 tff(11557,plain,
% 2.42/2.63 ($false),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[11556, 75, 1457, 372, 309, 402, 1893])).
% 2.42/2.63 tff(11558,plain,((~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.63 tff(11559,plain,
% 2.42/2.63 (~b(s(z), s(s(z)))),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[11558, 11550, 372, 11407, 11547])).
% 2.42/2.63 tff(11560,plain,
% 2.42/2.63 (r(s(z), s(s(z)))),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[416, 11559])).
% 2.42/2.63 tff(11561,plain,
% 2.42/2.63 (r(elem!1, s(s(z)))),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[9003, 11560, 8607])).
% 2.42/2.63 tff(11562,plain,
% 2.42/2.63 (~r(s(s(elem!1)), s(s(z)))),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[1498, 11561, 11544])).
% 2.42/2.63 tff(11563,plain,
% 2.42/2.63 (b(s(s(elem!1)), s(elem!1))),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[4966, 11562, 17])).
% 2.42/2.63 tff(11564,plain,
% 2.42/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))))),
% 2.42/2.63 inference(rewrite,[status(thm)],[])).
% 2.42/2.63 tff(11565,plain,
% 2.42/2.63 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))))),
% 2.42/2.63 inference(rewrite,[status(thm)],[])).
% 2.42/2.63 tff(11566,plain,
% 2.42/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(elem!1)), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z)))))),
% 2.42/2.63 inference(monotonicity,[status(thm)],[11565])).
% 2.42/2.63 tff(11567,plain,
% 2.42/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(elem!1)), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))))),
% 2.42/2.63 inference(transitivity,[status(thm)],[11566, 11564])).
% 2.42/2.63 tff(11568,plain,
% 2.42/2.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))))),
% 2.42/2.63 inference(quant_inst,[status(thm)],[])).
% 2.42/2.63 tff(11569,plain,
% 2.42/2.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z)))),
% 2.42/2.64 inference(modus_ponens,[status(thm)],[11568, 11567])).
% 2.42/2.64 tff(11570,plain,
% 2.42/2.64 (~b(s(s(elem!1)), s(s(z)))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[11569, 75, 1457, 309, 402])).
% 2.42/2.64 tff(11571,plain,
% 2.42/2.64 (r(s(s(elem!1)), s(s(z)))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[504, 58, 266, 11570])).
% 2.42/2.64 tff(11572,plain,
% 2.42/2.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))))),
% 2.42/2.64 inference(rewrite,[status(thm)],[])).
% 2.42/2.64 tff(11573,plain,
% 2.42/2.64 (((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))))),
% 2.42/2.64 inference(rewrite,[status(thm)],[])).
% 2.42/2.64 tff(11574,plain,
% 2.42/2.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(z))) | (~b(s(z), s(s(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(X1, 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(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z)))))),
% 2.42/2.64 inference(monotonicity,[status(thm)],[11573])).
% 2.42/2.64 tff(11575,plain,
% 2.42/2.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(z))) | (~b(s(z), s(s(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(X1, 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(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))))),
% 2.42/2.64 inference(transitivity,[status(thm)],[11574, 11572])).
% 2.42/2.64 tff(11576,plain,
% 2.42/2.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))),
% 2.42/2.64 inference(quant_inst,[status(thm)],[])).
% 2.42/2.64 tff(11577,plain,
% 2.42/2.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z)))),
% 2.42/2.64 inference(modus_ponens,[status(thm)],[11576, 11575])).
% 2.42/2.64 tff(11578,plain,
% 2.42/2.64 (~b(s(s(elem!1)), z)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[11577, 75, 1457, 372, 309, 402])).
% 2.42/2.64 tff(11579,plain,
% 2.42/2.64 (r(s(s(elem!1)), z)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[518, 58, 515, 11578])).
% 2.42/2.64 tff(11580,plain,
% 2.42/2.64 ($false),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[2319, 37, 320, 11579, 11571])).
% 2.42/2.64 tff(11581,plain,((~b(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (s(s(elem!1)) = s(s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.64 tff(11582,plain,
% 2.42/2.64 (~b(s(z), s(s(z)))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[11581, 320, 266, 372, 309, 1457])).
% 2.42/2.64 tff(11583,plain,
% 2.42/2.64 ($false),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[416, 11582, 11410])).
% 2.42/2.64 tff(11584,plain,((~r(s(s(z)), z)) | (s(s(elem!1)) = s(s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.64 tff(11585,plain,
% 2.42/2.64 (~r(s(s(z)), z)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[11584, 11550, 372, 11407, 266, 11409])).
% 2.42/2.64 tff(11586,plain,
% 2.42/2.64 (b(s(s(z)), z)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[202, 11585])).
% 2.42/2.64 tff(11587,plain,
% 2.42/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 2.42/2.64 inference(rewrite,[status(thm)],[])).
% 2.42/2.64 tff(11588,plain,
% 2.42/2.64 (((~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(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 2.42/2.64 inference(rewrite,[status(thm)],[])).
% 2.42/2.64 tff(11589,plain,
% 2.42/2.64 (((~![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(s(z), s(s(z)))) | (~r(z, s(s(z))))))),
% 2.42/2.64 inference(monotonicity,[status(thm)],[11588])).
% 2.42/2.64 tff(11590,plain,
% 2.42/2.64 (((~![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(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 2.42/2.64 inference(transitivity,[status(thm)],[11589, 11587])).
% 2.42/2.64 tff(11591,plain,
% 2.42/2.64 ((~![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)))),
% 2.42/2.64 inference(quant_inst,[status(thm)],[])).
% 2.42/2.64 tff(11592,plain,
% 2.42/2.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z))))),
% 2.42/2.64 inference(modus_ponens,[status(thm)],[11591, 11590])).
% 2.42/2.64 tff(11593,plain,
% 2.42/2.64 (~r(s(z), z)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[11592, 37, 1997, 331])).
% 2.42/2.64 tff(11594,plain,
% 2.42/2.64 (b(s(z), z)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[169, 11593])).
% 2.42/2.64 tff(11595,plain,
% 2.42/2.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))))),
% 2.42/2.64 inference(rewrite,[status(thm)],[])).
% 2.42/2.64 tff(11596,plain,
% 2.42/2.64 (((~b(z, s(z))) | (~b(s(s(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(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))))),
% 2.42/2.64 inference(rewrite,[status(thm)],[])).
% 2.42/2.64 tff(11597,plain,
% 2.42/2.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z)))))),
% 2.42/2.64 inference(monotonicity,[status(thm)],[11596])).
% 2.42/2.64 tff(11598,plain,
% 2.42/2.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))))),
% 2.42/2.64 inference(transitivity,[status(thm)],[11597, 11595])).
% 2.42/2.64 tff(11599,plain,
% 2.42/2.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))))),
% 2.42/2.64 inference(quant_inst,[status(thm)],[])).
% 2.42/2.64 tff(11600,plain,
% 2.42/2.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z)))),
% 2.42/2.64 inference(modus_ponens,[status(thm)],[11599, 11598])).
% 2.42/2.64 tff(11601,plain,
% 2.42/2.64 (~b(s(s(elem!1)), s(s(z)))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[11600, 75, 1457, 372, 11594, 309])).
% 2.42/2.64 tff(11602,plain,
% 2.42/2.64 (r(s(s(elem!1)), s(s(z)))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[504, 58, 266, 11601])).
% 2.42/2.64 tff(11603,plain,
% 2.42/2.64 (~b(s(s(elem!1)), z)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[4752, 75, 1457, 372, 11594])).
% 2.42/2.64 tff(11604,plain,
% 2.42/2.64 (r(s(s(elem!1)), z)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[518, 58, 515, 11603])).
% 2.42/2.64 tff(11605,plain,
% 2.42/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(elem!1)))))),
% 2.42/2.64 inference(rewrite,[status(thm)],[])).
% 2.42/2.64 tff(11606,plain,
% 2.42/2.64 (((~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(elem!1)))))),
% 2.42/2.64 inference(rewrite,[status(thm)],[])).
% 2.42/2.64 tff(11607,plain,
% 2.42/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(elem!1))))))),
% 2.42/2.64 inference(monotonicity,[status(thm)],[11606])).
% 2.42/2.64 tff(11608,plain,
% 2.42/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(elem!1)))))),
% 2.42/2.64 inference(transitivity,[status(thm)],[11607, 11605])).
% 2.42/2.64 tff(11609,plain,
% 2.42/2.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))))),
% 2.42/2.64 inference(quant_inst,[status(thm)],[])).
% 2.42/2.64 tff(11610,plain,
% 2.42/2.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(elem!1))))),
% 2.42/2.64 inference(modus_ponens,[status(thm)],[11609, 11608])).
% 2.42/2.64 tff(11611,plain,
% 2.42/2.64 ($false),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[11610, 37, 1871, 1997, 11604, 11602])).
% 2.42/2.64 tff(11612,plain,((~r(s(z), s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (s(s(elem!1)) = s(s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.64 tff(11613,plain,
% 2.42/2.64 (~r(z, s(s(z)))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[11612, 11560, 266, 11407, 11550, 372, 11545])).
% 2.42/2.64 tff(11614,plain,
% 2.42/2.64 (b(z, s(s(z)))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[351, 11613])).
% 2.42/2.64 tff(11615,plain,
% 2.42/2.64 (r(s(z), s(elem!1))),
% 2.42/2.64 inference(modus_ponens,[status(thm)],[11560, 11452])).
% 2.42/2.64 tff(11616,plain,
% 2.42/2.64 (~r(s(elem!1), z)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[1761, 11615, 11409])).
% 2.42/2.64 tff(11617,plain,
% 2.42/2.64 (b(s(elem!1), z)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[766, 11616])).
% 2.42/2.64 tff(11618,plain,
% 2.42/2.64 (~b(s(s(elem!1)), z)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[6654, 11617, 11614, 11586, 11563])).
% 2.42/2.64 tff(11619,plain,
% 2.42/2.64 (r(s(s(elem!1)), z)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[2696, 11618])).
% 2.42/2.64 tff(11620,plain,
% 2.42/2.64 (r(s(s(s(z))), z)),
% 2.42/2.64 inference(modus_ponens,[status(thm)],[11619, 11398])).
% 2.42/2.64 tff(11621,plain,
% 2.42/2.64 (r(elem!1, s(s(s(z)))) <=> r(s(z), s(s(s(z))))),
% 2.42/2.64 inference(monotonicity,[status(thm)],[17])).
% 2.42/2.64 tff(11622,plain,
% 2.42/2.64 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 2.42/2.64 inference(symmetry,[status(thm)],[11621])).
% 2.42/2.64 tff(11623,plain,
% 2.42/2.64 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(s(z))))),
% 2.42/2.64 inference(transitivity,[status(thm)],[8608, 8627, 11622])).
% 2.42/2.64 tff(11624,plain,
% 2.42/2.64 (r(elem!1, s(s(s(z))))),
% 2.42/2.64 inference(modus_ponens,[status(thm)],[11544, 11623])).
% 2.42/2.64 tff(11625,plain,
% 2.42/2.64 (~r(s(s(s(z))), z)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[6474, 11624, 155])).
% 2.42/2.64 tff(11626,plain,
% 2.42/2.64 ($false),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[11625, 11620])).
% 2.42/2.64 tff(11627,plain,((~r(elem!1, z)) | (~(elem!1 = s(z))) | (s(s(elem!1)) = s(s(z))) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.64 tff(11628,plain,
% 2.42/2.64 (~r(elem!1, z)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[11627, 17, 266, 11396, 1518, 964, 11394])).
% 2.42/2.64 tff(11629,plain,
% 2.42/2.64 (b(elem!1, z)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[387, 11628, 353])).
% 2.42/2.64 tff(11630,plain,
% 2.42/2.64 (~b(s(s(z)), z)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[6452, 11629, 1518, 964])).
% 2.42/2.64 tff(11631,plain,
% 2.42/2.64 (~b(s(elem!1), z)),
% 2.42/2.64 inference(modus_ponens,[status(thm)],[11630, 11393])).
% 2.42/2.64 tff(11632,plain,
% 2.42/2.64 (b(s(elem!1), elem!1)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[968, 8607, 964])).
% 2.42/2.64 tff(11633,plain,
% 2.42/2.64 (~(s(elem!1) = s(s(s(s(s(s(s(z))))))))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[736, 8607])).
% 2.42/2.64 tff(11634,plain,
% 2.42/2.64 (~b(s(s(elem!1)), elem!1)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[4702, 11629, 1518, 964, 266])).
% 2.42/2.64 tff(11635,plain,
% 2.42/2.64 (~r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[11541, 11634, 11394, 17])).
% 2.42/2.64 tff(11636,plain,
% 2.42/2.64 (b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[813, 11635, 11404])).
% 2.42/2.64 tff(11637,plain,
% 2.42/2.64 (~r(s(elem!1), z)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[10257, 11636, 11633, 1518, 11629, 11632])).
% 2.42/2.64 tff(11638,plain,
% 2.42/2.64 (b(s(elem!1), z)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[766, 11637])).
% 2.42/2.64 tff(11639,plain,
% 2.42/2.64 ($false),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[11638, 11631])).
% 2.42/2.64 tff(11640,plain,((~(elem!1 = s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (s(s(elem!1)) = s(s(z))) | (elem!1 = z) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.42/2.64 tff(11641,plain,
% 2.42/2.64 (~(elem!1 = s(z))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[11640, 9866, 11390, 9981, 9867, 13])).
% 2.42/2.64 tff(11642,plain,
% 2.42/2.64 (r(elem!1, s(z))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[89, 11641, 14])).
% 2.42/2.64 tff(11643,plain,
% 2.42/2.64 (~(s(z) = elem!1)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[97, 11641])).
% 2.42/2.64 tff(11644,plain,
% 2.42/2.64 (~r(elem!1, z)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[177, 506, 114])).
% 2.42/2.64 tff(11645,plain,
% 2.42/2.64 (b(elem!1, z)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[387, 11644, 353])).
% 2.42/2.64 tff(11646,plain,
% 2.42/2.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)))),
% 2.42/2.64 inference(rewrite,[status(thm)],[])).
% 2.42/2.64 tff(11647,plain,
% 2.42/2.64 (((~b(z, elem!1)) | (~b(s(s(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(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)))),
% 2.42/2.64 inference(rewrite,[status(thm)],[])).
% 2.42/2.64 tff(11648,plain,
% 2.42/2.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z))))),
% 2.42/2.64 inference(monotonicity,[status(thm)],[11647])).
% 2.42/2.64 tff(11649,plain,
% 2.42/2.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)))),
% 2.42/2.64 inference(transitivity,[status(thm)],[11648, 11646])).
% 2.42/2.64 tff(11650,plain,
% 2.42/2.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(z)))))),
% 2.42/2.64 inference(quant_inst,[status(thm)],[])).
% 2.42/2.64 tff(11651,plain,
% 2.42/2.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z))),
% 2.42/2.64 inference(modus_ponens,[status(thm)],[11650, 11649])).
% 2.42/2.64 tff(11652,plain,
% 2.42/2.64 (~b(z, s(s(z)))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[11651, 75, 1518, 11645, 964])).
% 2.42/2.64 tff(11653,plain,
% 2.42/2.64 (r(z, s(s(z)))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[351, 11652])).
% 2.42/2.64 tff(11654,plain,
% 2.42/2.64 (~r(s(z), s(s(z)))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[2005, 11653, 506])).
% 2.42/2.64 tff(11655,plain,
% 2.42/2.64 (b(s(z), s(s(z)))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[416, 11654])).
% 2.42/2.64 tff(11656,plain,
% 2.42/2.64 (~b(s(s(z)), z)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[6452, 11645, 1518, 964])).
% 2.42/2.64 tff(11657,plain,
% 2.42/2.64 (r(s(s(z)), z)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[202, 11656])).
% 2.42/2.64 tff(11658,plain,
% 2.42/2.64 (~b(s(s(elem!1)), elem!1)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[4702, 11645, 1518, 964, 266])).
% 2.42/2.64 tff(11659,plain,
% 2.42/2.64 (~r(s(s(z)), s(z))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[6456, 11653, 506])).
% 2.42/2.64 tff(11660,plain,
% 2.42/2.64 (b(s(s(z)), s(z))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[153, 11659])).
% 2.42/2.64 tff(11661,plain,
% 2.42/2.64 (~(s(s(z)) = elem!1)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[9897, 11656, 11645])).
% 2.42/2.64 tff(11662,plain,
% 2.42/2.64 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[1425, 11661])).
% 2.42/2.65 tff(11663,plain,
% 2.42/2.65 (elem!1 = s(s(elem!1))),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[1617, 9521, 6956])).
% 2.42/2.65 tff(11664,plain,
% 2.42/2.65 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(elem!1)))),
% 2.42/2.65 inference(monotonicity,[status(thm)],[11663])).
% 2.42/2.65 tff(11665,plain,
% 2.42/2.65 (~(s(s(s(z))) = elem!1)),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[1612, 11663])).
% 2.42/2.65 tff(11666,plain,
% 2.42/2.65 (b(s(s(s(z))), elem!1)),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[1115, 11665, 1710])).
% 2.42/2.65 tff(11667,plain,
% 2.42/2.65 (b(s(s(s(z))), s(s(elem!1)))),
% 2.42/2.65 inference(modus_ponens,[status(thm)],[11666, 11664])).
% 2.42/2.65 tff(11668,plain,
% 2.42/2.65 (~b(s(s(s(z))), z)),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[7537, 75, 11667, 6368, 6958])).
% 2.42/2.65 tff(11669,plain,
% 2.42/2.65 (r(s(s(s(z))), z)),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[1334, 58, 221, 11668])).
% 2.42/2.65 tff(11670,plain,
% 2.42/2.65 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(elem!1)))),
% 2.42/2.65 inference(monotonicity,[status(thm)],[11663])).
% 2.42/2.65 tff(11671,plain,
% 2.42/2.65 (b(s(s(z)), s(s(elem!1)))),
% 2.42/2.65 inference(modus_ponens,[status(thm)],[964, 11670])).
% 2.42/2.65 tff(11672,plain,
% 2.42/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.42/2.65 inference(rewrite,[status(thm)],[])).
% 2.42/2.65 tff(11673,plain,
% 2.42/2.65 (((~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.42/2.65 inference(rewrite,[status(thm)],[])).
% 2.42/2.65 tff(11674,plain,
% 2.42/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 2.42/2.65 inference(monotonicity,[status(thm)],[11673])).
% 2.42/2.65 tff(11675,plain,
% 2.42/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.42/2.65 inference(transitivity,[status(thm)],[11674, 11672])).
% 2.42/2.65 tff(11676,plain,
% 2.42/2.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.42/2.65 inference(quant_inst,[status(thm)],[])).
% 2.42/2.65 tff(11677,plain,
% 2.42/2.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 2.42/2.65 inference(modus_ponens,[status(thm)],[11676, 11675])).
% 2.42/2.65 tff(11678,plain,
% 2.42/2.65 (~b(s(s(z)), s(s(s(z))))),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[11677, 75, 11667, 11671, 6368, 6958])).
% 2.42/2.65 tff(11679,plain,
% 2.42/2.65 (r(s(s(z)), s(s(s(z))))),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[1559, 58, 1556, 11678])).
% 2.42/2.65 tff(11680,plain,
% 2.42/2.65 ($false),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[4806, 37, 320, 11679, 11669])).
% 2.42/2.65 tff(11681,plain,((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | r(s(s(s(z))), elem!1) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.65 tff(11682,plain,
% 2.42/2.65 (~r(s(s(elem!1)), s(z))),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[11681, 10227, 964, 320, 114, 506, 1518])).
% 2.42/2.65 tff(11683,plain,
% 2.42/2.65 (b(s(s(elem!1)), s(z))),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[561, 11682])).
% 2.42/2.65 tff(11684,plain,
% 2.42/2.65 (~(elem!1 = s(s(elem!1)))),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[8581, 11683, 14])).
% 2.42/2.65 tff(11685,plain,
% 2.42/2.65 (~(s(s(elem!1)) = elem!1)),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[2555, 11684])).
% 2.42/2.65 tff(11686,plain,
% 2.42/2.65 (r(s(s(elem!1)), elem!1)),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[2673, 11685, 1])).
% 2.42/2.65 tff(11687,plain,
% 2.42/2.65 (~r(s(z), s(s(elem!1)))),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[3753, 11686, 588])).
% 2.42/2.65 tff(11688,plain,
% 2.42/2.65 (b(s(z), s(s(elem!1)))),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[1890, 11687])).
% 2.42/2.65 tff(11689,plain,
% 2.42/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))))),
% 2.42/2.65 inference(rewrite,[status(thm)],[])).
% 2.42/2.65 tff(11690,plain,
% 2.42/2.65 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(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(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))))),
% 2.42/2.65 inference(rewrite,[status(thm)],[])).
% 2.42/2.65 tff(11691,plain,
% 2.42/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z)))))),
% 2.42/2.65 inference(monotonicity,[status(thm)],[11690])).
% 2.42/2.65 tff(11692,plain,
% 2.42/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))))),
% 2.42/2.65 inference(transitivity,[status(thm)],[11691, 11689])).
% 2.42/2.65 tff(11693,plain,
% 2.42/2.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))))),
% 2.42/2.65 inference(quant_inst,[status(thm)],[])).
% 2.42/2.65 tff(11694,plain,
% 2.42/2.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z)))),
% 2.42/2.65 inference(modus_ponens,[status(thm)],[11693, 11692])).
% 2.42/2.65 tff(11695,plain,
% 2.42/2.65 (~b(s(s(z)), s(s(elem!1)))),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[11694, 75, 11683, 11688, 309])).
% 2.42/2.65 tff(11696,plain,
% 2.42/2.65 (r(s(s(z)), s(s(elem!1)))),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[6336, 58, 11695, 8001])).
% 2.42/2.65 tff(11697,plain,
% 2.42/2.65 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[3906, 10265, 309, 10223])).
% 2.42/2.65 tff(11698,plain,
% 2.42/2.65 (r(s(s(z)), s(s(s(s(z)))))),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[465, 11697])).
% 2.42/2.65 tff(11699,plain,
% 2.42/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.42/2.65 inference(rewrite,[status(thm)],[])).
% 2.42/2.65 tff(11700,plain,
% 2.42/2.65 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.42/2.65 inference(rewrite,[status(thm)],[])).
% 2.42/2.65 tff(11701,plain,
% 2.42/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 2.42/2.65 inference(monotonicity,[status(thm)],[11700])).
% 2.42/2.65 tff(11702,plain,
% 2.42/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.42/2.65 inference(transitivity,[status(thm)],[11701, 11699])).
% 2.42/2.65 tff(11703,plain,
% 2.42/2.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.42/2.65 inference(quant_inst,[status(thm)],[])).
% 2.42/2.65 tff(11704,plain,
% 2.42/2.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 2.42/2.65 inference(modus_ponens,[status(thm)],[11703, 11702])).
% 2.42/2.65 tff(11705,plain,
% 2.42/2.65 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[11704, 75, 11683, 11688, 10265])).
% 2.42/2.65 tff(11706,plain,
% 2.42/2.65 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[1660, 11705, 1011])).
% 2.42/2.65 tff(11707,plain,
% 2.42/2.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.42/2.65 inference(rewrite,[status(thm)],[])).
% 2.42/2.65 tff(11708,plain,
% 2.42/2.65 (((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(elem!1))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.42/2.65 inference(rewrite,[status(thm)],[])).
% 2.42/2.65 tff(11709,plain,
% 2.42/2.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(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(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(z))))))))),
% 2.42/2.65 inference(monotonicity,[status(thm)],[11708])).
% 2.42/2.65 tff(11710,plain,
% 2.42/2.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(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(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.42/2.65 inference(transitivity,[status(thm)],[11709, 11707])).
% 2.42/2.65 tff(11711,plain,
% 2.42/2.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(elem!1)))))),
% 2.42/2.65 inference(quant_inst,[status(thm)],[])).
% 2.42/2.65 tff(11712,plain,
% 2.42/2.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(z))))))),
% 2.42/2.65 inference(modus_ponens,[status(thm)],[11711, 11710])).
% 2.42/2.65 tff(11713,plain,
% 2.42/2.65 ($false),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[11712, 37, 11706, 11698, 11696])).
% 2.42/2.65 tff(11714,plain,((~r(s(z), elem!1)) | (s(s(z)) = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(s(z))))) | (~b(s(s(z)), s(z))) | b(s(s(elem!1)), elem!1) | b(elem!1, s(z)) | (~b(s(s(z)), elem!1)) | (~r(s(s(z)), z)) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~b(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.65 tff(11715,plain,
% 2.42/2.65 (~r(s(z), elem!1)),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[11714, 11662, 7548, 11660, 11658, 14, 964, 11657, 114, 506, 1518, 698])).
% 2.42/2.65 tff(11716,plain,
% 2.42/2.65 (b(s(z), elem!1)),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[601, 11715, 108])).
% 2.42/2.65 tff(11717,plain,
% 2.42/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)))),
% 2.42/2.65 inference(rewrite,[status(thm)],[])).
% 2.42/2.65 tff(11718,plain,
% 2.42/2.65 (((~b(z, elem!1)) | (~b(s(s(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), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)))),
% 2.42/2.65 inference(rewrite,[status(thm)],[])).
% 2.42/2.65 tff(11719,plain,
% 2.42/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), 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(X1, 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(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z))))),
% 2.42/2.65 inference(monotonicity,[status(thm)],[11718])).
% 2.42/2.65 tff(11720,plain,
% 2.42/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), 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(X1, 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(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)))),
% 2.42/2.65 inference(transitivity,[status(thm)],[11719, 11717])).
% 2.42/2.65 tff(11721,plain,
% 2.42/2.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))))),
% 2.42/2.65 inference(quant_inst,[status(thm)],[])).
% 2.42/2.65 tff(11722,plain,
% 2.42/2.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z))),
% 2.42/2.65 inference(modus_ponens,[status(thm)],[11721, 11720])).
% 2.42/2.65 tff(11723,plain,
% 2.42/2.65 ($false),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[11722, 75, 1518, 11645, 11716, 964, 11655])).
% 2.42/2.65 tff(11724,plain,((~r(z, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (s(z) = elem!1) | b(elem!1, s(z)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (s(s(elem!1)) = s(s(z))) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 2.42/2.65 tff(11725,plain,
% 2.42/2.65 (~r(z, s(z))),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[11724, 9866, 11390, 11643, 14, 11642, 9474, 9981, 9867])).
% 2.42/2.65 tff(11726,plain,
% 2.42/2.65 (b(z, s(z))),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[187, 11725])).
% 2.42/2.65 tff(11727,plain,
% 2.42/2.65 (~r(elem!1, s(s(z)))),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[4456, 37, 11642, 115])).
% 2.42/2.65 tff(11728,plain,
% 2.42/2.65 (b(z, s(s(elem!1)))),
% 2.42/2.65 inference(modus_ponens,[status(thm)],[1518, 9954])).
% 2.42/2.65 tff(11729,plain,
% 2.42/2.65 (r(elem!1, s(s(z))) <=> r(s(s(elem!1)), s(s(z)))),
% 2.42/2.65 inference(monotonicity,[status(thm)],[1602])).
% 2.42/2.65 tff(11730,plain,
% 2.42/2.65 ((~r(elem!1, s(s(z)))) <=> (~r(s(s(elem!1)), s(s(z))))),
% 2.42/2.65 inference(monotonicity,[status(thm)],[11729])).
% 2.42/2.65 tff(11731,plain,
% 2.42/2.65 (~r(s(s(elem!1)), s(s(z)))),
% 2.42/2.65 inference(modus_ponens,[status(thm)],[9001, 11730])).
% 2.42/2.65 tff(11732,plain,
% 2.42/2.65 (b(s(s(elem!1)), s(s(z)))),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[504, 58, 266, 11731])).
% 2.42/2.65 tff(11733,plain,
% 2.42/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, 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(X1, 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(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.42/2.66 inference(rewrite,[status(thm)],[])).
% 2.42/2.66 tff(11734,plain,
% 2.42/2.66 (((~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z)))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.42/2.66 inference(rewrite,[status(thm)],[])).
% 2.42/2.66 tff(11735,plain,
% 2.42/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(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(X1, 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(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))))),
% 2.42/2.66 inference(monotonicity,[status(thm)],[11734])).
% 2.42/2.66 tff(11736,plain,
% 2.42/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(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(X1, 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(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.42/2.66 inference(transitivity,[status(thm)],[11735, 11733])).
% 2.42/2.66 tff(11737,plain,
% 2.42/2.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))),
% 2.42/2.66 inference(quant_inst,[status(thm)],[])).
% 2.42/2.66 tff(11738,plain,
% 2.42/2.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))),
% 2.42/2.66 inference(modus_ponens,[status(thm)],[11737, 11736])).
% 2.42/2.66 tff(11739,plain,
% 2.42/2.66 ($false),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[11738, 75, 372, 9967, 11732, 9079, 11728])).
% 2.42/2.66 tff(11740,plain,((~(elem!1 = s(s(elem!1)))) | (~b(z, s(z))) | (s(s(elem!1)) = s(s(z))) | r(elem!1, s(s(z))) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.66 tff(11741,plain,
% 2.42/2.66 (~(elem!1 = s(s(elem!1)))),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[11740, 107, 266, 9001, 964, 1518, 372])).
% 2.42/2.66 tff(11742,plain,
% 2.42/2.66 (~(s(s(elem!1)) = elem!1)),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[2555, 11741])).
% 2.42/2.66 tff(11743,plain,
% 2.42/2.66 (r(s(s(elem!1)), elem!1)),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[2673, 11742, 1])).
% 2.42/2.66 tff(11744,plain,
% 2.42/2.66 (~r(elem!1, z)),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[4786, 11743, 114])).
% 2.42/2.66 tff(11745,plain,
% 2.42/2.66 (b(elem!1, z)),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[387, 11744, 353])).
% 2.42/2.66 tff(11746,plain,
% 2.42/2.66 ($false),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[4527, 75, 1518, 11745, 372, 107])).
% 2.42/2.66 tff(11747,plain,((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))) | (elem!1 = z) | (~r(elem!1, s(z))) | b(s(s(elem!1)), elem!1) | (s(s(elem!1)) = s(s(z))) | r(elem!1, s(s(z))) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.66 tff(11748,plain,
% 2.42/2.66 (~b(s(z), elem!1)),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[11747, 1, 11726, 9867, 11642, 9866, 9981, 11727, 11390])).
% 2.42/2.66 tff(11749,plain,
% 2.42/2.66 (r(s(z), elem!1)),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[601, 11748, 11643])).
% 2.42/2.66 tff(11750,plain,
% 2.42/2.66 (~r(s(s(s(s(z)))), s(z))),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[10206, 37, 11749, 9474])).
% 2.42/2.66 tff(11751,plain,
% 2.42/2.66 (b(s(s(s(s(z)))), s(z))),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[1406, 58, 483, 11750])).
% 2.42/2.66 tff(11752,plain,
% 2.42/2.66 (~r(s(s(s(z))), s(z))),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[6502, 6494, 115])).
% 2.42/2.66 tff(11753,plain,
% 2.42/2.66 (b(s(s(s(z))), s(z))),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[1081, 11752])).
% 2.42/2.66 tff(11754,plain,
% 2.42/2.66 (~b(s(z), s(s(s(z))))),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[5290, 11753, 982, 372])).
% 2.42/2.66 tff(11755,plain,
% 2.42/2.66 (r(s(z), s(s(s(z))))),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[1263, 11754])).
% 2.42/2.66 tff(11756,plain,
% 2.42/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(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(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 2.42/2.66 inference(rewrite,[status(thm)],[])).
% 2.42/2.66 tff(11757,plain,
% 2.42/2.66 (((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 2.42/2.66 inference(rewrite,[status(thm)],[])).
% 2.42/2.66 tff(11758,plain,
% 2.42/2.66 (((~![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(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))))),
% 2.42/2.66 inference(monotonicity,[status(thm)],[11757])).
% 2.42/2.66 tff(11759,plain,
% 2.42/2.66 (((~![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(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 2.42/2.66 inference(transitivity,[status(thm)],[11758, 11756])).
% 2.42/2.66 tff(11760,plain,
% 2.42/2.66 ((~![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(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 2.42/2.66 inference(quant_inst,[status(thm)],[])).
% 2.42/2.66 tff(11761,plain,
% 2.42/2.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))),
% 2.42/2.66 inference(modus_ponens,[status(thm)],[11760, 11759])).
% 2.42/2.66 tff(11762,plain,
% 2.42/2.66 ($false),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[11761, 37, 115, 11755, 6494])).
% 2.42/2.66 tff(11763,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.66 tff(11764,plain,
% 2.42/2.66 (~r(s(s(z)), s(s(s(z))))),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[11763, 11751, 11726, 115])).
% 2.42/2.66 tff(11765,plain,
% 2.42/2.66 (b(s(s(z)), s(s(s(z))))),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[8252, 11764])).
% 2.42/2.66 tff(11766,plain,
% 2.42/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(z)))), z)))),
% 2.42/2.66 inference(rewrite,[status(thm)],[])).
% 2.42/2.66 tff(11767,plain,
% 2.42/2.66 (((~b(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(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)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 2.42/2.66 inference(rewrite,[status(thm)],[])).
% 2.42/2.66 tff(11768,plain,
% 2.42/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(s(s(s(s(z)))), z))))),
% 2.42/2.66 inference(monotonicity,[status(thm)],[11767])).
% 2.42/2.66 tff(11769,plain,
% 2.42/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(s(s(s(s(z)))), z)))),
% 2.42/2.66 inference(transitivity,[status(thm)],[11768, 11766])).
% 2.42/2.66 tff(11770,plain,
% 2.42/2.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))),
% 2.42/2.66 inference(quant_inst,[status(thm)],[])).
% 2.42/2.66 tff(11771,plain,
% 2.42/2.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(z)))), z))),
% 2.42/2.66 inference(modus_ponens,[status(thm)],[11770, 11769])).
% 2.42/2.66 tff(11772,plain,
% 2.42/2.66 (~b(s(s(s(s(z)))), z)),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[11771, 75, 372, 10223, 10265])).
% 2.42/2.66 tff(11773,plain,
% 2.42/2.66 (r(s(s(s(s(z)))), z)),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[1421, 58, 1143, 11772])).
% 2.42/2.66 tff(11774,plain,
% 2.42/2.66 (~r(elem!1, z)),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[4786, 2647, 114])).
% 2.42/2.66 tff(11775,plain,
% 2.42/2.66 (b(elem!1, z)),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[387, 11774, 353])).
% 2.42/2.66 tff(11776,plain,
% 2.42/2.66 (~b(s(s(z)), z)),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[6452, 11775, 1518, 964])).
% 2.42/2.66 tff(11777,plain,
% 2.42/2.66 (r(s(s(z)), z)),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[202, 11776])).
% 2.42/2.66 tff(11778,plain,
% 2.42/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~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(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z)))),
% 2.42/2.66 inference(rewrite,[status(thm)],[])).
% 2.42/2.66 tff(11779,plain,
% 2.42/2.66 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z)))),
% 2.42/2.66 inference(rewrite,[status(thm)],[])).
% 2.42/2.66 tff(11780,plain,
% 2.42/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~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)), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z))))),
% 2.42/2.66 inference(monotonicity,[status(thm)],[11779])).
% 2.42/2.66 tff(11781,plain,
% 2.42/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~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)), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z)))),
% 2.42/2.66 inference(transitivity,[status(thm)],[11780, 11778])).
% 2.42/2.66 tff(11782,plain,
% 2.42/2.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.42/2.66 inference(quant_inst,[status(thm)],[])).
% 2.42/2.66 tff(11783,plain,
% 2.42/2.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z))),
% 2.42/2.66 inference(modus_ponens,[status(thm)],[11782, 11781])).
% 2.42/2.66 tff(11784,plain,
% 2.42/2.66 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[11783, 37, 11777, 698, 11773])).
% 2.42/2.66 tff(11785,plain,
% 2.42/2.66 (b(s(s(z)), s(s(s(s(z)))))),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[465, 11784])).
% 2.42/2.66 tff(11786,plain,
% 2.42/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~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(X1, 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(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.42/2.66 inference(rewrite,[status(thm)],[])).
% 2.42/2.66 tff(11787,plain,
% 2.42/2.66 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.42/2.66 inference(rewrite,[status(thm)],[])).
% 2.42/2.66 tff(11788,plain,
% 2.42/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))))),
% 2.42/2.66 inference(monotonicity,[status(thm)],[11787])).
% 2.42/2.66 tff(11789,plain,
% 2.42/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.42/2.66 inference(transitivity,[status(thm)],[11788, 11786])).
% 2.42/2.66 tff(11790,plain,
% 2.42/2.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))),
% 2.42/2.67 inference(quant_inst,[status(thm)],[])).
% 2.42/2.67 tff(11791,plain,
% 2.42/2.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))),
% 2.42/2.67 inference(modus_ponens,[status(thm)],[11790, 11789])).
% 2.42/2.67 tff(11792,plain,
% 2.42/2.67 (~b(s(z), s(s(z)))),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[11791, 75, 10223, 11785, 10265])).
% 2.42/2.67 tff(11793,plain,
% 2.42/2.67 (r(s(z), s(s(z)))),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[416, 11792])).
% 2.42/2.67 tff(11794,plain,
% 2.42/2.67 (~r(s(z), z)),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[2015, 11793, 11777])).
% 2.42/2.67 tff(11795,plain,
% 2.42/2.67 (b(s(z), z)),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[169, 11794])).
% 2.42/2.67 tff(11796,plain,
% 2.42/2.67 (~r(s(s(elem!1)), s(z))),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[9102, 2647, 114])).
% 2.42/2.67 tff(11797,plain,
% 2.42/2.67 (b(s(s(elem!1)), s(z))),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[561, 11796])).
% 2.42/2.67 tff(11798,plain,
% 2.42/2.67 (~b(s(s(elem!1)), z)),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[4754, 11797, 372, 11795])).
% 2.42/2.67 tff(11799,plain,
% 2.42/2.67 (r(s(s(elem!1)), z)),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[2696, 11798])).
% 2.42/2.67 tff(11800,plain,
% 2.42/2.67 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[2707, 11799, 11773])).
% 2.42/2.67 tff(11801,plain,
% 2.42/2.67 (~(s(s(z)) = elem!1)),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[10273, 588, 698, 1518, 353, 114])).
% 2.42/2.67 tff(11802,plain,
% 2.42/2.67 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[1425, 11801])).
% 2.42/2.67 tff(11803,plain,
% 2.42/2.67 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[5700, 11802])).
% 2.42/2.67 tff(11804,plain,
% 2.42/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.42/2.67 inference(rewrite,[status(thm)],[])).
% 2.42/2.67 tff(11805,plain,
% 2.42/2.67 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.42/2.67 inference(rewrite,[status(thm)],[])).
% 2.42/2.67 tff(11806,plain,
% 2.42/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1))))))),
% 2.42/2.67 inference(monotonicity,[status(thm)],[11805])).
% 2.42/2.67 tff(11807,plain,
% 2.42/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.42/2.67 inference(transitivity,[status(thm)],[11806, 11804])).
% 2.42/2.67 tff(11808,plain,
% 2.42/2.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.42/2.67 inference(quant_inst,[status(thm)],[])).
% 2.42/2.67 tff(11809,plain,
% 2.42/2.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 2.42/2.67 inference(modus_ponens,[status(thm)],[11808, 11807])).
% 2.42/2.67 tff(11810,plain,
% 2.42/2.67 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[11809, 75, 11797, 5674, 10265])).
% 2.42/2.67 tff(11811,plain,
% 2.42/2.67 ($false),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[3876, 58, 11810, 11803, 11800])).
% 2.42/2.67 tff(11812,plain,((~r(s(s(elem!1)), elem!1)) | (~b(z, s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (elem!1 = z) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.67 tff(11813,plain,
% 2.42/2.67 (~r(s(s(elem!1)), elem!1)),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[11812, 11749, 11642, 9474, 9866, 11390, 9867, 11726])).
% 2.42/2.67 tff(11814,plain,
% 2.42/2.67 (s(s(elem!1)) = elem!1),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[2673, 11813, 1])).
% 2.42/2.67 tff(11815,plain,
% 2.42/2.67 (elem!1 = s(s(elem!1))),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[2555, 11814])).
% 2.42/2.67 tff(11816,plain,
% 2.42/2.67 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(elem!1)))),
% 2.42/2.67 inference(monotonicity,[status(thm)],[11815])).
% 2.42/2.67 tff(11817,plain,
% 2.42/2.67 (b(s(s(z)), s(s(elem!1)))),
% 2.42/2.67 inference(modus_ponens,[status(thm)],[11390, 11816])).
% 2.42/2.67 tff(11818,plain,
% 2.42/2.67 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(elem!1)))),
% 2.42/2.67 inference(monotonicity,[status(thm)],[11815])).
% 2.42/2.67 tff(11819,plain,
% 2.42/2.67 (~r(s(z), s(s(s(s(z)))))),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[10214, 37, 11749, 9474])).
% 2.42/2.67 tff(11820,plain,
% 2.42/2.67 (b(s(z), s(s(s(s(z)))))),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[489, 11819])).
% 2.42/2.67 tff(11821,plain,
% 2.42/2.67 (~r(s(s(s(z))), elem!1)),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[10226, 11820, 9474, 11642])).
% 2.42/2.67 tff(11822,plain,
% 2.42/2.67 (~(s(s(s(z))) = elem!1)),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[1612, 11815])).
% 2.42/2.67 tff(11823,plain,
% 2.42/2.67 (b(s(s(s(z))), elem!1)),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[1115, 11822, 11821])).
% 2.42/2.67 tff(11824,plain,
% 2.42/2.67 (b(s(s(s(z))), s(s(elem!1)))),
% 2.42/2.67 inference(modus_ponens,[status(thm)],[11823, 11818])).
% 2.42/2.67 tff(11825,plain,
% 2.42/2.67 ((s(s(s(z))) = elem!1) <=> (s(s(s(z))) = s(s(elem!1)))),
% 2.42/2.67 inference(monotonicity,[status(thm)],[11815])).
% 2.42/2.67 tff(11826,plain,
% 2.42/2.67 ((s(s(s(z))) = elem!1) <=> (s(s(elem!1)) = s(s(s(z))))),
% 2.42/2.67 inference(transitivity,[status(thm)],[11825, 1909])).
% 2.42/2.67 tff(11827,plain,
% 2.42/2.67 ((~(s(s(s(z))) = elem!1)) <=> (~(s(s(elem!1)) = s(s(s(z)))))),
% 2.42/2.67 inference(monotonicity,[status(thm)],[11826])).
% 2.42/2.67 tff(11828,plain,
% 2.42/2.67 (~(s(s(elem!1)) = s(s(s(z))))),
% 2.42/2.67 inference(modus_ponens,[status(thm)],[11822, 11827])).
% 2.42/2.67 tff(11829,plain,
% 2.42/2.67 (r(z, elem!1) <=> r(z, s(s(elem!1)))),
% 2.42/2.67 inference(monotonicity,[status(thm)],[11815])).
% 2.42/2.67 tff(11830,plain,
% 2.42/2.67 ((~r(z, elem!1)) <=> (~r(z, s(s(elem!1))))),
% 2.42/2.67 inference(monotonicity,[status(thm)],[11829])).
% 2.42/2.67 tff(11831,plain,
% 2.42/2.67 (~r(z, s(s(elem!1)))),
% 2.42/2.67 inference(modus_ponens,[status(thm)],[13, 11830])).
% 2.42/2.67 tff(11832,plain,
% 2.42/2.67 (~b(s(s(s(s(z)))), z)),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[11771, 75, 11726, 11820, 11751])).
% 2.42/2.67 tff(11833,plain,
% 2.42/2.67 (r(s(s(s(s(z)))), z)),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[1421, 58, 1143, 11832])).
% 2.42/2.67 tff(11834,plain,
% 2.42/2.67 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.42/2.67 inference(monotonicity,[status(thm)],[11815])).
% 2.42/2.67 tff(11835,plain,
% 2.42/2.67 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.42/2.67 inference(modus_ponens,[status(thm)],[9474, 11834])).
% 2.42/2.67 tff(11836,plain,
% 2.42/2.67 (~r(s(s(elem!1)), z)),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[2707, 11835, 11833])).
% 2.42/2.67 tff(11837,plain,
% 2.42/2.67 (b(s(s(elem!1)), z)),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[2696, 11836])).
% 2.42/2.67 tff(11838,plain,
% 2.42/2.67 (~b(s(s(s(z))), z)),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[5576, 11837, 11824, 11831])).
% 2.42/2.67 tff(11839,plain,
% 2.42/2.67 (r(s(s(s(z))), z)),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[1334, 58, 221, 11838])).
% 2.42/2.67 tff(11840,plain,
% 2.42/2.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)))),
% 2.42/2.67 inference(rewrite,[status(thm)],[])).
% 2.42/2.67 tff(11841,plain,
% 2.42/2.67 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)))),
% 2.42/2.67 inference(rewrite,[status(thm)],[])).
% 2.42/2.67 tff(11842,plain,
% 2.42/2.67 (((~![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(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z))))),
% 2.42/2.67 inference(monotonicity,[status(thm)],[11841])).
% 2.42/2.67 tff(11843,plain,
% 2.42/2.67 (((~![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(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)))),
% 2.42/2.67 inference(transitivity,[status(thm)],[11842, 11840])).
% 2.42/2.67 tff(11844,plain,
% 2.42/2.67 ((~![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(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.42/2.67 inference(quant_inst,[status(thm)],[])).
% 2.42/2.67 tff(11845,plain,
% 2.42/2.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z))),
% 2.42/2.67 inference(modus_ponens,[status(thm)],[11844, 11843])).
% 2.42/2.67 tff(11846,plain,
% 2.42/2.67 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[11845, 37, 11833, 11839])).
% 2.42/2.67 tff(11847,plain,
% 2.42/2.67 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[575, 11846])).
% 2.42/2.67 tff(11848,plain,
% 2.42/2.67 (~b(s(s(s(z))), s(z))),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[991, 11847, 11820, 11751])).
% 2.42/2.67 tff(11849,plain,
% 2.42/2.67 (r(s(s(s(z))), s(z))),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[1081, 11848])).
% 2.42/2.67 tff(11850,plain,
% 2.42/2.67 (~b(s(s(elem!1)), s(z))),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[8581, 11815, 14])).
% 2.42/2.67 tff(11851,plain,
% 2.42/2.67 (r(s(s(elem!1)), s(z))),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[561, 11850])).
% 2.42/2.67 tff(11852,plain,
% 2.42/2.67 (((~![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(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.42/2.67 inference(rewrite,[status(thm)],[])).
% 2.42/2.67 tff(11853,plain,
% 2.42/2.67 (((~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z)))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.42/2.67 inference(rewrite,[status(thm)],[])).
% 2.42/2.67 tff(11854,plain,
% 2.42/2.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 2.42/2.67 inference(monotonicity,[status(thm)],[11853])).
% 2.42/2.67 tff(11855,plain,
% 2.42/2.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.42/2.67 inference(transitivity,[status(thm)],[11854, 11852])).
% 2.42/2.67 tff(11856,plain,
% 2.42/2.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.42/2.67 inference(quant_inst,[status(thm)],[])).
% 2.42/2.67 tff(11857,plain,
% 2.42/2.67 ((~![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(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 2.42/2.67 inference(modus_ponens,[status(thm)],[11856, 11855])).
% 2.42/2.67 tff(11858,plain,
% 2.42/2.67 (~r(s(s(elem!1)), s(s(s(z))))),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[11857, 37, 11851, 11849])).
% 2.42/2.67 tff(11859,plain,
% 2.42/2.67 (b(s(s(elem!1)), s(s(s(z))))),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[1936, 11858, 11828])).
% 2.42/2.67 tff(11860,plain,
% 2.42/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.42/2.67 inference(rewrite,[status(thm)],[])).
% 2.42/2.67 tff(11861,plain,
% 2.42/2.67 (((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.42/2.67 inference(rewrite,[status(thm)],[])).
% 2.42/2.67 tff(11862,plain,
% 2.42/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 2.42/2.67 inference(monotonicity,[status(thm)],[11861])).
% 2.42/2.67 tff(11863,plain,
% 2.42/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.42/2.67 inference(transitivity,[status(thm)],[11862, 11860])).
% 2.42/2.67 tff(11864,plain,
% 2.42/2.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.42/2.67 inference(quant_inst,[status(thm)],[])).
% 2.42/2.67 tff(11865,plain,
% 2.42/2.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 2.42/2.67 inference(modus_ponens,[status(thm)],[11864, 11863])).
% 2.42/2.67 tff(11866,plain,
% 2.42/2.67 ($false),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[11865, 75, 11859, 11824, 11817, 11765])).
% 2.42/2.67 tff(11867,plain,(b(s(s(elem!1)), elem!1) | r(z, elem!1) | b(elem!1, s(z)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.67 tff(11868,plain,
% 2.42/2.67 (b(s(s(elem!1)), elem!1)),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[11867, 115, 14, 13])).
% 2.42/2.67 tff(11869,plain,
% 2.42/2.67 (~b(elem!1, z)),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[4702, 11868, 9866, 11390, 9981])).
% 2.42/2.67 tff(11870,plain,
% 2.42/2.67 (r(elem!1, z)),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[387, 11869, 9867])).
% 2.42/2.67 tff(11871,plain,
% 2.42/2.67 (~r(s(z), z)),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[162, 11870, 11642])).
% 2.42/2.67 tff(11872,plain,
% 2.42/2.67 (b(s(z), z)),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[169, 11871])).
% 2.42/2.67 tff(11873,plain,
% 2.42/2.67 (~b(elem!1, s(s(elem!1)))),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[4730, 707, 1518, 964, 266])).
% 2.42/2.67 tff(11874,plain,
% 2.42/2.67 (r(elem!1, s(s(elem!1)))),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[1617, 11741, 11873])).
% 2.42/2.67 tff(11875,plain,
% 2.42/2.67 (~r(s(z), s(s(elem!1)))),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[3615, 11874, 114])).
% 2.42/2.67 tff(11876,plain,
% 2.42/2.67 (b(s(z), s(s(elem!1)))),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[1890, 11875])).
% 2.42/2.67 tff(11877,plain,
% 2.42/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(z), elem!1)))),
% 2.42/2.67 inference(rewrite,[status(thm)],[])).
% 2.42/2.67 tff(11878,plain,
% 2.42/2.67 (((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(z), elem!1)))),
% 2.42/2.67 inference(rewrite,[status(thm)],[])).
% 2.42/2.67 tff(11879,plain,
% 2.42/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~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(X1, 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(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(z), elem!1))))),
% 2.42/2.67 inference(monotonicity,[status(thm)],[11878])).
% 2.42/2.67 tff(11880,plain,
% 2.42/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~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(X1, 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(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(z), elem!1)))),
% 2.42/2.68 inference(transitivity,[status(thm)],[11879, 11877])).
% 2.42/2.68 tff(11881,plain,
% 2.42/2.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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), elem!1)) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))),
% 2.42/2.68 inference(quant_inst,[status(thm)],[])).
% 2.42/2.68 tff(11882,plain,
% 2.42/2.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(z), elem!1))),
% 2.42/2.68 inference(modus_ponens,[status(thm)],[11881, 11880])).
% 2.42/2.68 tff(11883,plain,
% 2.42/2.68 (~b(s(s(elem!1)), z)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[11882, 75, 372, 107, 170, 11876, 707])).
% 2.42/2.68 tff(11884,plain,
% 2.42/2.68 (r(s(s(elem!1)), z)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[2696, 11883])).
% 2.42/2.68 tff(11885,plain,
% 2.42/2.68 ($false),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[7591, 37, 155, 11874, 11884])).
% 2.42/2.68 tff(11886,plain,((~b(s(z), elem!1)) | (~r(elem!1, z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~r(elem!1, s(z))) | (s(s(elem!1)) = s(s(z))) | r(elem!1, s(s(z))) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.68 tff(11887,plain,
% 2.42/2.68 (~b(s(z), elem!1)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[11886, 11870, 11726, 11868, 11642, 9981, 11727, 11390, 9866])).
% 2.42/2.68 tff(11888,plain,
% 2.42/2.68 (r(s(z), elem!1)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[601, 11887, 11643])).
% 2.42/2.68 tff(11889,plain,
% 2.42/2.68 (~r(s(z), s(s(s(s(z)))))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[10214, 37, 11888, 9474])).
% 2.42/2.68 tff(11890,plain,
% 2.42/2.68 (b(s(z), s(s(s(s(z)))))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[489, 11889])).
% 2.42/2.68 tff(11891,plain,
% 2.42/2.68 (~b(s(s(s(s(z)))), z)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[4839, 11890, 11726, 11872])).
% 2.42/2.68 tff(11892,plain,
% 2.42/2.68 (r(s(s(s(s(z)))), z)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[1421, 58, 1143, 11891])).
% 2.42/2.68 tff(11893,plain,
% 2.42/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), 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(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z)))),
% 2.42/2.68 inference(rewrite,[status(thm)],[])).
% 2.42/2.68 tff(11894,plain,
% 2.42/2.68 (((~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z)))),
% 2.42/2.68 inference(rewrite,[status(thm)],[])).
% 2.42/2.68 tff(11895,plain,
% 2.42/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z))))),
% 2.42/2.68 inference(monotonicity,[status(thm)],[11894])).
% 2.42/2.68 tff(11896,plain,
% 2.42/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z)))),
% 2.42/2.68 inference(transitivity,[status(thm)],[11895, 11893])).
% 2.42/2.68 tff(11897,plain,
% 2.42/2.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.42/2.68 inference(quant_inst,[status(thm)],[])).
% 2.42/2.68 tff(11898,plain,
% 2.42/2.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z))),
% 2.42/2.68 inference(modus_ponens,[status(thm)],[11897, 11896])).
% 2.42/2.68 tff(11899,plain,
% 2.42/2.68 ($false),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[11898, 37, 11870, 9474, 11892])).
% 2.42/2.68 tff(11900,plain,((~r(s(s(z)), s(z))) | b(elem!1, s(z)) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.42/2.68 tff(11901,plain,
% 2.42/2.68 (~r(s(s(z)), s(z))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[11900, 14, 13])).
% 2.42/2.68 tff(11902,plain,
% 2.42/2.68 (b(s(s(z)), s(z))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[153, 11901])).
% 2.42/2.68 tff(11903,plain,
% 2.42/2.68 (~(s(s(z)) = elem!1)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[316, 11902, 14])).
% 2.42/2.68 tff(11904,plain,
% 2.42/2.68 (b(elem!1, z)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[387, 2614, 2615])).
% 2.42/2.68 tff(11905,plain,
% 2.42/2.68 (~b(s(s(z)), z)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[6452, 11904, 2617, 964])).
% 2.42/2.68 tff(11906,plain,
% 2.42/2.68 (r(s(s(z)), z)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[202, 11905])).
% 2.42/2.68 tff(11907,plain,
% 2.42/2.68 (~(elem!1 = s(z))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[11640, 2617, 964, 6699, 2615, 13])).
% 2.42/2.68 tff(11908,plain,
% 2.42/2.68 (~(s(z) = elem!1)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[97, 11907])).
% 2.42/2.68 tff(11909,plain,
% 2.42/2.68 (~r(s(s(elem!1)), elem!1)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[11812, 588, 114, 698, 1518, 964, 353, 372])).
% 2.42/2.68 tff(11910,plain,
% 2.42/2.68 (s(s(elem!1)) = elem!1),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[2673, 11909, 1])).
% 2.42/2.68 tff(11911,plain,
% 2.42/2.68 (elem!1 = s(s(elem!1))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[2555, 11910])).
% 2.42/2.68 tff(11912,plain,
% 2.42/2.68 (b(elem!1, z) <=> b(s(s(elem!1)), z)),
% 2.42/2.68 inference(monotonicity,[status(thm)],[11911])).
% 2.42/2.68 tff(11913,plain,
% 2.42/2.68 (b(s(s(elem!1)), z)),
% 2.42/2.68 inference(modus_ponens,[status(thm)],[1958, 11912])).
% 2.42/2.68 tff(11914,plain,
% 2.42/2.68 (b(z, elem!1) <=> b(z, s(s(elem!1)))),
% 2.42/2.68 inference(monotonicity,[status(thm)],[11911])).
% 2.42/2.68 tff(11915,plain,
% 2.42/2.68 (b(z, s(s(elem!1)))),
% 2.42/2.68 inference(modus_ponens,[status(thm)],[1518, 11914])).
% 2.42/2.68 tff(11916,plain,
% 2.42/2.68 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(elem!1)))),
% 2.42/2.68 inference(monotonicity,[status(thm)],[11911])).
% 2.42/2.68 tff(11917,plain,
% 2.42/2.68 (~(s(s(s(z))) = elem!1)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[1612, 11911])).
% 2.42/2.68 tff(11918,plain,
% 2.42/2.68 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.42/2.68 inference(monotonicity,[status(thm)],[11911])).
% 2.42/2.68 tff(11919,plain,
% 2.42/2.68 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.42/2.68 inference(modus_ponens,[status(thm)],[698, 11918])).
% 2.42/2.68 tff(11920,plain,
% 2.42/2.68 (r(s(z), elem!1) <=> r(s(z), s(s(elem!1)))),
% 2.42/2.68 inference(monotonicity,[status(thm)],[11911])).
% 2.42/2.68 tff(11921,plain,
% 2.42/2.68 (r(s(z), s(s(elem!1)))),
% 2.42/2.68 inference(modus_ponens,[status(thm)],[588, 11920])).
% 2.42/2.68 tff(11922,plain,
% 2.42/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.42/2.68 inference(rewrite,[status(thm)],[])).
% 2.42/2.68 tff(11923,plain,
% 2.42/2.68 (((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.42/2.68 inference(rewrite,[status(thm)],[])).
% 2.42/2.68 tff(11924,plain,
% 2.42/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))))),
% 2.42/2.68 inference(monotonicity,[status(thm)],[11923])).
% 2.42/2.68 tff(11925,plain,
% 2.42/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.42/2.68 inference(transitivity,[status(thm)],[11924, 11922])).
% 2.42/2.68 tff(11926,plain,
% 2.42/2.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.42/2.68 inference(quant_inst,[status(thm)],[])).
% 2.42/2.68 tff(11927,plain,
% 2.42/2.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 2.42/2.68 inference(modus_ponens,[status(thm)],[11926, 11925])).
% 2.42/2.68 tff(11928,plain,
% 2.42/2.68 (~r(s(z), s(s(s(s(z)))))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[11927, 37, 11921, 11919])).
% 2.42/2.68 tff(11929,plain,
% 2.42/2.68 (b(s(z), s(s(s(s(z)))))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[489, 11928])).
% 2.42/2.68 tff(11930,plain,
% 2.42/2.68 (~r(s(s(s(z))), elem!1)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[10226, 11929, 698, 114])).
% 2.42/2.68 tff(11931,plain,
% 2.42/2.68 (b(s(s(s(z))), elem!1)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[1115, 11930, 11917])).
% 2.42/2.68 tff(11932,plain,
% 2.42/2.68 (b(s(s(s(z))), s(s(elem!1)))),
% 2.42/2.68 inference(modus_ponens,[status(thm)],[11931, 11916])).
% 2.42/2.68 tff(11933,plain,
% 2.42/2.68 (~b(s(s(s(z))), z)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[7537, 75, 11932, 11915, 11913])).
% 2.42/2.68 tff(11934,plain,
% 2.42/2.68 (r(s(s(s(z))), z)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[1334, 58, 221, 11933])).
% 2.42/2.68 tff(11935,plain,
% 2.42/2.68 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(elem!1)))),
% 2.42/2.68 inference(monotonicity,[status(thm)],[11911])).
% 2.42/2.68 tff(11936,plain,
% 2.42/2.68 (b(s(s(z)), s(s(elem!1)))),
% 2.42/2.68 inference(modus_ponens,[status(thm)],[964, 11935])).
% 2.42/2.68 tff(11937,plain,
% 2.42/2.68 (~b(s(s(z)), s(s(s(z))))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[11677, 75, 11932, 11936, 11915, 11913])).
% 2.42/2.68 tff(11938,plain,
% 2.42/2.68 (r(s(s(z)), s(s(s(z))))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[8252, 11937])).
% 2.42/2.68 tff(11939,plain,
% 2.42/2.68 (~b(s(s(z)), z)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[6452, 1958, 1518, 964])).
% 2.42/2.68 tff(11940,plain,
% 2.42/2.68 (r(s(s(z)), z)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[202, 11939])).
% 2.42/2.68 tff(11941,plain,
% 2.42/2.68 ($false),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[4806, 37, 11940, 11938, 11934])).
% 2.42/2.68 tff(11942,plain,((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | b(s(s(elem!1)), elem!1) | (elem!1 = z) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.68 tff(11943,plain,
% 2.42/2.68 (~r(s(z), elem!1)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[11942, 11904, 114, 964, 9474, 2617, 1, 2615, 372])).
% 2.42/2.68 tff(11944,plain,
% 2.42/2.68 (b(s(z), elem!1)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[601, 11943, 11908])).
% 2.42/2.68 tff(11945,plain,
% 2.42/2.68 (~b(s(z), z)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[2625, 11944, 13, 235, 2614])).
% 2.42/2.68 tff(11946,plain,
% 2.42/2.68 (r(s(z), z)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[169, 11945])).
% 2.42/2.68 tff(11947,plain,
% 2.42/2.68 (~b(s(s(elem!1)), s(z))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[11584, 11946, 372, 309, 6699, 11906])).
% 2.42/2.68 tff(11948,plain,
% 2.42/2.68 (r(s(s(elem!1)), s(z))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[561, 11947])).
% 2.42/2.68 tff(11949,plain,
% 2.42/2.68 (~r(s(s(elem!1)), elem!1)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[9102, 11948, 114])).
% 2.42/2.68 tff(11950,plain,
% 2.42/2.68 (s(s(elem!1)) = elem!1),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[2673, 11949, 1])).
% 2.42/2.68 tff(11951,plain,
% 2.42/2.68 (elem!1 = s(s(elem!1))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[2555, 11950])).
% 2.42/2.68 tff(11952,plain,
% 2.42/2.68 (b(elem!1, z) <=> b(s(s(elem!1)), z)),
% 2.42/2.68 inference(monotonicity,[status(thm)],[11951])).
% 2.42/2.68 tff(11953,plain,
% 2.42/2.68 (b(s(s(elem!1)), z)),
% 2.42/2.68 inference(modus_ponens,[status(thm)],[11904, 11952])).
% 2.42/2.68 tff(11954,plain,
% 2.42/2.68 (b(z, elem!1) <=> b(z, s(s(elem!1)))),
% 2.42/2.68 inference(monotonicity,[status(thm)],[11951])).
% 2.42/2.68 tff(11955,plain,
% 2.42/2.68 (b(z, s(s(elem!1)))),
% 2.42/2.68 inference(modus_ponens,[status(thm)],[2617, 11954])).
% 2.42/2.68 tff(11956,plain,
% 2.42/2.68 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(elem!1)))),
% 2.42/2.68 inference(monotonicity,[status(thm)],[11951])).
% 2.42/2.68 tff(11957,plain,
% 2.42/2.68 (b(s(s(z)), s(s(elem!1)))),
% 2.42/2.68 inference(modus_ponens,[status(thm)],[964, 11956])).
% 2.42/2.68 tff(11958,plain,
% 2.42/2.68 (~r(s(z), s(s(z)))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[2015, 11946, 11906])).
% 2.42/2.68 tff(11959,plain,
% 2.42/2.68 (b(s(z), s(s(z)))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[416, 11958])).
% 2.42/2.68 tff(11960,plain,
% 2.42/2.68 (b(s(z), s(s(elem!1)))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[2329, 11951, 11944])).
% 2.42/2.68 tff(11961,plain,
% 2.42/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(s(elem!1)), z)) | (~b(z, 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(X1, 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(z)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.42/2.68 inference(rewrite,[status(thm)],[])).
% 2.42/2.68 tff(11962,plain,
% 2.42/2.68 (((~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.42/2.68 inference(rewrite,[status(thm)],[])).
% 2.42/2.68 tff(11963,plain,
% 2.42/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1))))))),
% 2.42/2.68 inference(monotonicity,[status(thm)],[11962])).
% 2.42/2.68 tff(11964,plain,
% 2.42/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.42/2.68 inference(transitivity,[status(thm)],[11963, 11961])).
% 2.42/2.68 tff(11965,plain,
% 2.42/2.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))))),
% 2.42/2.68 inference(quant_inst,[status(thm)],[])).
% 2.42/2.68 tff(11966,plain,
% 2.42/2.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1))))),
% 2.42/2.68 inference(modus_ponens,[status(thm)],[11965, 11964])).
% 2.42/2.68 tff(11967,plain,
% 2.42/2.68 ($false),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[11966, 75, 11960, 11959, 11957, 11955, 11953])).
% 2.42/2.68 tff(11968,plain,(r(elem!1, z) | (~b(s(s(z)), elem!1)) | b(s(s(elem!1)), elem!1) | (~r(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | r(z, elem!1) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.42/2.68 tff(11969,plain,
% 2.42/2.68 (r(elem!1, z)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[11968, 1, 964, 114, 372, 309, 13, 235])).
% 2.42/2.68 tff(11970,plain,
% 2.42/2.68 (~r(s(s(s(z))), elem!1)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[4519, 11969, 114, 372])).
% 2.42/2.68 tff(11971,plain,
% 2.42/2.68 (~r(s(s(elem!1)), elem!1)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[4786, 11969, 114])).
% 2.42/2.68 tff(11972,plain,
% 2.42/2.68 (s(s(elem!1)) = elem!1),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[2673, 11971, 1])).
% 2.42/2.68 tff(11973,plain,
% 2.42/2.68 (elem!1 = s(s(elem!1))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[2555, 11972])).
% 2.42/2.68 tff(11974,plain,
% 2.42/2.68 (~(s(s(s(z))) = elem!1)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[1612, 11973])).
% 2.42/2.68 tff(11975,plain,
% 2.42/2.68 (b(s(s(s(z))), elem!1)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[1115, 11974, 11970])).
% 2.42/2.68 tff(11976,plain,
% 2.42/2.68 (~(elem!1 = s(s(s(z))))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[1033, 11974])).
% 2.42/2.68 tff(11977,plain,
% 2.42/2.68 (~r(s(z), z)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[162, 11969, 114])).
% 2.42/2.68 tff(11978,plain,
% 2.42/2.68 (b(s(z), z)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[169, 11977])).
% 2.42/2.68 tff(11979,plain,
% 2.42/2.68 (~b(s(s(z)), z)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[194, 75, 372, 11978, 309])).
% 2.42/2.68 tff(11980,plain,
% 2.42/2.68 (r(s(s(z)), z)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[202, 11979])).
% 2.42/2.68 tff(11981,plain,
% 2.42/2.68 (~r(elem!1, s(s(z)))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[4401, 11980, 11969])).
% 2.42/2.68 tff(11982,plain,
% 2.42/2.68 (~b(s(z), elem!1)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[11747, 11981, 372, 2615, 114, 2617, 6699, 1, 964])).
% 2.42/2.68 tff(11983,plain,
% 2.42/2.68 (r(s(z), elem!1)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[601, 11982, 11908])).
% 2.42/2.68 tff(11984,plain,
% 2.42/2.68 (~b(s(s(s(z))), z)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[6855, 11983, 309, 11969, 11978, 964, 11976, 2617, 15, 11975])).
% 2.42/2.68 tff(11985,plain,
% 2.42/2.68 (r(s(s(s(z))), z)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[1334, 58, 221, 11984])).
% 2.42/2.68 tff(11986,plain,
% 2.42/2.68 (~r(s(s(z)), s(s(s(z))))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[4806, 37, 11980, 11985])).
% 2.42/2.68 tff(11987,plain,
% 2.42/2.68 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(elem!1)))),
% 2.42/2.68 inference(monotonicity,[status(thm)],[11973])).
% 2.42/2.68 tff(11988,plain,
% 2.42/2.68 (b(s(s(z)), s(s(elem!1)))),
% 2.42/2.68 inference(modus_ponens,[status(thm)],[964, 11987])).
% 2.42/2.68 tff(11989,plain,
% 2.42/2.68 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(elem!1)))),
% 2.42/2.68 inference(monotonicity,[status(thm)],[11973])).
% 2.42/2.68 tff(11990,plain,
% 2.42/2.68 (b(s(s(s(z))), s(s(elem!1)))),
% 2.42/2.68 inference(modus_ponens,[status(thm)],[11975, 11989])).
% 2.42/2.68 tff(11991,plain,
% 2.42/2.68 (b(elem!1, s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 2.42/2.68 inference(monotonicity,[status(thm)],[11973])).
% 2.42/2.68 tff(11992,plain,
% 2.42/2.68 (~r(elem!1, s(s(s(z))))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[6474, 11985, 11969])).
% 2.42/2.68 tff(11993,plain,
% 2.42/2.68 (b(elem!1, s(s(s(z))))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[1279, 11992, 11976])).
% 2.42/2.68 tff(11994,plain,
% 2.42/2.68 (b(s(s(elem!1)), s(s(s(z))))),
% 2.42/2.68 inference(modus_ponens,[status(thm)],[11993, 11991])).
% 2.42/2.68 tff(11995,plain,
% 2.42/2.68 (~b(s(s(z)), s(s(s(z))))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[11865, 75, 11994, 11990, 11988])).
% 2.42/2.68 tff(11996,plain,
% 2.42/2.68 ($false),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[8252, 11995, 11986])).
% 2.42/2.68 tff(11997,plain,(b(s(s(elem!1)), elem!1) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (s(s(z)) = elem!1) | (~b(z, s(z))) | (~r(elem!1, s(z))) | r(z, elem!1) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.42/2.68 tff(11998,plain,
% 2.42/2.68 (b(s(s(elem!1)), elem!1)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[11997, 11902, 11390, 11903, 11726, 11642, 13, 9865])).
% 2.42/2.68 tff(11999,plain,
% 2.42/2.68 (~b(elem!1, z)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[4702, 11998, 9866, 11390, 9981])).
% 2.42/2.68 tff(12000,plain,
% 2.42/2.68 (r(elem!1, z)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[387, 11999, 9867])).
% 2.42/2.68 tff(12001,plain,
% 2.42/2.68 (~r(s(z), z)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[162, 12000, 11642])).
% 2.42/2.68 tff(12002,plain,
% 2.42/2.68 (b(s(z), z)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[169, 12001])).
% 2.42/2.68 tff(12003,plain,
% 2.42/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(z, elem!1)))),
% 2.42/2.68 inference(rewrite,[status(thm)],[])).
% 2.42/2.68 tff(12004,plain,
% 2.42/2.68 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~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)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(z, elem!1)))),
% 2.42/2.68 inference(rewrite,[status(thm)],[])).
% 2.42/2.68 tff(12005,plain,
% 2.42/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~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(X1, 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)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(z, elem!1))))),
% 2.42/2.68 inference(monotonicity,[status(thm)],[12004])).
% 2.42/2.68 tff(12006,plain,
% 2.42/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~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(X1, 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)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(z, elem!1)))),
% 2.42/2.68 inference(transitivity,[status(thm)],[12005, 12003])).
% 2.42/2.68 tff(12007,plain,
% 2.42/2.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.42/2.68 inference(quant_inst,[status(thm)],[])).
% 2.42/2.68 tff(12008,plain,
% 2.42/2.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(z, elem!1))),
% 2.42/2.68 inference(modus_ponens,[status(thm)],[12007, 12006])).
% 2.42/2.68 tff(12009,plain,
% 2.42/2.68 (~b(s(s(z)), z)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[12008, 75, 9866, 11726, 12002, 11390, 11902])).
% 2.42/2.68 tff(12010,plain,
% 2.42/2.68 (r(s(s(z)), z)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[202, 12009])).
% 2.42/2.68 tff(12011,plain,
% 2.42/2.68 (~r(elem!1, s(s(z)))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[4401, 12010, 12000])).
% 2.42/2.68 tff(12012,plain,
% 2.42/2.68 (~b(s(z), elem!1)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[11886, 12011, 11726, 11998, 11642, 9981, 12000, 11390, 9866])).
% 2.42/2.68 tff(12013,plain,
% 2.42/2.68 (r(s(z), elem!1)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[601, 12012, 11643])).
% 2.42/2.68 tff(12014,plain,
% 2.42/2.68 (~r(s(z), s(s(s(s(z)))))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[10214, 37, 12013, 9474])).
% 2.42/2.68 tff(12015,plain,
% 2.42/2.69 (b(s(z), s(s(s(s(z)))))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[489, 12014])).
% 2.42/2.69 tff(12016,plain,
% 2.42/2.69 (~b(s(s(s(s(z)))), z)),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[4839, 12015, 11726, 12002])).
% 2.42/2.69 tff(12017,plain,
% 2.42/2.69 (r(s(s(s(s(z)))), z)),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[1421, 58, 1143, 12016])).
% 2.42/2.69 tff(12018,plain,
% 2.42/2.69 (~r(s(s(s(s(z)))), s(z))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[10206, 37, 12013, 9474])).
% 2.42/2.69 tff(12019,plain,
% 2.42/2.69 (b(s(s(s(s(z)))), s(z))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[1406, 58, 483, 12018])).
% 2.42/2.69 tff(12020,plain,
% 2.42/2.69 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[3906, 12019, 11902, 12015])).
% 2.42/2.69 tff(12021,plain,
% 2.42/2.69 (r(s(s(z)), s(s(s(s(z)))))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[465, 12020])).
% 2.42/2.69 tff(12022,plain,
% 2.42/2.69 ($false),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[4419, 37, 12010, 12021, 12017])).
% 2.42/2.69 tff(12023,plain,(b(elem!1, s(z)) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.42/2.69 tff(12024,plain,
% 2.42/2.69 (r(z, elem!1)),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[12023, 14])).
% 2.42/2.69 tff(12025,plain,
% 2.42/2.69 (~(s(s(s(s(z)))) = elem!1)),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[8920, 14, 11389, 12024])).
% 2.42/2.69 tff(12026,plain,
% 2.42/2.69 (~(elem!1 = s(s(s(s(z)))))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[273, 12025])).
% 2.42/2.69 tff(12027,plain,
% 2.42/2.69 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.42/2.69 inference(monotonicity,[status(thm)],[8924])).
% 2.42/2.69 tff(12028,plain,
% 2.42/2.69 (r(s(s(s(s(z)))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 2.42/2.69 inference(symmetry,[status(thm)],[12027])).
% 2.42/2.69 tff(12029,plain,
% 2.42/2.69 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.42/2.69 inference(monotonicity,[status(thm)],[8926])).
% 2.42/2.69 tff(12030,plain,
% 2.42/2.69 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 2.42/2.69 inference(transitivity,[status(thm)],[12029, 12028])).
% 2.42/2.69 tff(12031,plain,
% 2.42/2.69 ((~r(s(s(s(elem!1))), s(s(elem!1)))) <=> (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 2.42/2.69 inference(monotonicity,[status(thm)],[12030])).
% 2.42/2.69 tff(12032,plain,
% 2.42/2.69 (r(s(s(s(elem!1))), elem!1)),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[702, 93, 9473])).
% 2.42/2.69 tff(12033,plain,
% 2.42/2.69 (~b(s(s(s(z))), elem!1)),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[11529, 909, 1])).
% 2.42/2.69 tff(12034,plain,
% 2.42/2.69 (r(z, elem!1) <=> r(z, s(s(elem!1)))),
% 2.42/2.69 inference(monotonicity,[status(thm)],[1602])).
% 2.42/2.69 tff(12035,plain,
% 2.42/2.69 (r(z, s(s(elem!1)))),
% 2.42/2.69 inference(modus_ponens,[status(thm)],[300, 12034])).
% 2.42/2.69 tff(12036,plain,
% 2.42/2.69 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(elem!1)))),
% 2.42/2.69 inference(monotonicity,[status(thm)],[1602])).
% 2.42/2.69 tff(12037,plain,
% 2.42/2.69 (r(s(s(s(z))), elem!1)),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[1115, 2267, 100])).
% 2.42/2.69 tff(12038,plain,
% 2.42/2.69 (r(s(s(s(z))), s(s(elem!1)))),
% 2.42/2.69 inference(modus_ponens,[status(thm)],[12037, 12036])).
% 2.42/2.69 tff(12039,plain,
% 2.42/2.69 (~r(s(s(s(z))), z)),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[8224, 37, 12038, 12035])).
% 2.42/2.69 tff(12040,plain,
% 2.42/2.69 (b(s(s(s(z))), z)),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[1334, 58, 221, 12039])).
% 2.42/2.69 tff(12041,plain,
% 2.42/2.69 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.42/2.69 inference(monotonicity,[status(thm)],[1602])).
% 2.42/2.69 tff(12042,plain,
% 2.42/2.69 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.42/2.69 inference(modus_ponens,[status(thm)],[698, 12041])).
% 2.42/2.69 tff(12043,plain,
% 2.42/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.42/2.69 inference(rewrite,[status(thm)],[])).
% 2.42/2.69 tff(12044,plain,
% 2.42/2.69 (((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.42/2.69 inference(rewrite,[status(thm)],[])).
% 2.42/2.69 tff(12045,plain,
% 2.42/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))))),
% 2.42/2.69 inference(monotonicity,[status(thm)],[12044])).
% 2.42/2.69 tff(12046,plain,
% 2.42/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 2.42/2.69 inference(transitivity,[status(thm)],[12045, 12043])).
% 2.42/2.69 tff(12047,plain,
% 2.42/2.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.42/2.69 inference(quant_inst,[status(thm)],[])).
% 2.42/2.69 tff(12048,plain,
% 2.42/2.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 2.42/2.69 inference(modus_ponens,[status(thm)],[12047, 12046])).
% 2.42/2.69 tff(12049,plain,
% 2.42/2.69 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[12048, 37, 12038, 12042])).
% 2.42/2.69 tff(12050,plain,
% 2.42/2.69 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[575, 12049])).
% 2.42/2.69 tff(12051,plain,
% 2.42/2.69 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[11328, 37, 12038, 12042])).
% 2.42/2.69 tff(12052,plain,
% 2.42/2.69 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[2898, 12051])).
% 2.42/2.69 tff(12053,plain,
% 2.42/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.42/2.69 inference(rewrite,[status(thm)],[])).
% 2.42/2.69 tff(12054,plain,
% 2.42/2.69 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.42/2.69 inference(rewrite,[status(thm)],[])).
% 2.42/2.69 tff(12055,plain,
% 2.42/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 2.42/2.69 inference(monotonicity,[status(thm)],[12054])).
% 2.42/2.69 tff(12056,plain,
% 2.42/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.42/2.69 inference(transitivity,[status(thm)],[12055, 12053])).
% 2.42/2.69 tff(12057,plain,
% 2.42/2.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 2.42/2.69 inference(quant_inst,[status(thm)],[])).
% 2.42/2.69 tff(12058,plain,
% 2.42/2.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 2.42/2.69 inference(modus_ponens,[status(thm)],[12057, 12056])).
% 2.42/2.69 tff(12059,plain,
% 2.42/2.69 ($false),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[12058, 75, 12052, 12050, 12040, 7167])).
% 2.42/2.69 tff(12060,plain,((~(elem!1 = s(s(elem!1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | b(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.42/2.69 tff(12061,plain,
% 2.42/2.69 (~(elem!1 = s(s(elem!1)))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[12060, 12033, 9473, 300])).
% 2.42/2.69 tff(12062,plain,
% 2.42/2.69 (~(s(s(elem!1)) = elem!1)),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[2555, 12061])).
% 2.42/2.69 tff(12063,plain,
% 2.42/2.69 (r(s(s(elem!1)), elem!1)),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[2673, 12062, 1])).
% 2.42/2.69 tff(12064,plain,
% 2.42/2.69 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[10371, 37, 12063, 12032])).
% 2.42/2.69 tff(12065,plain,
% 2.42/2.69 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.42/2.69 inference(modus_ponens,[status(thm)],[12064, 12031])).
% 2.42/2.69 tff(12066,plain,
% 2.42/2.69 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[2898, 12065])).
% 2.42/2.69 tff(12067,plain,
% 2.42/2.69 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.42/2.69 inference(modus_ponens,[status(thm)],[12066, 8930])).
% 2.42/2.69 tff(12068,plain,
% 2.42/2.69 (b(s(s(s(s(z)))), z) <=> b(s(s(s(elem!1))), z)),
% 2.42/2.69 inference(monotonicity,[status(thm)],[8925])).
% 2.42/2.69 tff(12069,plain,
% 2.42/2.69 (~r(s(s(s(s(z)))), z)),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[7173, 37, 300, 9473])).
% 2.42/2.69 tff(12070,plain,
% 2.42/2.69 (b(s(s(s(s(z)))), z)),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[1421, 58, 1143, 12069])).
% 2.42/2.69 tff(12071,plain,
% 2.42/2.69 (b(s(s(s(elem!1))), z)),
% 2.42/2.69 inference(modus_ponens,[status(thm)],[12070, 12068])).
% 2.42/2.69 tff(12072,plain,
% 2.42/2.69 (~r(s(s(elem!1)), z)),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[5114, 37, 300, 12063])).
% 2.42/2.69 tff(12073,plain,
% 2.42/2.69 (b(s(s(elem!1)), z)),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[2696, 12072])).
% 2.42/2.69 tff(12074,plain,
% 2.42/2.69 (~r(z, s(s(elem!1)))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[7137, 37, 300, 12063])).
% 2.42/2.69 tff(12075,plain,
% 2.42/2.69 (b(z, s(s(elem!1)))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[6314, 12074])).
% 2.42/2.69 tff(12076,plain,
% 2.42/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(X1, 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)))),
% 2.42/2.69 inference(rewrite,[status(thm)],[])).
% 2.42/2.69 tff(12077,plain,
% 2.42/2.69 (((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))),
% 2.42/2.69 inference(rewrite,[status(thm)],[])).
% 2.42/2.69 tff(12078,plain,
% 2.42/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(elem!1))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))))),
% 2.42/2.69 inference(monotonicity,[status(thm)],[12077])).
% 2.42/2.69 tff(12079,plain,
% 2.42/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(elem!1))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)))),
% 2.42/2.69 inference(transitivity,[status(thm)],[12078, 12076])).
% 2.42/2.69 tff(12080,plain,
% 2.42/2.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(elem!1))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.42/2.69 inference(quant_inst,[status(thm)],[])).
% 2.42/2.69 tff(12081,plain,
% 2.42/2.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))),
% 2.42/2.69 inference(modus_ponens,[status(thm)],[12080, 12079])).
% 2.42/2.69 tff(12082,plain,
% 2.42/2.69 ($false),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[12081, 75, 12075, 12073, 12071, 12067])).
% 2.42/2.69 tff(12083,plain,((~(s(z) = elem!1)) | (~r(z, elem!1)) | b(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.42/2.69 tff(12084,plain,
% 2.42/2.69 (~(s(z) = elem!1)),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[12083, 12024, 1])).
% 2.42/2.69 tff(12085,plain,
% 2.42/2.69 (~(elem!1 = s(z))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[111, 12084])).
% 2.42/2.69 tff(12086,plain,
% 2.42/2.69 (r(elem!1, s(z))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[89, 12085, 14])).
% 2.42/2.69 tff(12087,plain,
% 2.42/2.69 (~r(elem!1, s(s(s(s(z)))))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[8127, 12086, 12024])).
% 2.42/2.69 tff(12088,plain,
% 2.42/2.69 (b(elem!1, s(s(s(s(z)))))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[278, 12087, 12026])).
% 2.42/2.69 tff(12089,plain,
% 2.42/2.69 (~r(z, s(s(s(s(z)))))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[7164, 37, 12024, 9473])).
% 2.42/2.69 tff(12090,plain,
% 2.42/2.69 ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z)))))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[1515, 58, 12089])).
% 2.42/2.69 tff(12091,plain,
% 2.42/2.69 (b(z, s(s(s(s(z)))))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[12090, 1503])).
% 2.42/2.69 tff(12092,plain,
% 2.42/2.69 (~r(s(s(s(s(z)))), z)),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[7173, 37, 12024, 9473])).
% 2.42/2.69 tff(12093,plain,
% 2.42/2.69 (b(s(s(s(s(z)))), z)),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[1421, 58, 1143, 12092])).
% 2.42/2.69 tff(12094,plain,
% 2.42/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.42/2.69 inference(rewrite,[status(thm)],[])).
% 2.42/2.69 tff(12095,plain,
% 2.42/2.69 (((~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.42/2.69 inference(rewrite,[status(thm)],[])).
% 2.42/2.69 tff(12096,plain,
% 2.42/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))))),
% 2.42/2.69 inference(monotonicity,[status(thm)],[12095])).
% 2.42/2.69 tff(12097,plain,
% 2.42/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.42/2.69 inference(transitivity,[status(thm)],[12096, 12094])).
% 2.42/2.69 tff(12098,plain,
% 2.42/2.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, elem!1)))),
% 2.42/2.69 inference(quant_inst,[status(thm)],[])).
% 2.42/2.69 tff(12099,plain,
% 2.42/2.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))),
% 2.42/2.69 inference(modus_ponens,[status(thm)],[12098, 12097])).
% 2.42/2.69 tff(12100,plain,
% 2.42/2.69 (~b(z, elem!1)),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[12099, 75, 12088, 12093, 12091])).
% 2.42/2.69 tff(12101,plain,
% 2.42/2.69 (~b(s(z), z)),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[10345, 12100, 9473, 12086, 12024, 12088])).
% 2.42/2.69 tff(12102,plain,
% 2.42/2.69 (~(z = elem!1)),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[9484, 12092, 9473])).
% 2.42/2.69 tff(12103,plain,
% 2.42/2.69 (~(elem!1 = z)),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[304, 12102])).
% 2.42/2.69 tff(12104,plain,
% 2.42/2.69 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, z))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.42/2.69 inference(rewrite,[status(thm)],[])).
% 2.42/2.69 tff(12105,plain,
% 2.42/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))))),
% 2.42/2.69 inference(monotonicity,[status(thm)],[12104])).
% 2.42/2.69 tff(12106,plain,
% 2.42/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.42/2.70 inference(transitivity,[status(thm)],[12105, 10329])).
% 2.42/2.70 tff(12107,plain,
% 2.42/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, z)))),
% 2.42/2.70 inference(quant_inst,[status(thm)],[])).
% 2.42/2.70 tff(12108,plain,
% 2.42/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))),
% 2.42/2.70 inference(modus_ponens,[status(thm)],[12107, 12106])).
% 2.42/2.70 tff(12109,plain,
% 2.42/2.70 (~b(elem!1, z)),
% 2.42/2.70 inference(unit_resolution,[status(thm)],[12108, 75, 12088, 12093, 12091])).
% 2.42/2.70 tff(12110,plain,
% 2.42/2.70 (r(elem!1, z)),
% 2.42/2.70 inference(unit_resolution,[status(thm)],[387, 12109, 12103])).
% 2.42/2.70 tff(12111,plain,
% 2.42/2.70 (~r(s(z), z)),
% 2.42/2.70 inference(unit_resolution,[status(thm)],[162, 12110, 12086])).
% 2.42/2.70 tff(12112,plain,
% 2.42/2.70 ($false),
% 2.42/2.70 inference(unit_resolution,[status(thm)],[169, 12111, 12101])).
% 2.42/2.70 tff(12113,plain,(b(elem!1, s(z)) | b(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.42/2.70 tff(12114,plain,
% 2.42/2.70 (b(elem!1, s(z))),
% 2.42/2.70 inference(unit_resolution,[status(thm)],[12113, 1])).
% 2.42/2.70 tff(12115,plain,
% 2.42/2.70 (~(s(z) = elem!1)),
% 2.42/2.70 inference(unit_resolution,[status(thm)],[1393, 12114])).
% 2.42/2.70 tff(12116,plain,
% 2.42/2.70 (~(z = elem!1)),
% 2.42/2.70 inference(unit_resolution,[status(thm)],[11002, 12114, 9473])).
% 2.42/2.70 tff(12117,plain,
% 2.42/2.70 (~r(s(s(s(s(z)))), s(z))),
% 2.42/2.70 inference(unit_resolution,[status(thm)],[10206, 37, 588, 9473])).
% 2.42/2.70 tff(12118,plain,
% 2.42/2.70 (b(s(s(s(s(z)))), s(z))),
% 2.42/2.70 inference(unit_resolution,[status(thm)],[1406, 58, 483, 12117])).
% 2.42/2.70 tff(12119,plain,
% 2.42/2.70 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 2.42/2.70 inference(unit_resolution,[status(thm)],[8898, 11389])).
% 2.42/2.70 tff(12120,plain,
% 2.42/2.70 (~r(s(z), s(s(s(s(z)))))),
% 2.42/2.70 inference(unit_resolution,[status(thm)],[10214, 37, 588, 9473])).
% 2.42/2.70 tff(12121,plain,
% 2.42/2.70 (~(s(s(s(s(z)))) = elem!1)),
% 2.42/2.70 inference(unit_resolution,[status(thm)],[3664, 12120, 588])).
% 2.42/2.70 tff(12122,plain,
% 2.42/2.70 (~(elem!1 = s(s(s(s(z)))))),
% 2.42/2.70 inference(unit_resolution,[status(thm)],[273, 12121])).
% 2.42/2.70 tff(12123,plain,
% 2.42/2.70 (b(s(z), s(s(s(s(z)))))),
% 2.42/2.70 inference(unit_resolution,[status(thm)],[489, 12120])).
% 2.42/2.70 tff(12124,plain,
% 2.42/2.70 (~b(elem!1, s(s(s(s(z)))))),
% 2.42/2.70 inference(unit_resolution,[status(thm)],[10456, 75, 12114, 12123, 12118])).
% 2.42/2.70 tff(12125,plain,
% 2.42/2.70 (r(elem!1, s(s(s(s(z)))))),
% 2.42/2.70 inference(unit_resolution,[status(thm)],[278, 12124, 12122])).
% 2.42/2.70 tff(12126,plain,
% 2.42/2.70 (~b(elem!1, s(s(elem!1)))),
% 2.42/2.70 inference(unit_resolution,[status(thm)],[5690, 11303, 12114, 588])).
% 2.42/2.70 tff(12127,plain,
% 2.42/2.70 (r(elem!1, s(s(elem!1)))),
% 2.42/2.70 inference(unit_resolution,[status(thm)],[1617, 12126, 1630])).
% 2.42/2.70 tff(12128,plain,
% 2.42/2.70 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.42/2.70 inference(unit_resolution,[status(thm)],[3811, 12127, 12125])).
% 2.42/2.70 tff(12129,plain,
% 2.42/2.70 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.42/2.70 inference(unit_resolution,[status(thm)],[1660, 12128, 12119])).
% 2.42/2.70 tff(12130,plain,
% 2.42/2.70 (~r(s(z), s(s(elem!1)))),
% 2.42/2.70 inference(unit_resolution,[status(thm)],[3753, 11303, 588])).
% 2.42/2.70 tff(12131,plain,
% 2.42/2.70 (b(s(z), s(s(elem!1)))),
% 2.42/2.70 inference(unit_resolution,[status(thm)],[1890, 12130])).
% 2.42/2.70 tff(12132,plain,
% 2.42/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), s(z))) | (~b(s(s(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(X1, 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(z)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.52/2.70 inference(rewrite,[status(thm)],[])).
% 2.52/2.70 tff(12133,plain,
% 2.52/2.70 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.52/2.70 inference(rewrite,[status(thm)],[])).
% 2.52/2.70 tff(12134,plain,
% 2.52/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))))),
% 2.52/2.70 inference(monotonicity,[status(thm)],[12133])).
% 2.52/2.70 tff(12135,plain,
% 2.52/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.52/2.70 inference(transitivity,[status(thm)],[12134, 12132])).
% 2.52/2.70 tff(12136,plain,
% 2.52/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(elem!1)))))),
% 2.52/2.70 inference(quant_inst,[status(thm)],[])).
% 2.52/2.70 tff(12137,plain,
% 2.52/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))),
% 2.52/2.70 inference(modus_ponens,[status(thm)],[12136, 12135])).
% 2.52/2.70 tff(12138,plain,
% 2.52/2.70 ($false),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[12137, 75, 12131, 12123, 12129, 12118])).
% 2.52/2.70 tff(12139,plain,((elem!1 = s(s(elem!1))) | (~r(s(z), elem!1)) | b(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.52/2.70 tff(12140,plain,
% 2.52/2.70 (elem!1 = s(s(elem!1))),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[12139, 588, 1])).
% 2.52/2.70 tff(12141,plain,
% 2.52/2.70 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(elem!1)))),
% 2.52/2.70 inference(monotonicity,[status(thm)],[12140])).
% 2.52/2.70 tff(12142,plain,
% 2.52/2.70 (b(s(s(z)), s(s(elem!1)))),
% 2.52/2.70 inference(modus_ponens,[status(thm)],[11389, 12141])).
% 2.52/2.70 tff(12143,plain,
% 2.52/2.70 (b(elem!1, s(z)) <=> b(s(s(elem!1)), s(z))),
% 2.52/2.70 inference(monotonicity,[status(thm)],[12140])).
% 2.52/2.70 tff(12144,plain,
% 2.52/2.70 (b(s(s(elem!1)), s(z))),
% 2.52/2.70 inference(modus_ponens,[status(thm)],[12114, 12143])).
% 2.52/2.70 tff(12145,plain,
% 2.52/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.52/2.70 inference(rewrite,[status(thm)],[])).
% 2.52/2.70 tff(12146,plain,
% 2.52/2.70 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1))))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.52/2.70 inference(rewrite,[status(thm)],[])).
% 2.52/2.70 tff(12147,plain,
% 2.52/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 2.52/2.70 inference(monotonicity,[status(thm)],[12146])).
% 2.52/2.70 tff(12148,plain,
% 2.52/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.52/2.70 inference(transitivity,[status(thm)],[12147, 12145])).
% 2.52/2.70 tff(12149,plain,
% 2.52/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.52/2.70 inference(quant_inst,[status(thm)],[])).
% 2.52/2.70 tff(12150,plain,
% 2.52/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 2.52/2.70 inference(modus_ponens,[status(thm)],[12149, 12148])).
% 2.52/2.70 tff(12151,plain,
% 2.52/2.70 ($false),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[12150, 75, 1457, 309, 578, 982, 7613])).
% 2.52/2.70 tff(12152,plain,((~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.70 tff(12153,plain,
% 2.52/2.70 (~b(s(s(z)), s(z))),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[12152, 12144, 12123, 12118, 12142])).
% 2.52/2.70 tff(12154,plain,
% 2.52/2.70 (r(s(s(z)), s(z))),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[153, 12153])).
% 2.52/2.70 tff(12155,plain,
% 2.52/2.70 (b(z, elem!1) <=> b(z, s(s(elem!1)))),
% 2.52/2.70 inference(monotonicity,[status(thm)],[12140])).
% 2.52/2.70 tff(12156,plain,
% 2.52/2.70 (b(z, s(s(elem!1)))),
% 2.52/2.70 inference(modus_ponens,[status(thm)],[1518, 12155])).
% 2.52/2.70 tff(12157,plain,
% 2.52/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.52/2.70 inference(rewrite,[status(thm)],[])).
% 2.52/2.70 tff(12158,plain,
% 2.52/2.70 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.52/2.70 inference(rewrite,[status(thm)],[])).
% 2.52/2.70 tff(12159,plain,
% 2.52/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(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(X1, 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(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 2.52/2.70 inference(monotonicity,[status(thm)],[12158])).
% 2.52/2.70 tff(12160,plain,
% 2.52/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(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(X1, 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(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.52/2.70 inference(transitivity,[status(thm)],[12159, 12157])).
% 2.52/2.70 tff(12161,plain,
% 2.52/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))),
% 2.52/2.70 inference(quant_inst,[status(thm)],[])).
% 2.52/2.70 tff(12162,plain,
% 2.52/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 2.52/2.70 inference(modus_ponens,[status(thm)],[12161, 12160])).
% 2.52/2.70 tff(12163,plain,
% 2.52/2.70 ($false),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[12162, 75, 1457, 372, 578, 982, 1893])).
% 2.52/2.70 tff(12164,plain,((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.70 tff(12165,plain,
% 2.52/2.70 (~b(z, s(z))),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[12164, 12144, 12123, 12118, 12156])).
% 2.52/2.70 tff(12166,plain,
% 2.52/2.70 (r(z, s(z))),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[187, 12165])).
% 2.52/2.70 tff(12167,plain,
% 2.52/2.70 (~r(z, s(s(z)))),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[6456, 12166, 12154])).
% 2.52/2.70 tff(12168,plain,
% 2.52/2.70 (b(z, s(s(z)))),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[351, 12167])).
% 2.52/2.70 tff(12169,plain,
% 2.52/2.70 (~(s(s(s(z))) = elem!1)),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[1612, 12140])).
% 2.52/2.70 tff(12170,plain,
% 2.52/2.70 (~(elem!1 = s(s(s(z))))),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[1033, 12169])).
% 2.52/2.70 tff(12171,plain,
% 2.52/2.70 (~(s(s(z)) = s(elem!1))),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[3261, 12115])).
% 2.52/2.70 tff(12172,plain,
% 2.52/2.70 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[4541, 12171])).
% 2.52/2.70 tff(12173,plain,
% 2.52/2.70 (r(s(z), elem!1) <=> r(s(z), s(s(elem!1)))),
% 2.52/2.70 inference(monotonicity,[status(thm)],[12140])).
% 2.52/2.70 tff(12174,plain,
% 2.52/2.70 (r(s(z), s(s(elem!1)))),
% 2.52/2.70 inference(modus_ponens,[status(thm)],[588, 12173])).
% 2.52/2.70 tff(12175,plain,
% 2.52/2.70 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[3632, 100, 1602])).
% 2.52/2.70 tff(12176,plain,
% 2.52/2.70 (r(s(s(s(z))), s(s(elem!1)))),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[62, 12175, 16])).
% 2.52/2.70 tff(12177,plain,
% 2.52/2.70 (r(s(s(s(z))), elem!1)),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[1115, 100, 2267])).
% 2.52/2.70 tff(12178,plain,
% 2.52/2.70 (~b(s(z), s(s(s(z))))),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[10528, 12177, 9473, 578])).
% 2.52/2.70 tff(12179,plain,
% 2.52/2.70 (r(s(z), s(s(s(z))))),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[1263, 12178])).
% 2.52/2.70 tff(12180,plain,
% 2.52/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))))),
% 2.52/2.70 inference(rewrite,[status(thm)],[])).
% 2.52/2.70 tff(12181,plain,
% 2.52/2.70 (((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))))),
% 2.52/2.70 inference(rewrite,[status(thm)],[])).
% 2.52/2.70 tff(12182,plain,
% 2.52/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z)))))))),
% 2.52/2.70 inference(monotonicity,[status(thm)],[12181])).
% 2.52/2.70 tff(12183,plain,
% 2.52/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))))),
% 2.52/2.70 inference(transitivity,[status(thm)],[12182, 12180])).
% 2.52/2.70 tff(12184,plain,
% 2.52/2.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))))),
% 2.52/2.70 inference(quant_inst,[status(thm)],[])).
% 2.52/2.70 tff(12185,plain,
% 2.52/2.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(s(z)))))),
% 2.52/2.70 inference(modus_ponens,[status(thm)],[12184, 12183])).
% 2.52/2.70 tff(12186,plain,
% 2.52/2.70 ($false),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[12185, 37, 1871, 12179, 12176])).
% 2.52/2.70 tff(12187,plain,(b(s(s(s(z))), elem!1) | (~r(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))) | (s(s(s(z))) = s(s(elem!1))) | (~(elem!1 = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.70 tff(12188,plain,
% 2.52/2.70 (b(s(s(s(z))), elem!1)),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[12187, 12174, 12123, 12172, 12140])).
% 2.52/2.70 tff(12189,plain,
% 2.52/2.70 (r(elem!1, z) <=> r(s(s(elem!1)), z)),
% 2.52/2.70 inference(monotonicity,[status(thm)],[1602])).
% 2.52/2.70 tff(12190,plain,
% 2.52/2.70 (~(z = elem!1)),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[11002, 1391, 9473])).
% 2.52/2.70 tff(12191,plain,
% 2.52/2.70 (~(elem!1 = z)),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[304, 12190])).
% 2.52/2.70 tff(12192,plain,
% 2.52/2.70 (~(s(s(z)) = elem!1)),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[1013, 9278])).
% 2.52/2.70 tff(12193,plain,
% 2.52/2.70 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[6569, 1561, 12192, 1391, 1518, 3195])).
% 2.52/2.70 tff(12194,plain,
% 2.52/2.70 (b(s(s(z)), s(s(s(s(z)))))),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[465, 12193])).
% 2.52/2.70 tff(12195,plain,
% 2.52/2.70 (~b(s(s(z)), s(z))),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[3906, 12194, 578, 982])).
% 2.52/2.70 tff(12196,plain,
% 2.52/2.70 (r(s(s(z)), s(z))),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[153, 12195])).
% 2.52/2.71 tff(12197,plain,
% 2.52/2.71 (~r(s(s(z)), z)),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[6161, 37, 506, 12196])).
% 2.52/2.71 tff(12198,plain,
% 2.52/2.71 (b(s(s(z)), z)),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[202, 12197])).
% 2.52/2.71 tff(12199,plain,
% 2.52/2.71 (~b(elem!1, z)),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[6452, 12198, 964, 1518])).
% 2.52/2.71 tff(12200,plain,
% 2.52/2.71 (r(elem!1, z)),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[387, 12199, 12191])).
% 2.52/2.71 tff(12201,plain,
% 2.52/2.71 (r(s(s(elem!1)), z)),
% 2.52/2.71 inference(modus_ponens,[status(thm)],[12200, 12189])).
% 2.52/2.71 tff(12202,plain,
% 2.52/2.71 (((~![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)))))),
% 2.52/2.71 inference(rewrite,[status(thm)],[])).
% 2.52/2.71 tff(12203,plain,
% 2.52/2.71 (((~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)))))),
% 2.52/2.71 inference(rewrite,[status(thm)],[])).
% 2.52/2.71 tff(12204,plain,
% 2.52/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(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))))))),
% 2.52/2.71 inference(monotonicity,[status(thm)],[12203])).
% 2.52/2.71 tff(12205,plain,
% 2.52/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(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)))))),
% 2.52/2.71 inference(transitivity,[status(thm)],[12204, 12202])).
% 2.52/2.71 tff(12206,plain,
% 2.52/2.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))))),
% 2.52/2.71 inference(quant_inst,[status(thm)],[])).
% 2.52/2.71 tff(12207,plain,
% 2.52/2.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1))))),
% 2.52/2.71 inference(modus_ponens,[status(thm)],[12206, 12205])).
% 2.52/2.71 tff(12208,plain,
% 2.52/2.71 ($false),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[12207, 37, 1561, 1871, 12201])).
% 2.52/2.71 tff(12209,plain,((~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~(elem!1 = s(s(elem!1)))) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~r(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.71 tff(12210,plain,
% 2.52/2.71 (~r(s(z), z)),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[12209, 12166, 12140, 11389, 1518, 12174, 12123, 12118, 12114, 12125])).
% 2.52/2.71 tff(12211,plain,
% 2.52/2.71 (b(s(z), z)),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[169, 12210])).
% 2.52/2.71 tff(12212,plain,
% 2.52/2.71 (~(elem!1 = z)),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[304, 12116])).
% 2.52/2.71 tff(12213,plain,
% 2.52/2.71 (~b(elem!1, z)),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[6636, 12211, 12114, 1518])).
% 2.52/2.71 tff(12214,plain,
% 2.52/2.71 (r(elem!1, z)),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[387, 12213, 12212])).
% 2.52/2.71 tff(12215,plain,
% 2.52/2.71 (~b(s(s(z)), z)),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[6504, 12214, 11389, 1518, 12154, 12211, 12188, 12170, 12168])).
% 2.52/2.71 tff(12216,plain,
% 2.52/2.71 (r(s(s(z)), z)),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[202, 12215])).
% 2.52/2.71 tff(12217,plain,
% 2.52/2.71 ($false),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[6161, 37, 12166, 12154, 12216])).
% 2.52/2.71 tff(12218,plain,((~r(s(z), elem!1)) | (~b(z, elem!1)) | b(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.52/2.71 tff(12219,plain,
% 2.52/2.71 (~r(s(z), elem!1)),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[12218, 1518, 1])).
% 2.52/2.71 tff(12220,plain,
% 2.52/2.71 (b(s(z), elem!1)),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[601, 12219, 12115])).
% 2.52/2.71 tff(12221,plain,
% 2.52/2.71 (~b(s(z), z)),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[1526, 12220, 12114, 1518])).
% 2.52/2.71 tff(12222,plain,
% 2.52/2.71 (r(s(z), z)),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[169, 12221])).
% 2.52/2.71 tff(12223,plain,
% 2.52/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 2.52/2.71 inference(rewrite,[status(thm)],[])).
% 2.52/2.71 tff(12224,plain,
% 2.52/2.71 (((~b(s(z), elem!1)) | (~b(s(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), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 2.52/2.71 inference(rewrite,[status(thm)],[])).
% 2.52/2.71 tff(12225,plain,
% 2.52/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))))),
% 2.52/2.71 inference(monotonicity,[status(thm)],[12224])).
% 2.52/2.71 tff(12226,plain,
% 2.52/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 2.52/2.71 inference(transitivity,[status(thm)],[12225, 12223])).
% 2.52/2.71 tff(12227,plain,
% 2.52/2.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))))),
% 2.52/2.71 inference(quant_inst,[status(thm)],[])).
% 2.52/2.71 tff(12228,plain,
% 2.52/2.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))),
% 2.52/2.71 inference(modus_ponens,[status(thm)],[12227, 12226])).
% 2.52/2.71 tff(12229,plain,
% 2.52/2.71 (~b(s(z), s(s(z)))),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[12228, 75, 12220, 12114, 11389])).
% 2.52/2.71 tff(12230,plain,
% 2.52/2.71 (r(s(z), s(s(z)))),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[416, 12229])).
% 2.52/2.71 tff(12231,plain,
% 2.52/2.71 (~b(s(s(z)), z)),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[6132, 75, 1518, 12220, 12114, 11389])).
% 2.52/2.71 tff(12232,plain,
% 2.52/2.71 (r(s(s(z)), z)),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[202, 12231])).
% 2.52/2.71 tff(12233,plain,
% 2.52/2.71 ($false),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[2015, 12232, 12230, 12222])).
% 2.52/2.71 tff(12234,plain,((~b(z, elem!1)) | b(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.52/2.71 tff(12235,plain,
% 2.52/2.71 (~b(z, elem!1)),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[12234, 1])).
% 2.52/2.71 tff(12236,plain,
% 2.52/2.71 (r(z, elem!1)),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[298, 12235, 12116])).
% 2.52/2.71 tff(12237,plain,
% 2.52/2.71 (~r(s(z), elem!1)),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[10304, 12236, 9473])).
% 2.52/2.71 tff(12238,plain,
% 2.52/2.71 (b(s(z), elem!1)),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[601, 12237, 12115])).
% 2.52/2.71 tff(12239,plain,
% 2.52/2.71 (~b(s(s(z)), s(z))),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[7471, 75, 12238, 12114, 11389])).
% 2.52/2.71 tff(12240,plain,
% 2.52/2.71 (r(s(s(z)), s(z))),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[153, 12239])).
% 2.52/2.71 tff(12241,plain,
% 2.52/2.71 (~r(z, s(s(s(s(z)))))),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[7164, 37, 300, 9473])).
% 2.52/2.71 tff(12242,plain,
% 2.52/2.71 ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z)))))),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[1515, 58, 12241])).
% 2.52/2.71 tff(12243,plain,
% 2.52/2.71 (b(z, s(s(s(s(z)))))),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[12242, 1503])).
% 2.52/2.71 tff(12244,plain,
% 2.52/2.71 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[3884, 37, 9473, 2647])).
% 2.52/2.71 tff(12245,plain,
% 2.52/2.71 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[1660, 12244, 1011])).
% 2.52/2.71 tff(12246,plain,
% 2.52/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.52/2.71 inference(rewrite,[status(thm)],[])).
% 2.52/2.71 tff(12247,plain,
% 2.52/2.71 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.52/2.71 inference(rewrite,[status(thm)],[])).
% 2.52/2.71 tff(12248,plain,
% 2.52/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))))),
% 2.52/2.71 inference(monotonicity,[status(thm)],[12247])).
% 2.52/2.71 tff(12249,plain,
% 2.52/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.52/2.71 inference(transitivity,[status(thm)],[12248, 12246])).
% 2.52/2.71 tff(12250,plain,
% 2.52/2.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), z)))),
% 2.52/2.71 inference(quant_inst,[status(thm)],[])).
% 2.52/2.71 tff(12251,plain,
% 2.52/2.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))),
% 2.52/2.71 inference(modus_ponens,[status(thm)],[12250, 12249])).
% 2.52/2.71 tff(12252,plain,
% 2.52/2.71 ($false),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[12251, 75, 12245, 5177, 12070, 12243])).
% 2.52/2.71 tff(12253,plain,((~r(s(s(elem!1)), elem!1)) | (s(s(elem!1)) = s(s(s(s(z))))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.71 tff(12254,plain,
% 2.52/2.71 (~r(s(s(elem!1)), elem!1)),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[12253, 12119, 12236])).
% 2.52/2.71 tff(12255,plain,
% 2.52/2.71 (s(s(elem!1)) = elem!1),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[2673, 12254, 1])).
% 2.52/2.71 tff(12256,plain,
% 2.52/2.71 (elem!1 = s(s(elem!1))),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[2555, 12255])).
% 2.52/2.71 tff(12257,plain,
% 2.52/2.71 (b(s(s(s(z))), elem!1)),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[12060, 12256, 9473, 12236])).
% 2.52/2.71 tff(12258,plain,
% 2.52/2.71 (~b(s(s(s(z))), s(z))),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[11174, 75, 12238, 12114, 12257])).
% 2.52/2.71 tff(12259,plain,
% 2.52/2.71 (r(s(s(s(z))), s(z))),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[1081, 12258])).
% 2.52/2.71 tff(12260,plain,
% 2.52/2.71 (~b(s(s(z)), s(s(s(z))))),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[7482, 75, 12238, 12114, 11389, 12257])).
% 2.52/2.71 tff(12261,plain,
% 2.52/2.71 (r(s(s(z)), s(s(s(z))))),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[8252, 12260])).
% 2.52/2.71 tff(12262,plain,
% 2.52/2.71 ($false),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[6502, 12261, 12259, 12240])).
% 2.52/2.71 tff(12263,plain,(b(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.52/2.71 tff(12264,plain,
% 2.52/2.71 (b(s(s(z)), elem!1)),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[10351, 14])).
% 2.52/2.71 tff(12265,plain,
% 2.52/2.71 (~(s(s(s(s(z)))) = elem!1)),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[8920, 14, 12264, 12024])).
% 2.52/2.71 tff(12266,plain,
% 2.52/2.71 (~(elem!1 = s(s(s(s(z)))))),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[273, 12265])).
% 2.52/2.71 tff(12267,plain,
% 2.52/2.71 ((s(s(s(s(s(s(s(z))))))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(s(s(s(z))))))))),
% 2.52/2.71 inference(symmetry,[status(thm)],[3309])).
% 2.52/2.71 tff(12268,plain,
% 2.52/2.71 ((~(s(s(s(s(s(s(s(z))))))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(s(s(s(s(z)))))))))),
% 2.52/2.71 inference(monotonicity,[status(thm)],[12267])).
% 2.52/2.71 tff(12269,plain,
% 2.52/2.71 (~(s(s(z)) = s(s(s(s(s(s(s(z))))))))),
% 2.52/2.71 inference(modus_ponens,[status(thm)],[1045, 12268])).
% 2.52/2.71 tff(12270,plain,
% 2.52/2.71 (~r(elem!1, s(s(s(s(z)))))),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[8127, 114, 300])).
% 2.52/2.71 tff(12271,plain,
% 2.52/2.71 (b(elem!1, s(s(s(s(z)))))),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[278, 12270, 860])).
% 2.52/2.71 tff(12272,plain,
% 2.52/2.71 ((~r(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(s(s(s(z)))))) | b(z, elem!1) | (~r(z, elem!1))),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[10345, 9473])).
% 2.52/2.71 tff(12273,plain,
% 2.52/2.71 (~b(s(z), z)),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[12272, 12271, 285, 300, 114])).
% 2.52/2.71 tff(12274,plain,
% 2.52/2.71 ((~b(elem!1, s(s(s(s(z)))))) | r(s(s(s(s(z)))), z) | r(elem!1, z) | b(z, elem!1)),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[10336, 9473])).
% 2.52/2.71 tff(12275,plain,
% 2.52/2.71 (r(elem!1, z)),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[12274, 12271, 285, 12069])).
% 2.52/2.71 tff(12276,plain,
% 2.52/2.71 (~r(s(z), z)),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[162, 12275, 114])).
% 2.52/2.71 tff(12277,plain,
% 2.52/2.71 ($false),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[169, 12276, 12273])).
% 2.52/2.71 tff(12278,plain,((~r(elem!1, s(z))) | b(z, elem!1) | (~r(z, elem!1)) | (elem!1 = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.71 tff(12279,plain,
% 2.52/2.71 (~r(elem!1, s(z))),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[12278, 285, 12024, 12266])).
% 2.52/2.71 tff(12280,plain,
% 2.52/2.71 (elem!1 = s(z)),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[89, 12279, 14])).
% 2.52/2.71 tff(12281,plain,
% 2.52/2.71 (s(z) = elem!1),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[111, 12280])).
% 2.52/2.71 tff(12282,plain,
% 2.52/2.71 (~b(z, s(z))),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[2093, 12281, 285])).
% 2.52/2.71 tff(12283,plain,
% 2.52/2.71 (r(z, s(z))),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[187, 12282])).
% 2.52/2.71 tff(12284,plain,
% 2.52/2.71 (~(s(s(s(elem!1))) = s(s(s(s(s(s(s(z))))))))),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[862, 12266])).
% 2.52/2.71 tff(12285,plain,
% 2.52/2.71 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1))))),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[870, 12284])).
% 2.52/2.71 tff(12286,plain,
% 2.52/2.71 (s(s(s(z))) = s(s(elem!1))),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[84, 12280])).
% 2.52/2.71 tff(12287,plain,
% 2.52/2.71 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.52/2.71 inference(monotonicity,[status(thm)],[12286])).
% 2.52/2.71 tff(12288,plain,
% 2.52/2.71 (b(s(s(s(s(z)))), z) <=> b(s(s(s(elem!1))), z)),
% 2.52/2.71 inference(monotonicity,[status(thm)],[12287])).
% 2.52/2.71 tff(12289,plain,
% 2.52/2.71 (b(s(s(s(elem!1))), z)),
% 2.52/2.71 inference(modus_ponens,[status(thm)],[12093, 12288])).
% 2.52/2.71 tff(12290,plain,
% 2.52/2.71 (r(s(s(s(elem!1))), elem!1) | (~(s(z) = elem!1))),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[702, 9473])).
% 2.52/2.71 tff(12291,plain,
% 2.52/2.71 (r(s(s(s(elem!1))), elem!1)),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[12290, 8607])).
% 2.52/2.71 tff(12292,plain,
% 2.52/2.71 (r(s(s(s(elem!1))), s(z))),
% 2.52/2.71 inference(modus_ponens,[status(thm)],[12291, 11516])).
% 2.52/2.71 tff(12293,plain,
% 2.52/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.52/2.71 inference(rewrite,[status(thm)],[])).
% 2.52/2.71 tff(12294,plain,
% 2.52/2.71 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.52/2.71 inference(rewrite,[status(thm)],[])).
% 2.52/2.71 tff(12295,plain,
% 2.52/2.71 (((~![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(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(elem!1))), s(z)))))),
% 2.52/2.71 inference(monotonicity,[status(thm)],[12294])).
% 2.52/2.71 tff(12296,plain,
% 2.52/2.71 (((~![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(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.52/2.71 inference(transitivity,[status(thm)],[12295, 12293])).
% 2.52/2.71 tff(12297,plain,
% 2.52/2.71 ((~![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(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 2.52/2.71 inference(quant_inst,[status(thm)],[])).
% 2.52/2.71 tff(12298,plain,
% 2.52/2.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(elem!1))), s(z)))),
% 2.52/2.71 inference(modus_ponens,[status(thm)],[12297, 12296])).
% 2.52/2.71 tff(12299,plain,
% 2.52/2.71 ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[12298, 37, 9429])).
% 2.52/2.71 tff(12300,plain,
% 2.52/2.71 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[12299, 12292])).
% 2.52/2.71 tff(12301,assumption,(~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))), introduced(assumption)).
% 2.52/2.71 tff(12302,assumption,(~r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))), introduced(assumption)).
% 2.52/2.71 tff(12303,plain,
% 2.52/2.71 ($false),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[874, 58, 4907, 12302, 12301])).
% 2.52/2.71 tff(12304,plain,(b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.71 tff(12305,plain,
% 2.52/2.71 (b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[12304, 12300, 4907])).
% 2.52/2.71 tff(12306,plain,
% 2.52/2.71 (((~![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(s(z))))))), z)) | (~r(s(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(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.52/2.71 inference(rewrite,[status(thm)],[])).
% 2.52/2.71 tff(12307,plain,
% 2.52/2.71 (((~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.52/2.71 inference(rewrite,[status(thm)],[])).
% 2.52/2.71 tff(12308,plain,
% 2.52/2.71 (((~![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(s(z))))))), s(z))) | (~r(z, s(z))) | (~r(s(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(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 2.52/2.72 inference(monotonicity,[status(thm)],[12307])).
% 2.52/2.72 tff(12309,plain,
% 2.52/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~r(s(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(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.52/2.72 inference(transitivity,[status(thm)],[12308, 12306])).
% 2.52/2.72 tff(12310,plain,
% 2.52/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 2.52/2.72 inference(quant_inst,[status(thm)],[])).
% 2.52/2.72 tff(12311,plain,
% 2.52/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.52/2.72 inference(modus_ponens,[status(thm)],[12310, 12309])).
% 2.52/2.72 tff(12312,plain,
% 2.52/2.72 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[12311, 37, 506, 9429])).
% 2.52/2.72 tff(12313,plain,
% 2.52/2.72 (b(s(s(s(s(s(s(s(z))))))), z)),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[750, 58, 747, 12312])).
% 2.52/2.72 tff(12314,plain,
% 2.52/2.72 (((~![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(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.52/2.72 inference(rewrite,[status(thm)],[])).
% 2.52/2.72 tff(12315,plain,
% 2.52/2.72 (((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.52/2.72 inference(rewrite,[status(thm)],[])).
% 2.52/2.72 tff(12316,plain,
% 2.52/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 2.52/2.72 inference(monotonicity,[status(thm)],[12315])).
% 2.52/2.72 tff(12317,plain,
% 2.52/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.52/2.72 inference(transitivity,[status(thm)],[12316, 12314])).
% 2.52/2.72 tff(12318,plain,
% 2.52/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 2.52/2.72 inference(quant_inst,[status(thm)],[])).
% 2.52/2.72 tff(12319,plain,
% 2.52/2.72 ((~![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(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.52/2.72 inference(modus_ponens,[status(thm)],[12318, 12317])).
% 2.52/2.72 tff(12320,plain,
% 2.52/2.72 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[12319, 37, 506, 9429])).
% 2.52/2.72 tff(12321,plain,
% 2.52/2.72 (b(z, s(s(s(s(s(s(s(z))))))))),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[781, 58, 778, 12320])).
% 2.52/2.72 tff(12322,plain,
% 2.52/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.52/2.72 inference(rewrite,[status(thm)],[])).
% 2.52/2.72 tff(12323,plain,
% 2.52/2.72 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.52/2.72 inference(rewrite,[status(thm)],[])).
% 2.52/2.72 tff(12324,plain,
% 2.52/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))))),
% 2.52/2.72 inference(monotonicity,[status(thm)],[12323])).
% 2.52/2.72 tff(12325,plain,
% 2.52/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(s(s(z))))))))))),
% 2.52/2.72 inference(transitivity,[status(thm)],[12324, 12322])).
% 2.52/2.72 tff(12326,plain,
% 2.52/2.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))))),
% 2.52/2.72 inference(quant_inst,[status(thm)],[])).
% 2.52/2.72 tff(12327,plain,
% 2.52/2.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(s(s(z)))))))))),
% 2.52/2.72 inference(modus_ponens,[status(thm)],[12326, 12325])).
% 2.52/2.72 tff(12328,plain,
% 2.52/2.72 ($false),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[12327, 75, 12321, 12313, 5384, 12305])).
% 2.52/2.72 tff(12329,plain,((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(elem!1))), z)) | (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))) | (~(elem!1 = s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.72 tff(12330,plain,
% 2.52/2.72 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[12329, 12289, 12285, 12280, 12283])).
% 2.52/2.72 tff(12331,plain,
% 2.52/2.72 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[1230, 58, 1227, 12330])).
% 2.52/2.72 tff(12332,plain,
% 2.52/2.72 (r(elem!1, s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 2.52/2.72 inference(monotonicity,[status(thm)],[12280])).
% 2.52/2.72 tff(12333,plain,
% 2.52/2.72 (r(s(z), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.52/2.72 inference(symmetry,[status(thm)],[12332])).
% 2.52/2.72 tff(12334,plain,
% 2.52/2.72 ((~r(s(s(z)), elem!1)) | (~r(z, elem!1))),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[10288, 9473])).
% 2.52/2.72 tff(12335,plain,
% 2.52/2.72 (~r(s(s(z)), elem!1)),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[12334, 12024])).
% 2.52/2.72 tff(12336,plain,
% 2.52/2.72 (~r(s(s(z)), s(z))),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[9876, 12280, 12335])).
% 2.52/2.72 tff(12337,plain,
% 2.52/2.72 (b(s(s(z)), s(z))),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[153, 12336])).
% 2.52/2.72 tff(12338,plain,
% 2.52/2.72 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(z))),
% 2.52/2.72 inference(monotonicity,[status(thm)],[12280])).
% 2.52/2.72 tff(12339,plain,
% 2.52/2.72 (b(s(s(elem!1)), s(z))),
% 2.52/2.72 inference(modus_ponens,[status(thm)],[12263, 12338])).
% 2.52/2.72 tff(12340,plain,
% 2.52/2.72 (~(s(s(elem!1)) = s(s(s(s(s(s(s(z))))))))),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[836, 12281])).
% 2.52/2.72 tff(12341,plain,
% 2.52/2.72 ((~(z = elem!1)) | r(s(s(s(s(z)))), z)),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[9484, 9473])).
% 2.52/2.72 tff(12342,plain,
% 2.52/2.72 (~(z = elem!1)),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[12341, 12092])).
% 2.52/2.72 tff(12343,plain,
% 2.52/2.72 (~(s(s(elem!1)) = s(s(z)))),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[237, 12342])).
% 2.52/2.72 tff(12344,plain,
% 2.52/2.72 (~(s(s(z)) = s(s(elem!1)))),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[6319, 12343])).
% 2.52/2.72 tff(12345,plain,
% 2.52/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.52/2.72 inference(rewrite,[status(thm)],[])).
% 2.52/2.72 tff(12346,plain,
% 2.52/2.72 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(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(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(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.52/2.72 inference(rewrite,[status(thm)],[])).
% 2.52/2.72 tff(12347,plain,
% 2.52/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(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(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 2.52/2.72 inference(monotonicity,[status(thm)],[12346])).
% 2.52/2.72 tff(12348,plain,
% 2.52/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(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(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.52/2.72 inference(transitivity,[status(thm)],[12347, 12345])).
% 2.52/2.72 tff(12349,plain,
% 2.52/2.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(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(s(z))))))))))),
% 2.52/2.72 inference(quant_inst,[status(thm)],[])).
% 2.52/2.72 tff(12350,plain,
% 2.52/2.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.52/2.72 inference(modus_ponens,[status(thm)],[12349, 12348])).
% 2.52/2.72 tff(12351,plain,
% 2.52/2.72 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[12350, 75, 1457, 1894, 309, 8629])).
% 2.52/2.72 tff(12352,plain,
% 2.52/2.72 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | r(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(s(s(z)))))))) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.52/2.72 inference(rewrite,[status(thm)],[])).
% 2.52/2.72 tff(12353,plain,
% 2.52/2.72 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | r(s(s(z)), s(s(s(s(s(s(s(z)))))))))),
% 2.52/2.72 inference(quant_inst,[status(thm)],[])).
% 2.52/2.72 tff(12354,plain,
% 2.52/2.72 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(s(s(z)))))))) | b(s(s(z)), s(s(s(s(s(s(s(z)))))))) | r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.52/2.72 inference(modus_ponens,[status(thm)],[12353, 12352])).
% 2.52/2.72 tff(12355,plain,
% 2.52/2.72 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) | r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[12354, 58, 12351])).
% 2.52/2.72 tff(12356,plain,
% 2.52/2.72 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[12355, 12269])).
% 2.52/2.72 tff(12357,plain,
% 2.52/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.52/2.72 inference(rewrite,[status(thm)],[])).
% 2.52/2.72 tff(12358,plain,
% 2.52/2.72 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.52/2.72 inference(rewrite,[status(thm)],[])).
% 2.52/2.72 tff(12359,plain,
% 2.52/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 2.52/2.72 inference(monotonicity,[status(thm)],[12358])).
% 2.52/2.72 tff(12360,plain,
% 2.52/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.52/2.72 inference(transitivity,[status(thm)],[12359, 12357])).
% 2.52/2.72 tff(12361,plain,
% 2.52/2.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.52/2.72 inference(quant_inst,[status(thm)],[])).
% 2.52/2.72 tff(12362,plain,
% 2.52/2.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 2.52/2.72 inference(modus_ponens,[status(thm)],[12361, 12360])).
% 2.52/2.72 tff(12363,plain,
% 2.52/2.72 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[12362, 75, 1457, 1894, 8629])).
% 2.52/2.72 tff(12364,plain,
% 2.52/2.72 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[8665, 12363, 4537, 3067])).
% 2.52/2.72 tff(12365,plain,
% 2.52/2.72 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.52/2.72 inference(modus_ponens,[status(thm)],[12364, 8658])).
% 2.52/2.72 tff(12366,plain,
% 2.52/2.72 (~b(s(s(z)), s(s(elem!1)))),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[11694, 75, 1457, 1894, 309])).
% 2.52/2.72 tff(12367,plain,
% 2.52/2.72 (r(s(s(z)), s(s(elem!1)))),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[6336, 58, 12366, 8001])).
% 2.52/2.72 tff(12368,plain,
% 2.52/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.52/2.72 inference(rewrite,[status(thm)],[])).
% 2.52/2.72 tff(12369,plain,
% 2.52/2.72 (((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.52/2.72 inference(rewrite,[status(thm)],[])).
% 2.52/2.72 tff(12370,plain,
% 2.52/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 2.52/2.73 inference(monotonicity,[status(thm)],[12369])).
% 2.52/2.73 tff(12371,plain,
% 2.52/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.52/2.73 inference(transitivity,[status(thm)],[12370, 12368])).
% 2.52/2.73 tff(12372,plain,
% 2.52/2.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.52/2.73 inference(quant_inst,[status(thm)],[])).
% 2.52/2.73 tff(12373,plain,
% 2.52/2.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 2.52/2.73 inference(modus_ponens,[status(thm)],[12372, 12371])).
% 2.52/2.73 tff(12374,plain,
% 2.52/2.73 ($false),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[12373, 37, 12367, 12365, 12356])).
% 2.52/2.73 tff(12375,plain,((~b(s(z), s(s(elem!1)))) | (~(s(s(s(z))) = s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.73 tff(12376,plain,
% 2.52/2.73 (~b(s(z), s(s(elem!1)))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[12375, 12286, 12344, 12340, 12339, 12337, 12331])).
% 2.52/2.73 tff(12377,plain,
% 2.52/2.73 (r(s(z), s(s(elem!1)))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[1890, 12376])).
% 2.52/2.73 tff(12378,plain,
% 2.52/2.73 (r(elem!1, s(s(elem!1)))),
% 2.52/2.73 inference(modus_ponens,[status(thm)],[12377, 12333])).
% 2.52/2.73 tff(12379,plain,
% 2.52/2.73 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[8898, 12264])).
% 2.52/2.73 tff(12380,plain,
% 2.52/2.73 (~r(s(s(elem!1)), elem!1)),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[12253, 12379, 12024])).
% 2.52/2.73 tff(12381,plain,
% 2.52/2.73 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.52/2.73 inference(symmetry,[status(thm)],[12287])).
% 2.52/2.73 tff(12382,plain,
% 2.52/2.73 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(s(z)))))),
% 2.52/2.73 inference(monotonicity,[status(thm)],[12381])).
% 2.52/2.73 tff(12383,plain,
% 2.52/2.73 (b(z, s(s(s(s(z))))) <=> b(z, s(s(s(elem!1))))),
% 2.52/2.73 inference(symmetry,[status(thm)],[12382])).
% 2.52/2.73 tff(12384,plain,
% 2.52/2.73 (b(z, s(s(s(elem!1))))),
% 2.52/2.73 inference(modus_ponens,[status(thm)],[12091, 12383])).
% 2.52/2.73 tff(12385,plain,
% 2.52/2.73 (b(s(elem!1), elem!1)),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[968, 12281, 12264])).
% 2.52/2.73 tff(12386,plain,
% 2.52/2.73 (b(s(z), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.52/2.73 inference(monotonicity,[status(thm)],[8682])).
% 2.52/2.73 tff(12387,plain,
% 2.52/2.73 (b(elem!1, s(s(s(elem!1)))) <=> b(s(z), s(s(s(elem!1))))),
% 2.52/2.73 inference(symmetry,[status(thm)],[12386])).
% 2.52/2.73 tff(12388,plain,
% 2.52/2.73 (b(elem!1, s(s(s(elem!1)))) <=> b(s(z), s(s(s(s(z)))))),
% 2.52/2.73 inference(monotonicity,[status(thm)],[17, 8602])).
% 2.52/2.73 tff(12389,plain,
% 2.52/2.73 (b(s(z), s(s(s(s(z))))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.52/2.73 inference(symmetry,[status(thm)],[12388])).
% 2.52/2.73 tff(12390,plain,
% 2.52/2.73 (b(s(z), s(s(s(s(z))))) <=> b(s(z), s(s(s(elem!1))))),
% 2.52/2.73 inference(transitivity,[status(thm)],[12389, 12387])).
% 2.52/2.73 tff(12391,plain,
% 2.52/2.73 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(s(z)))))),
% 2.52/2.73 inference(monotonicity,[status(thm)],[8602])).
% 2.52/2.73 tff(12392,plain,
% 2.52/2.73 (b(z, s(s(s(s(z))))) <=> b(z, s(s(s(elem!1))))),
% 2.52/2.73 inference(symmetry,[status(thm)],[12391])).
% 2.52/2.73 tff(12393,plain,
% 2.52/2.73 (b(z, s(s(s(elem!1))))),
% 2.52/2.73 inference(modus_ponens,[status(thm)],[12243, 12392])).
% 2.52/2.73 tff(12394,plain,
% 2.52/2.73 (r(elem!1, s(s(s(s(z))))) <=> r(s(z), s(s(s(s(z)))))),
% 2.52/2.73 inference(monotonicity,[status(thm)],[17])).
% 2.52/2.73 tff(12395,plain,
% 2.52/2.73 (r(s(z), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 2.52/2.73 inference(symmetry,[status(thm)],[12394])).
% 2.52/2.73 tff(12396,plain,
% 2.52/2.73 (r(elem!1, s(s(s(s(z)))))),
% 2.52/2.73 inference(modus_ponens,[status(thm)],[468, 12395])).
% 2.52/2.73 tff(12397,plain,
% 2.52/2.73 (~r(s(s(z)), elem!1)),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[12334, 300])).
% 2.52/2.73 tff(12398,plain,
% 2.52/2.73 (~r(s(s(z)), s(z))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[9876, 17, 12397])).
% 2.52/2.73 tff(12399,plain,
% 2.52/2.73 (b(s(s(z)), s(z))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[153, 12398])).
% 2.52/2.73 tff(12400,plain,
% 2.52/2.73 (~(z = elem!1)),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[12341, 12069])).
% 2.52/2.73 tff(12401,plain,
% 2.52/2.73 (~(s(s(elem!1)) = s(s(z)))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[237, 12400])).
% 2.52/2.73 tff(12402,plain,
% 2.52/2.73 (~(s(s(z)) = s(s(elem!1)))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[6319, 12401])).
% 2.52/2.73 tff(12403,plain,
% 2.52/2.73 (b(elem!1, z) <=> b(s(z), z)),
% 2.52/2.73 inference(monotonicity,[status(thm)],[17])).
% 2.52/2.73 tff(12404,plain,
% 2.52/2.73 (b(s(z), z) <=> b(elem!1, z)),
% 2.52/2.73 inference(symmetry,[status(thm)],[12403])).
% 2.52/2.73 tff(12405,plain,
% 2.52/2.73 (b(elem!1, z)),
% 2.52/2.73 inference(modus_ponens,[status(thm)],[371, 12404])).
% 2.52/2.73 tff(12406,plain,
% 2.52/2.73 (b(s(s(elem!1)), s(z))),
% 2.52/2.73 inference(modus_ponens,[status(thm)],[12263, 3642])).
% 2.52/2.73 tff(12407,plain,
% 2.52/2.73 (~b(s(s(z)), s(s(elem!1)))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[11694, 75, 12406, 1894, 309])).
% 2.52/2.73 tff(12408,plain,
% 2.52/2.73 (r(s(s(z)), s(s(elem!1)))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[6336, 58, 12407, 8001])).
% 2.52/2.73 tff(12409,plain,
% 2.52/2.73 (r(s(elem!1), z) <=> r(s(s(z)), z)),
% 2.52/2.73 inference(monotonicity,[status(thm)],[18])).
% 2.52/2.73 tff(12410,plain,
% 2.52/2.73 (r(s(s(z)), z) <=> r(s(elem!1), z)),
% 2.52/2.73 inference(symmetry,[status(thm)],[12409])).
% 2.52/2.73 tff(12411,plain,
% 2.52/2.73 ((~r(s(s(z)), z)) <=> (~r(s(elem!1), z))),
% 2.52/2.73 inference(monotonicity,[status(thm)],[12410])).
% 2.52/2.73 tff(12412,plain,
% 2.52/2.73 (((~![X0: $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)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)))),
% 2.52/2.73 inference(rewrite,[status(thm)],[])).
% 2.52/2.73 tff(12413,plain,
% 2.52/2.73 (((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), z))) <=> ((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)))),
% 2.52/2.73 inference(rewrite,[status(thm)],[])).
% 2.52/2.73 tff(12414,plain,
% 2.52/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), z))))),
% 2.52/2.73 inference(monotonicity,[status(thm)],[12413])).
% 2.52/2.73 tff(12415,plain,
% 2.52/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)))),
% 2.52/2.73 inference(transitivity,[status(thm)],[12414, 12412])).
% 2.52/2.73 tff(12416,plain,
% 2.52/2.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)))),
% 2.52/2.73 inference(quant_inst,[status(thm)],[])).
% 2.52/2.73 tff(12417,plain,
% 2.52/2.73 ((~![X0: $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)), z))),
% 2.52/2.73 inference(modus_ponens,[status(thm)],[12416, 12415])).
% 2.52/2.73 tff(12418,plain,
% 2.52/2.73 (~r(s(s(z)), z)),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[12417, 37, 8231, 2364])).
% 2.52/2.73 tff(12419,plain,
% 2.52/2.73 (~r(s(elem!1), z)),
% 2.52/2.73 inference(modus_ponens,[status(thm)],[12418, 12411])).
% 2.52/2.73 tff(12420,plain,
% 2.52/2.73 (((~![X0: $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(z)))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(elem!1)))))),
% 2.52/2.73 inference(rewrite,[status(thm)],[])).
% 2.52/2.73 tff(12421,plain,
% 2.52/2.73 (((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z))))) <=> ((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(elem!1)))))),
% 2.52/2.73 inference(rewrite,[status(thm)],[])).
% 2.52/2.73 tff(12422,plain,
% 2.52/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(elem!1))))))),
% 2.52/2.73 inference(monotonicity,[status(thm)],[12421])).
% 2.52/2.73 tff(12423,plain,
% 2.52/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(elem!1)))))),
% 2.52/2.73 inference(transitivity,[status(thm)],[12422, 12420])).
% 2.52/2.73 tff(12424,plain,
% 2.52/2.73 ((~![X0: $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)))))),
% 2.52/2.73 inference(quant_inst,[status(thm)],[])).
% 2.52/2.73 tff(12425,plain,
% 2.52/2.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(elem!1))))),
% 2.52/2.73 inference(modus_ponens,[status(thm)],[12424, 12423])).
% 2.52/2.73 tff(12426,plain,
% 2.52/2.73 (~r(z, s(s(z)))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[12425, 37, 8231, 2364])).
% 2.52/2.73 tff(12427,plain,
% 2.52/2.73 (b(z, s(s(z)))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[351, 12426])).
% 2.52/2.73 tff(12428,plain,
% 2.52/2.73 (b(s(s(z)), z)),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[202, 12418])).
% 2.52/2.73 tff(12429,plain,
% 2.52/2.73 (~b(s(elem!1), z)),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[10000, 12428, 921, 12427, 1958])).
% 2.52/2.73 tff(12430,plain,
% 2.52/2.73 (r(s(elem!1), z)),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[766, 12429])).
% 2.52/2.73 tff(12431,plain,
% 2.52/2.73 ($false),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[12430, 12419])).
% 2.52/2.73 tff(12432,plain,((~r(z, s(s(elem!1)))) | (~(elem!1 = s(z))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~r(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.73 tff(12433,plain,
% 2.52/2.73 (~r(z, s(s(elem!1)))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[12432, 12408, 921, 12405, 17])).
% 2.52/2.73 tff(12434,plain,
% 2.52/2.73 (b(z, s(s(elem!1)))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[6314, 12433])).
% 2.52/2.73 tff(12435,plain,
% 2.52/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)))) | (~b(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(X1, 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(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 2.52/2.73 inference(rewrite,[status(thm)],[])).
% 2.52/2.73 tff(12436,plain,
% 2.52/2.73 (((~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(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 2.52/2.73 inference(rewrite,[status(thm)],[])).
% 2.52/2.73 tff(12437,plain,
% 2.52/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), 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(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))))),
% 2.52/2.73 inference(monotonicity,[status(thm)],[12436])).
% 2.52/2.73 tff(12438,plain,
% 2.52/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), 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(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 2.52/2.73 inference(transitivity,[status(thm)],[12437, 12435])).
% 2.52/2.73 tff(12439,plain,
% 2.52/2.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), 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(s(z), z)))),
% 2.52/2.73 inference(quant_inst,[status(thm)],[])).
% 2.52/2.73 tff(12440,plain,
% 2.52/2.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))),
% 2.52/2.73 inference(modus_ponens,[status(thm)],[12439, 12438])).
% 2.52/2.73 tff(12441,plain,
% 2.52/2.73 ($false),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[12440, 75, 12406, 371, 1894, 12434])).
% 2.52/2.73 tff(12442,plain,((~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(elem!1), elem!1)) | (~(elem!1 = s(z))) | (s(s(z)) = s(s(elem!1))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.73 tff(12443,plain,
% 2.52/2.73 (~b(s(z), s(s(elem!1)))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[12442, 371, 921, 17, 12402, 12399])).
% 2.52/2.73 tff(12444,plain,
% 2.52/2.73 (r(s(z), s(s(elem!1)))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[1890, 12443])).
% 2.52/2.73 tff(12445,plain,
% 2.52/2.73 (r(elem!1, s(s(elem!1)))),
% 2.52/2.73 inference(modus_ponens,[status(thm)],[12444, 8609])).
% 2.52/2.73 tff(12446,plain,
% 2.52/2.73 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[5049, 12445, 8607, 12396])).
% 2.52/2.73 tff(12447,plain,
% 2.52/2.73 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[2898, 12446])).
% 2.52/2.73 tff(12448,plain,
% 2.52/2.73 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.52/2.73 inference(modus_ponens,[status(thm)],[12447, 8606])).
% 2.52/2.73 tff(12449,plain,
% 2.52/2.73 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.52/2.73 inference(monotonicity,[status(thm)],[8601])).
% 2.52/2.73 tff(12450,plain,
% 2.52/2.73 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.52/2.73 inference(monotonicity,[status(thm)],[7111])).
% 2.52/2.73 tff(12451,plain,
% 2.52/2.73 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.52/2.73 inference(transitivity,[status(thm)],[12450, 12449])).
% 2.52/2.73 tff(12452,plain,
% 2.52/2.73 (r(s(z), s(s(s(z))))),
% 2.52/2.73 inference(modus_ponens,[status(thm)],[12444, 8627])).
% 2.52/2.73 tff(12453,plain,
% 2.52/2.73 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[1316, 12452, 468])).
% 2.52/2.73 tff(12454,plain,
% 2.52/2.73 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[575, 12453])).
% 2.52/2.73 tff(12455,plain,
% 2.52/2.73 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.52/2.73 inference(modus_ponens,[status(thm)],[12454, 12451])).
% 2.52/2.73 tff(12456,plain,
% 2.52/2.73 (~r(z, s(s(elem!1)))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[2372, 12445, 300])).
% 2.52/2.73 tff(12457,plain,
% 2.52/2.73 (b(z, s(s(elem!1)))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[6314, 12456])).
% 2.52/2.73 tff(12458,plain,
% 2.52/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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))), 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(X1, 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))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 2.52/2.73 inference(rewrite,[status(thm)],[])).
% 2.52/2.73 tff(12459,plain,
% 2.52/2.73 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1))))) <=> ((~b(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(s(elem!1))))))),
% 2.52/2.73 inference(rewrite,[status(thm)],[])).
% 2.52/2.73 tff(12460,plain,
% 2.52/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(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(X1, 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))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))))),
% 2.52/2.73 inference(monotonicity,[status(thm)],[12459])).
% 2.52/2.73 tff(12461,plain,
% 2.52/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(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(X1, 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))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 2.52/2.73 inference(transitivity,[status(thm)],[12460, 12458])).
% 2.52/2.73 tff(12462,plain,
% 2.52/2.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))))),
% 2.52/2.73 inference(quant_inst,[status(thm)],[])).
% 2.52/2.73 tff(12463,plain,
% 2.52/2.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))),
% 2.52/2.73 inference(modus_ponens,[status(thm)],[12462, 12461])).
% 2.52/2.73 tff(12464,plain,
% 2.52/2.73 ($false),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[12463, 75, 12457, 12455, 12448, 12393])).
% 2.52/2.73 tff(12465,plain,((~b(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~(elem!1 = s(z))) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.73 tff(12466,plain,
% 2.52/2.73 (~r(s(z), s(s(s(s(z)))))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[12465, 371, 300, 17, 921])).
% 2.52/2.73 tff(12467,plain,
% 2.52/2.74 (b(s(z), s(s(s(s(z)))))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[489, 12466])).
% 2.52/2.74 tff(12468,plain,
% 2.52/2.74 (b(s(z), s(s(s(elem!1))))),
% 2.52/2.74 inference(modus_ponens,[status(thm)],[12467, 12390])).
% 2.52/2.74 tff(12469,plain,
% 2.52/2.74 (b(s(s(s(s(z)))), z) <=> b(s(s(s(elem!1))), z)),
% 2.52/2.74 inference(monotonicity,[status(thm)],[8601])).
% 2.52/2.74 tff(12470,plain,
% 2.52/2.74 (b(s(s(s(elem!1))), z)),
% 2.52/2.74 inference(modus_ponens,[status(thm)],[12070, 12469])).
% 2.52/2.74 tff(12471,plain,
% 2.52/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), s(s(s(elem!1))))))),
% 2.52/2.74 inference(rewrite,[status(thm)],[])).
% 2.52/2.74 tff(12472,plain,
% 2.52/2.74 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))))),
% 2.52/2.74 inference(rewrite,[status(thm)],[])).
% 2.52/2.74 tff(12473,plain,
% 2.52/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), z)) | (~b(z, s(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(X1, 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(z), s(s(s(elem!1)))))))),
% 2.52/2.74 inference(monotonicity,[status(thm)],[12472])).
% 2.52/2.74 tff(12474,plain,
% 2.52/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), z)) | (~b(z, s(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(X1, 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(z), s(s(s(elem!1))))))),
% 2.52/2.74 inference(transitivity,[status(thm)],[12473, 12471])).
% 2.52/2.74 tff(12475,plain,
% 2.52/2.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 2.52/2.74 inference(quant_inst,[status(thm)],[])).
% 2.52/2.74 tff(12476,plain,
% 2.52/2.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1)))))),
% 2.52/2.74 inference(modus_ponens,[status(thm)],[12475, 12474])).
% 2.52/2.74 tff(12477,plain,
% 2.52/2.74 ($false),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[12476, 75, 371, 12470, 12393, 12468])).
% 2.52/2.74 tff(12478,plain,((~b(s(z), z)) | (~(elem!1 = s(z))) | (~r(z, elem!1)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.74 tff(12479,plain,
% 2.52/2.74 (~b(s(z), z)),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[12478, 12280, 12024, 12385])).
% 2.52/2.74 tff(12480,plain,
% 2.52/2.74 (r(s(z), z)),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[169, 12479])).
% 2.52/2.74 tff(12481,plain,
% 2.52/2.74 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 2.52/2.74 inference(monotonicity,[status(thm)],[8602])).
% 2.52/2.74 tff(12482,plain,
% 2.52/2.74 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 2.52/2.74 inference(transitivity,[status(thm)],[12481, 640])).
% 2.52/2.74 tff(12483,plain,
% 2.52/2.74 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 2.52/2.74 inference(symmetry,[status(thm)],[12482])).
% 2.52/2.74 tff(12484,plain,
% 2.52/2.74 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = s(s(z))))),
% 2.52/2.74 inference(monotonicity,[status(thm)],[12483])).
% 2.52/2.74 tff(12485,plain,
% 2.52/2.74 (~(s(s(s(elem!1))) = s(s(z)))),
% 2.52/2.74 inference(modus_ponens,[status(thm)],[459, 12484])).
% 2.52/2.74 tff(12486,assumption,(b(z, s(s(s(elem!1))))), introduced(assumption)).
% 2.52/2.74 tff(12487,plain,
% 2.52/2.74 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.52/2.74 inference(monotonicity,[status(thm)],[7111])).
% 2.52/2.74 tff(12488,plain,
% 2.52/2.74 (r(s(s(s(s(z)))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 2.52/2.74 inference(symmetry,[status(thm)],[12487])).
% 2.52/2.74 tff(12489,plain,
% 2.52/2.74 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 2.52/2.74 inference(monotonicity,[status(thm)],[8602])).
% 2.52/2.74 tff(12490,plain,
% 2.52/2.74 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 2.52/2.74 inference(transitivity,[status(thm)],[12489, 12488])).
% 2.52/2.74 tff(12491,plain,
% 2.52/2.74 ((~r(s(s(s(elem!1))), s(s(elem!1)))) <=> (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 2.52/2.74 inference(monotonicity,[status(thm)],[12490])).
% 2.52/2.74 tff(12492,assumption,(~r(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 2.52/2.74 tff(12493,plain,
% 2.52/2.74 ($false),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[12492, 12292])).
% 2.52/2.74 tff(12494,plain,(r(s(s(s(elem!1))), s(z)) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.74 tff(12495,plain,
% 2.52/2.74 (r(s(s(s(elem!1))), s(z))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[12494, 17])).
% 2.52/2.74 tff(12496,plain,
% 2.52/2.74 (~(elem!1 = s(s(elem!1)))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[9470, 12263])).
% 2.52/2.74 tff(12497,plain,
% 2.52/2.74 ((~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), s(s(z)))) | r(s(s(elem!1)), elem!1) | r(elem!1, s(s(elem!1)))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[7699, 12496])).
% 2.52/2.74 tff(12498,plain,
% 2.52/2.74 (r(elem!1, s(s(elem!1)))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[12497, 1283, 964, 2668])).
% 2.52/2.74 tff(12499,plain,
% 2.52/2.74 (r(s(z), s(s(elem!1)))),
% 2.52/2.74 inference(modus_ponens,[status(thm)],[12498, 8608])).
% 2.52/2.74 tff(12500,assumption,(r(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 2.52/2.74 tff(12501,plain,
% 2.52/2.74 (((~![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))))),
% 2.52/2.74 inference(rewrite,[status(thm)],[])).
% 2.52/2.74 tff(12502,plain,
% 2.52/2.74 (((~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))))),
% 2.52/2.74 inference(rewrite,[status(thm)],[])).
% 2.52/2.74 tff(12503,plain,
% 2.52/2.74 (((~![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(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)))))),
% 2.52/2.74 inference(monotonicity,[status(thm)],[12502])).
% 2.52/2.74 tff(12504,plain,
% 2.52/2.74 (((~![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(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))))),
% 2.52/2.74 inference(transitivity,[status(thm)],[12503, 12501])).
% 2.52/2.74 tff(12505,plain,
% 2.52/2.74 ((~![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(s(elem!1))), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 2.52/2.74 inference(quant_inst,[status(thm)],[])).
% 2.52/2.74 tff(12506,plain,
% 2.52/2.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z)))),
% 2.52/2.74 inference(modus_ponens,[status(thm)],[12505, 12504])).
% 2.52/2.74 tff(12507,plain,
% 2.52/2.74 ($false),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[12506, 37, 1561, 1871, 8746, 12500])).
% 2.52/2.74 tff(12508,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,[]))).
% 2.52/2.74 tff(12509,plain,
% 2.52/2.74 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[12508, 12499, 1561, 12495])).
% 2.52/2.74 tff(12510,plain,
% 2.52/2.74 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.52/2.74 inference(modus_ponens,[status(thm)],[12509, 12491])).
% 2.52/2.74 tff(12511,plain,
% 2.52/2.74 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[2898, 12510])).
% 2.52/2.74 tff(12512,plain,
% 2.52/2.74 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.52/2.74 inference(modus_ponens,[status(thm)],[12511, 8606])).
% 2.52/2.74 tff(12513,plain,
% 2.52/2.74 ($false),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[11569, 75, 1457, 309, 402, 1283])).
% 2.52/2.74 tff(12514,plain,((~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.74 tff(12515,plain,
% 2.52/2.74 (~b(s(z), s(s(z)))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[12514, 1283, 309, 12406])).
% 2.52/2.74 tff(12516,plain,
% 2.52/2.74 (r(s(z), s(s(z)))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[416, 12515])).
% 2.52/2.74 tff(12517,plain,
% 2.52/2.74 (r(elem!1, s(s(z)))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[9003, 12516, 8607])).
% 2.52/2.74 tff(12518,plain,
% 2.52/2.74 (((~![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(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(z)))))),
% 2.52/2.74 inference(rewrite,[status(thm)],[])).
% 2.52/2.74 tff(12519,plain,
% 2.52/2.74 (((~r(s(s(z)), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(elem!1, s(s(z))))) <=> ((~r(s(s(z)), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(z)))))),
% 2.52/2.74 inference(rewrite,[status(thm)],[])).
% 2.52/2.74 tff(12520,plain,
% 2.52/2.74 (((~![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(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(z))))))),
% 2.52/2.74 inference(monotonicity,[status(thm)],[12519])).
% 2.52/2.74 tff(12521,plain,
% 2.52/2.74 (((~![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(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(z)))))),
% 2.52/2.74 inference(transitivity,[status(thm)],[12520, 12518])).
% 2.52/2.74 tff(12522,plain,
% 2.52/2.74 ((~![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(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(elem!1, s(s(z)))))),
% 2.52/2.74 inference(quant_inst,[status(thm)],[])).
% 2.52/2.74 tff(12523,plain,
% 2.52/2.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(z))))),
% 2.52/2.74 inference(modus_ponens,[status(thm)],[12522, 12521])).
% 2.52/2.74 tff(12524,plain,
% 2.52/2.74 ($false),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[12523, 37, 1490, 1489, 8231])).
% 2.52/2.74 tff(12525,plain,((~r(s(s(z)), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.74 tff(12526,plain,
% 2.52/2.74 (~r(s(s(z)), s(s(elem!1)))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[12525, 12517, 12498])).
% 2.52/2.74 tff(12527,plain,
% 2.52/2.74 (b(s(s(z)), s(s(elem!1)))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[6336, 58, 12526, 8001])).
% 2.52/2.74 tff(12528,plain,
% 2.52/2.74 (~r(s(s(z)), z)),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[2015, 12516, 1561])).
% 2.52/2.74 tff(12529,plain,
% 2.52/2.74 (b(s(s(z)), z)),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[202, 12528])).
% 2.52/2.74 tff(12530,plain,
% 2.52/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), 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(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(X1, 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)), 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(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.52/2.74 inference(rewrite,[status(thm)],[])).
% 2.52/2.74 tff(12531,plain,
% 2.52/2.74 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), 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(z)), 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))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.52/2.74 inference(rewrite,[status(thm)],[])).
% 2.52/2.74 tff(12532,plain,
% 2.52/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), 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(X1, 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)), 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(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 2.52/2.74 inference(monotonicity,[status(thm)],[12531])).
% 2.52/2.74 tff(12533,plain,
% 2.52/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), 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(X1, 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)), 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(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.52/2.74 inference(transitivity,[status(thm)],[12532, 12530])).
% 2.52/2.74 tff(12534,plain,
% 2.52/2.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), 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)))))),
% 2.52/2.74 inference(quant_inst,[status(thm)],[])).
% 2.52/2.74 tff(12535,plain,
% 2.52/2.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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)), 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(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 2.52/2.74 inference(modus_ponens,[status(thm)],[12534, 12533])).
% 2.52/2.74 tff(12536,plain,
% 2.52/2.74 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[12535, 75, 12529, 12527, 5384, 12512, 12486])).
% 2.52/2.74 tff(12537,plain,
% 2.52/2.74 ((s(s(s(elem!1))) = s(s(z))) | r(s(s(s(elem!1))), s(s(z)))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[4092, 58, 12536])).
% 2.52/2.74 tff(12538,plain,
% 2.52/2.74 (r(s(s(s(elem!1))), s(s(z)))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[12537, 12485])).
% 2.52/2.74 tff(12539,plain,
% 2.52/2.74 (((~![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(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(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.52/2.74 inference(rewrite,[status(thm)],[])).
% 2.52/2.74 tff(12540,plain,
% 2.52/2.74 (((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.52/2.74 inference(rewrite,[status(thm)],[])).
% 2.52/2.74 tff(12541,plain,
% 2.52/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(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(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z)))))),
% 2.52/2.74 inference(monotonicity,[status(thm)],[12540])).
% 2.52/2.74 tff(12542,plain,
% 2.52/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(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(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.52/2.74 inference(transitivity,[status(thm)],[12541, 12539])).
% 2.52/2.74 tff(12543,plain,
% 2.52/2.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 2.52/2.74 inference(quant_inst,[status(thm)],[])).
% 2.52/2.74 tff(12544,plain,
% 2.52/2.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z)))),
% 2.52/2.74 inference(modus_ponens,[status(thm)],[12543, 12542])).
% 2.52/2.74 tff(12545,plain,
% 2.52/2.74 ($false),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[12544, 37, 1561, 12516, 12495, 12538])).
% 2.52/2.74 tff(12546,plain,((~b(s(s(elem!1)), s(s(z)))) | (~r(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (s(s(z)) = s(s(elem!1))) | (~(elem!1 = s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.52/2.74 tff(12547,plain,
% 2.52/2.74 (~b(s(s(elem!1)), s(s(z)))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[12546, 12480, 12289, 12384, 12344, 12280, 12337, 12264, 12380])).
% 2.52/2.74 tff(12548,plain,
% 2.52/2.74 (r(s(s(elem!1)), s(s(z)))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[1476, 12547, 12343])).
% 2.52/2.74 tff(12549,plain,
% 2.52/2.74 (~r(elem!1, s(s(z)))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[1498, 12548, 12378])).
% 2.52/2.74 tff(12550,plain,
% 2.52/2.74 (~r(s(z), s(s(z)))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[9003, 12549, 12281])).
% 2.52/2.74 tff(12551,plain,
% 2.52/2.74 (b(s(z), s(s(z)))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[416, 12550])).
% 2.52/2.74 tff(12552,plain,
% 2.52/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.52/2.75 inference(rewrite,[status(thm)],[])).
% 2.52/2.75 tff(12553,plain,
% 2.52/2.75 (((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(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(s(z)))))))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.52/2.75 inference(rewrite,[status(thm)],[])).
% 2.52/2.75 tff(12554,plain,
% 2.52/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 2.52/2.75 inference(monotonicity,[status(thm)],[12553])).
% 2.52/2.75 tff(12555,plain,
% 2.52/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 2.52/2.75 inference(transitivity,[status(thm)],[12554, 12552])).
% 2.52/2.75 tff(12556,plain,
% 2.52/2.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))))),
% 2.52/2.75 inference(quant_inst,[status(thm)],[])).
% 2.52/2.75 tff(12557,plain,
% 2.52/2.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 2.52/2.75 inference(modus_ponens,[status(thm)],[12556, 12555])).
% 2.52/2.75 tff(12558,plain,
% 2.52/2.75 (~b(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[12557, 75, 12337, 12551, 12331])).
% 2.52/2.75 tff(12559,plain,
% 2.52/2.75 ((s(s(z)) = s(s(s(s(s(s(s(z)))))))) | r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[12354, 58, 12558])).
% 2.52/2.75 tff(12560,plain,
% 2.52/2.75 (r(s(s(z)), s(s(s(s(s(s(s(z))))))))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[12559, 12269])).
% 2.52/2.75 tff(12561,plain,
% 2.52/2.75 (s(s(elem!1)) = s(s(s(z)))),
% 2.52/2.75 inference(symmetry,[status(thm)],[12286])).
% 2.52/2.75 tff(12562,plain,
% 2.52/2.75 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.52/2.75 inference(monotonicity,[status(thm)],[12561])).
% 2.52/2.75 tff(12563,plain,
% 2.52/2.75 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) <=> r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.52/2.75 inference(symmetry,[status(thm)],[12562])).
% 2.52/2.75 tff(12564,plain,
% 2.52/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.52/2.75 inference(rewrite,[status(thm)],[])).
% 2.52/2.75 tff(12565,plain,
% 2.52/2.75 (((~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.52/2.75 inference(rewrite,[status(thm)],[])).
% 2.52/2.75 tff(12566,plain,
% 2.52/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))))),
% 2.52/2.75 inference(monotonicity,[status(thm)],[12565])).
% 2.52/2.75 tff(12567,plain,
% 2.52/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.52/2.75 inference(transitivity,[status(thm)],[12566, 12564])).
% 2.52/2.75 tff(12568,plain,
% 2.52/2.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))))),
% 2.52/2.75 inference(quant_inst,[status(thm)],[])).
% 2.52/2.75 tff(12569,plain,
% 2.52/2.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1))))),
% 2.52/2.75 inference(modus_ponens,[status(thm)],[12568, 12567])).
% 2.52/2.75 tff(12570,plain,
% 2.52/2.75 (~b(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[12569, 75, 12339, 12337, 12551, 12331])).
% 2.52/2.75 tff(12571,plain,
% 2.52/2.75 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[8665, 12570, 12286, 12340])).
% 2.52/2.75 tff(12572,plain,
% 2.52/2.75 (r(s(s(s(s(s(s(s(z))))))), s(s(elem!1)))),
% 2.52/2.75 inference(modus_ponens,[status(thm)],[12571, 12563])).
% 2.52/2.75 tff(12573,plain,
% 2.52/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))))),
% 2.52/2.75 inference(rewrite,[status(thm)],[])).
% 2.52/2.75 tff(12574,plain,
% 2.52/2.75 (((~b(s(s(z)), 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(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))))),
% 2.52/2.75 inference(rewrite,[status(thm)],[])).
% 2.52/2.75 tff(12575,plain,
% 2.52/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z)))))),
% 2.52/2.75 inference(monotonicity,[status(thm)],[12574])).
% 2.52/2.75 tff(12576,plain,
% 2.52/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))))),
% 2.52/2.75 inference(transitivity,[status(thm)],[12575, 12573])).
% 2.52/2.75 tff(12577,plain,
% 2.52/2.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.52/2.75 inference(quant_inst,[status(thm)],[])).
% 2.52/2.75 tff(12578,plain,
% 2.52/2.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z)))),
% 2.52/2.75 inference(modus_ponens,[status(thm)],[12577, 12576])).
% 2.52/2.75 tff(12579,plain,
% 2.52/2.75 (~b(s(s(z)), s(s(elem!1)))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[12578, 75, 12339, 12337, 12551])).
% 2.52/2.75 tff(12580,plain,
% 2.52/2.75 (r(s(s(z)), s(s(elem!1)))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[6336, 58, 12579, 12344])).
% 2.52/2.75 tff(12581,plain,
% 2.52/2.75 ($false),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[12373, 37, 12580, 12572, 12560])).
% 2.52/2.75 tff(12582,plain,(b(z, elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.75 tff(12583,plain,
% 2.52/2.75 (b(z, elem!1)),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[12582, 14])).
% 2.52/2.75 tff(12584,plain,
% 2.52/2.75 ($false),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[12099, 75, 1518, 286, 1423, 1582])).
% 2.52/2.75 tff(12585,plain,((~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.75 tff(12586,plain,
% 2.52/2.75 (~b(elem!1, s(s(s(s(z)))))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[12585, 12583, 12093, 12091])).
% 2.52/2.75 tff(12587,plain,
% 2.52/2.75 (r(elem!1, s(s(s(s(z)))))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[278, 12586, 12266])).
% 2.52/2.75 tff(12588,plain,
% 2.52/2.75 (~r(elem!1, s(z))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[8127, 12587, 12024])).
% 2.52/2.75 tff(12589,plain,
% 2.52/2.75 (elem!1 = s(z)),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[89, 12588, 14])).
% 2.52/2.75 tff(12590,plain,
% 2.52/2.75 (b(z, elem!1) <=> b(z, s(z))),
% 2.52/2.75 inference(monotonicity,[status(thm)],[12589])).
% 2.52/2.75 tff(12591,plain,
% 2.52/2.75 (b(z, s(z)) <=> b(z, elem!1)),
% 2.52/2.75 inference(symmetry,[status(thm)],[12590])).
% 2.52/2.75 tff(12592,plain,
% 2.52/2.75 ((~b(z, s(z))) <=> (~b(z, elem!1))),
% 2.52/2.75 inference(monotonicity,[status(thm)],[12591])).
% 2.52/2.75 tff(12593,plain,
% 2.52/2.75 (~(elem!1 = z)),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[304, 12342])).
% 2.52/2.75 tff(12594,plain,
% 2.52/2.75 ((~b(elem!1, z)) | (s(s(elem!1)) = s(s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[4702, 12263])).
% 2.52/2.75 tff(12595,plain,
% 2.52/2.75 (~b(elem!1, z)),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[12594, 12583, 12264, 12343])).
% 2.52/2.75 tff(12596,plain,
% 2.52/2.75 (r(elem!1, z)),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[387, 12595, 12593])).
% 2.52/2.75 tff(12597,plain,
% 2.52/2.75 (s(z) = elem!1),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[111, 12589])).
% 2.52/2.75 tff(12598,plain,
% 2.52/2.75 (r(s(s(s(elem!1))), elem!1)),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[12290, 12597])).
% 2.52/2.75 tff(12599,plain,
% 2.52/2.75 (~b(z, s(z))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[11627, 12598, 12264, 12583, 12343, 12596, 12589])).
% 2.52/2.75 tff(12600,plain,
% 2.52/2.75 (~b(z, elem!1)),
% 2.52/2.75 inference(modus_ponens,[status(thm)],[12599, 12592])).
% 2.52/2.75 tff(12601,plain,
% 2.52/2.75 ($false),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[12583, 12600])).
% 2.52/2.75 tff(12602,plain,(b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.75 tff(12603,plain,
% 2.52/2.75 (~(s(z) = elem!1)),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[1393, 12602])).
% 2.52/2.75 tff(12604,plain,
% 2.52/2.75 ((~(z = elem!1)) | (~b(elem!1, s(z)))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[11002, 9473])).
% 2.52/2.75 tff(12605,plain,
% 2.52/2.75 (~(z = elem!1)),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[12604, 12602])).
% 2.52/2.75 tff(12606,plain,
% 2.52/2.75 ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(z)))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[6911, 12263])).
% 2.52/2.75 tff(12607,plain,
% 2.52/2.75 (~b(s(z), elem!1)),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[12606, 1518, 12602])).
% 2.52/2.75 tff(12608,plain,
% 2.52/2.75 (r(s(z), elem!1)),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[601, 12607, 12603])).
% 2.52/2.75 tff(12609,plain,
% 2.52/2.75 (~r(s(s(s(s(z)))), s(z))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[10206, 37, 12608, 9473])).
% 2.52/2.75 tff(12610,plain,
% 2.52/2.75 (b(s(s(s(s(z)))), s(z))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[1406, 58, 483, 12609])).
% 2.52/2.75 tff(12611,plain,
% 2.52/2.75 ((~r(s(z), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | b(s(s(z)), elem!1)),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[11130, 9473])).
% 2.52/2.75 tff(12612,plain,
% 2.52/2.75 (b(s(s(z)), elem!1)),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[12611, 12608, 1518, 12602])).
% 2.52/2.75 tff(12613,plain,
% 2.52/2.75 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[8898, 12612])).
% 2.52/2.75 tff(12614,plain,
% 2.52/2.75 (~(s(s(elem!1)) = s(s(z)))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[237, 12605])).
% 2.52/2.75 tff(12615,plain,
% 2.52/2.75 ((s(s(elem!1)) = s(s(z))) | (~b(z, elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), elem!1))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[4730, 12263])).
% 2.52/2.75 tff(12616,plain,
% 2.52/2.75 (~b(elem!1, s(s(elem!1)))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[12615, 12612, 1518, 12614])).
% 2.52/2.75 tff(12617,plain,
% 2.52/2.75 (b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1)))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[1617, 12496])).
% 2.52/2.75 tff(12618,plain,
% 2.52/2.75 (r(elem!1, s(s(elem!1)))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[12617, 12616])).
% 2.52/2.75 tff(12619,plain,
% 2.52/2.75 (~r(s(z), s(s(s(s(z)))))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[10214, 37, 12608, 9473])).
% 2.52/2.75 tff(12620,plain,
% 2.52/2.75 (~(s(s(s(s(z)))) = elem!1)),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[3664, 12619, 12608])).
% 2.52/2.75 tff(12621,plain,
% 2.52/2.75 (~(elem!1 = s(s(s(s(z)))))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[273, 12620])).
% 2.52/2.75 tff(12622,plain,
% 2.52/2.75 (b(s(z), s(s(s(s(z)))))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[489, 12619])).
% 2.52/2.75 tff(12623,plain,
% 2.52/2.75 (~b(elem!1, s(s(s(s(z)))))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[10456, 75, 12602, 12622, 12610])).
% 2.52/2.75 tff(12624,plain,
% 2.52/2.75 (r(elem!1, s(s(s(s(z)))))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[278, 12623, 12621])).
% 2.52/2.75 tff(12625,plain,
% 2.52/2.75 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[3811, 12624, 12618])).
% 2.52/2.75 tff(12626,plain,
% 2.52/2.75 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[1660, 12625, 12613])).
% 2.52/2.75 tff(12627,plain,
% 2.52/2.75 (~r(s(z), s(s(elem!1)))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[6974, 12618, 12608])).
% 2.52/2.75 tff(12628,plain,
% 2.52/2.75 (b(s(z), s(s(elem!1)))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[1890, 12627])).
% 2.52/2.75 tff(12629,plain,
% 2.52/2.75 ($false),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[12137, 75, 12628, 12622, 12626, 12610])).
% 2.52/2.75 tff(12630,plain,(~b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.52/2.75 tff(12631,plain,
% 2.52/2.75 (r(z, elem!1)),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[298, 12630, 12605])).
% 2.52/2.75 tff(12632,plain,
% 2.52/2.75 ((~r(s(z), elem!1)) | (~r(z, elem!1))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[10304, 9473])).
% 2.52/2.75 tff(12633,plain,
% 2.52/2.75 (~r(s(z), elem!1)),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[12632, 12631])).
% 2.52/2.75 tff(12634,plain,
% 2.52/2.75 (b(s(z), elem!1)),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[601, 12633, 12603])).
% 2.52/2.75 tff(12635,plain,
% 2.52/2.75 (~b(s(s(elem!1)), s(z))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[8773, 75, 12634, 12602, 12263])).
% 2.52/2.75 tff(12636,plain,
% 2.52/2.75 (r(s(s(elem!1)), s(z))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[561, 12635])).
% 2.52/2.75 tff(12637,plain,
% 2.52/2.75 (~r(s(s(z)), elem!1)),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[12334, 12631])).
% 2.52/2.75 tff(12638,plain,
% 2.52/2.75 (~(elem!1 = z)),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[304, 12605])).
% 2.52/2.75 tff(12639,plain,
% 2.52/2.75 (~(s(s(s(s(z)))) = elem!1)),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[8091, 12631, 12630, 12614, 12603, 12638])).
% 2.52/2.75 tff(12640,plain,
% 2.52/2.75 (~(elem!1 = s(s(s(s(z)))))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[273, 12639])).
% 2.52/2.75 tff(12641,plain,
% 2.52/2.75 (~(s(s(z)) = s(elem!1))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[3261, 12603])).
% 2.52/2.75 tff(12642,plain,
% 2.52/2.75 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[4541, 12641])).
% 2.52/2.75 tff(12643,plain,
% 2.52/2.75 ((~(s(s(z)) = elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (s(s(s(z))) = s(s(elem!1))) | (~r(z, elem!1)) | (elem!1 = s(s(s(s(z)))))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[11265, 9473])).
% 2.52/2.75 tff(12644,plain,
% 2.52/2.75 (~(s(s(z)) = elem!1)),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[12643, 12634, 12602, 12642, 12631, 12640])).
% 2.52/2.75 tff(12645,plain,
% 2.52/2.75 (b(s(s(z)), elem!1)),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[104, 12644, 12637])).
% 2.52/2.75 tff(12646,plain,
% 2.52/2.75 (~b(s(s(z)), s(z))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[7471, 75, 12634, 12602, 12645])).
% 2.52/2.75 tff(12647,plain,
% 2.52/2.75 (r(s(s(z)), s(z))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[153, 12646])).
% 2.52/2.75 tff(12648,plain,
% 2.52/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 2.52/2.75 inference(rewrite,[status(thm)],[])).
% 2.52/2.75 tff(12649,plain,
% 2.52/2.75 (((~b(s(z), elem!1)) | (~b(s(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(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 2.52/2.75 inference(rewrite,[status(thm)],[])).
% 2.52/2.75 tff(12650,plain,
% 2.52/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))))),
% 2.52/2.75 inference(monotonicity,[status(thm)],[12649])).
% 2.52/2.75 tff(12651,plain,
% 2.52/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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(X1, 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(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 2.52/2.76 inference(transitivity,[status(thm)],[12650, 12648])).
% 2.52/2.76 tff(12652,plain,
% 2.52/2.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, 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(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)))))),
% 2.52/2.76 inference(quant_inst,[status(thm)],[])).
% 2.52/2.76 tff(12653,plain,
% 2.52/2.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))),
% 2.52/2.76 inference(modus_ponens,[status(thm)],[12652, 12651])).
% 2.52/2.76 tff(12654,plain,
% 2.52/2.76 (~b(s(s(elem!1)), s(s(z)))),
% 2.52/2.76 inference(unit_resolution,[status(thm)],[12653, 75, 12634, 12602, 12645, 12263])).
% 2.52/2.76 tff(12655,plain,
% 2.52/2.76 (r(s(s(elem!1)), s(s(z)))),
% 2.52/2.76 inference(unit_resolution,[status(thm)],[1476, 12654, 12614])).
% 2.52/2.76 tff(12656,plain,
% 2.52/2.76 ($false),
% 2.52/2.76 inference(unit_resolution,[status(thm)],[9392, 12655, 12647, 12636])).
% 2.52/2.76 % SZS output end Proof
% 2.52/2.76 % E exiting
%------------------------------------------------------------------------------